TSTP Solution File: SWV419-1.010 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV419-1.010 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 15:11:46 EDT 2022
% Result : Unsatisfiable 16.06s 10.52s
% Output : Proof 16.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV419-1.010 : TPTP v8.1.0. Released v3.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 02:56:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 16.06/10.52 % SZS status Unsatisfiable
% 16.06/10.52 % SZS output start Proof
% 16.06/10.52 tff(m_and_h_gate_v_out_type, type, (
% 16.06/10.52 m_and_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(s1_type, type, (
% 16.06/10.52 s1: $i)).
% 16.06/10.52 tff(c_l_type, type, (
% 16.06/10.52 c_l: $i)).
% 16.06/10.52 tff(c_e_h_2_type, type, (
% 16.06/10.52 c_e_h_2: $i)).
% 16.06/10.52 tff(s0_type, type, (
% 16.06/10.52 s0: $i)).
% 16.06/10.52 tff(node22_type, type, (
% 16.06/10.52 node22: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node21_type, type, (
% 16.06/10.52 node21: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node20_type, type, (
% 16.06/10.52 node20: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_and_h_gate_v_in2_type, type, (
% 16.06/10.52 m_and_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_and_h_gate_h_init_v_out_type, type, (
% 16.06/10.52 m_and_h_gate_h_init_v_out: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_m_type, type, (
% 16.06/10.52 c_m: $i)).
% 16.06/10.52 tff(m_and_h_gate_h_init_v_init_h_out_type, type, (
% 16.06/10.52 m_and_h_gate_h_init_v_init_h_out: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_cell_v_token_type, type, (
% 16.06/10.52 m_cell_v_token: ( $i * $i ) > $o)).
% 16.06/10.52 tff(trans_type, type, (
% 16.06/10.52 trans: ( $i * $i ) > $o)).
% 16.06/10.52 tff(succ_type, type, (
% 16.06/10.52 succ: ( $i * $i ) > $o)).
% 16.06/10.52 tff(s2_type, type, (
% 16.06/10.52 s2: $i)).
% 16.06/10.52 tff(m_or_h_gate_v_in1_type, type, (
% 16.06/10.52 m_or_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_j_type, type, (
% 16.06/10.52 c_j: $i)).
% 16.06/10.52 tff(m_or_h_gate_v_out_type, type, (
% 16.06/10.52 m_or_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(s3_type, type, (
% 16.06/10.52 s3: $i)).
% 16.06/10.52 tff(m_c_h_element_v_in2_type, type, (
% 16.06/10.52 m_c_h_element_v_in2: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_h_type, type, (
% 16.06/10.52 c_h: $i)).
% 16.06/10.52 tff(m_c_h_element_v_out_type, type, (
% 16.06/10.52 m_c_h_element_v_out: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(s4_type, type, (
% 16.06/10.52 s4: $i)).
% 16.06/10.52 tff(m_and_h_gate_v_in1_type, type, (
% 16.06/10.52 m_and_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_i_type, type, (
% 16.06/10.52 c_i: $i)).
% 16.06/10.52 tff(s6_type, type, (
% 16.06/10.52 s6: $i)).
% 16.06/10.52 tff(c_e_type, type, (
% 16.06/10.52 c_e: $i)).
% 16.06/10.52 tff(m_and_h_gate_h_init_v_in1_type, type, (
% 16.06/10.52 m_and_h_gate_h_init_v_in1: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_n_type, type, (
% 16.06/10.52 c_n: $i)).
% 16.06/10.52 tff(s8_type, type, (
% 16.06/10.52 s8: $i)).
% 16.06/10.52 tff(c_r_type, type, (
% 16.06/10.52 c_r: $i)).
% 16.06/10.52 tff(s9_type, type, (
% 16.06/10.52 s9: $i)).
% 16.06/10.52 tff(m_user_v_ack_type, type, (
% 16.06/10.52 m_user_v_ack: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_u_type, type, (
% 16.06/10.52 c_u: $i)).
% 16.06/10.52 tff(node25_type, type, (
% 16.06/10.52 node25: $i > $o)).
% 16.06/10.52 tff(until27_type, type, (
% 16.06/10.52 until27: $i > $o)).
% 16.06/10.52 tff(xuntil28_type, type, (
% 16.06/10.52 xuntil28: $i > $o)).
% 16.06/10.52 tff(s7_type, type, (
% 16.06/10.52 s7: $i)).
% 16.06/10.52 tff(c_e_h_1_type, type, (
% 16.06/10.52 c_e_h_1: $i)).
% 16.06/10.52 tff(node9_type, type, (
% 16.06/10.52 node9: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(s5_type, type, (
% 16.06/10.52 s5: $i)).
% 16.06/10.52 tff(m_and_h_gate_h_init_v_in2_type, type, (
% 16.06/10.52 m_and_h_gate_h_init_v_in2: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_c_h_element_v_in1_type, type, (
% 16.06/10.52 m_c_h_element_v_in1: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_g_type, type, (
% 16.06/10.52 c_g: $i)).
% 16.06/10.52 tff(node14_type, type, (
% 16.06/10.52 node14: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node15_type, type, (
% 16.06/10.52 node15: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node16_type, type, (
% 16.06/10.52 node16: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node19_type, type, (
% 16.06/10.52 node19: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node18_type, type, (
% 16.06/10.52 node18: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node17_type, type, (
% 16.06/10.52 node17: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_or_h_gate_v_in2_type, type, (
% 16.06/10.52 m_or_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_cell_v_ack_type, type, (
% 16.06/10.52 m_cell_v_ack: ( $i * $i ) > $o)).
% 16.06/10.52 tff(c_q_type, type, (
% 16.06/10.52 c_q: $i)).
% 16.06/10.52 tff(c_e_h_3_type, type, (
% 16.06/10.52 c_e_h_3: $i)).
% 16.06/10.52 tff(node3_type, type, (
% 16.06/10.52 node3: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_cell_v_left_type, type, (
% 16.06/10.52 m_cell_v_left: ( $i * $i ) > $o)).
% 16.06/10.52 tff(node5_type, type, (
% 16.06/10.52 node5: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node6_type, type, (
% 16.06/10.52 node6: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_c_type, type, (
% 16.06/10.52 c_c: $i)).
% 16.06/10.52 tff(m_mutex_h_half_v_out_type, type, (
% 16.06/10.52 m_mutex_h_half_v_out: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(c_a_type, type, (
% 16.06/10.52 c_a: $i)).
% 16.06/10.52 tff(m_mutex_h_half_v_inp_type, type, (
% 16.06/10.52 m_mutex_h_half_v_inp: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(m_user_v_req_type, type, (
% 16.06/10.52 m_user_v_req: ( $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node12_type, type, (
% 16.06/10.52 node12: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node13_type, type, (
% 16.06/10.52 node13: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node11_type, type, (
% 16.06/10.52 node11: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node10_type, type, (
% 16.06/10.52 node10: ( $i * $i * $i * $i ) > $o)).
% 16.06/10.52 tff(node24_type, type, (
% 16.06/10.52 node24: $i > $o)).
% 16.06/10.52 tff(node26_type, type, (
% 16.06/10.52 node26: $i > $o)).
% 16.06/10.52 tff(node23_type, type, (
% 16.06/10.52 node23: $i > $o)).
% 16.06/10.52 tff(c_f_type, type, (
% 16.06/10.52 c_f: $i)).
% 16.06/10.52 tff(c_d_type, type, (
% 16.06/10.52 c_d: $i)).
% 16.06/10.52 tff(c_b_type, type, (
% 16.06/10.52 c_b: $i)).
% 16.06/10.52 tff(until2p29_type, type, (
% 16.06/10.52 until2p29: $i > $o)).
% 16.06/10.52 tff(xuntil2p30_type, type, (
% 16.06/10.52 xuntil2p30: $i > $o)).
% 16.06/10.52 tff(last_type, type, (
% 16.06/10.52 last: $i > $o)).
% 16.06/10.52 tff(loop_type, type, (
% 16.06/10.52 loop: $o)).
% 16.06/10.52 tff(1,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s1)), introduced(assumption)).
% 16.06/10.52 tff(2,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s0)), introduced(assumption)).
% 16.06/10.52 tff(3,plain,
% 16.06/10.52 (^[I0: $i, I1: $i] : refl((~m_and_h_gate_v_out(I0, I1, s0)) <=> (~m_and_h_gate_v_out(I0, I1, s0)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(4,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[3])).
% 16.06/10.52 tff(5,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(6,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')).
% 16.06/10.52 tff(7,plain,
% 16.06/10.52 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[6, 5])).
% 16.06/10.52 tff(8,plain,(
% 16.06/10.52 ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 16.06/10.52 inference(skolemize,[status(sab)],[7])).
% 16.06/10.52 tff(9,plain,
% 16.06/10.52 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[8, 4])).
% 16.06/10.52 tff(10,plain,
% 16.06/10.52 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(11,plain,
% 16.06/10.52 ($false),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 16.06/10.52 tff(12,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.52 tff(13,assumption,(node21(c_e_h_2, c_l, s0, s1)), introduced(assumption)).
% 16.06/10.52 tff(14,assumption,(m_cell_v_token(c_e_h_2, s0)), introduced(assumption)).
% 16.06/10.52 tff(15,plain,
% 16.06/10.52 (^[X: $i] : refl((~m_cell_v_token(c_e_h_2, X)) <=> (~m_cell_v_token(c_e_h_2, X)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(16,plain,
% 16.06/10.52 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[15])).
% 16.06/10.52 tff(17,plain,
% 16.06/10.52 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(18,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_2, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_6')).
% 16.06/10.52 tff(19,plain,
% 16.06/10.52 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[18, 17])).
% 16.06/10.52 tff(20,plain,(
% 16.06/10.52 ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 16.06/10.52 inference(skolemize,[status(sab)],[19])).
% 16.06/10.52 tff(21,plain,
% 16.06/10.52 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[20, 16])).
% 16.06/10.52 tff(22,plain,
% 16.06/10.52 ((~![X: $i] : (~m_cell_v_token(c_e_h_2, X))) | (~m_cell_v_token(c_e_h_2, s0))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(23,plain,
% 16.06/10.52 ($false),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 16.06/10.52 tff(24,plain,(~m_cell_v_token(c_e_h_2, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.52 tff(25,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(26,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[25])).
% 16.06/10.52 tff(27,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(28,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')).
% 16.06/10.52 tff(29,plain,
% 16.06/10.52 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[28, 27])).
% 16.06/10.52 tff(30,plain,(
% 16.06/10.52 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 16.06/10.52 inference(skolemize,[status(sab)],[29])).
% 16.06/10.52 tff(31,plain,
% 16.06/10.52 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[30, 26])).
% 16.06/10.52 tff(32,plain,
% 16.06/10.52 (((~![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(33,plain,
% 16.06/10.52 ((~![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))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(34,plain,
% 16.06/10.52 ((~![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)),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[33, 32])).
% 16.06/10.52 tff(35,plain,
% 16.06/10.52 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[34, 31, 24])).
% 16.06/10.52 tff(36,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(37,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[36])).
% 16.06/10.52 tff(38,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(39,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')).
% 16.06/10.52 tff(40,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[39, 38])).
% 16.06/10.52 tff(41,plain,(
% 16.06/10.52 ![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))),
% 16.06/10.52 inference(skolemize,[status(sab)],[40])).
% 16.06/10.52 tff(42,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[41, 37])).
% 16.06/10.52 tff(43,plain,
% 16.06/10.52 (((~![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(44,plain,
% 16.06/10.52 ((~![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))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(45,plain,
% 16.06/10.52 ((~![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)),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[44, 43])).
% 16.06/10.52 tff(46,plain,
% 16.06/10.52 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[45, 42, 35])).
% 16.06/10.52 tff(47,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(48,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[47])).
% 16.06/10.52 tff(49,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(50,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')).
% 16.06/10.52 tff(51,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[50, 49])).
% 16.06/10.52 tff(52,plain,(
% 16.06/10.52 ![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))),
% 16.06/10.52 inference(skolemize,[status(sab)],[51])).
% 16.06/10.52 tff(53,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[52, 48])).
% 16.06/10.52 tff(54,plain,
% 16.06/10.52 (((~![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(55,plain,
% 16.06/10.52 ((~![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))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(56,plain,
% 16.06/10.52 ((~![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)),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[55, 54])).
% 16.06/10.52 tff(57,plain,
% 16.06/10.52 ((~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)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[56, 53])).
% 16.06/10.52 tff(58,plain,
% 16.06/10.52 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[57, 46])).
% 16.06/10.52 tff(59,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(60,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[59])).
% 16.06/10.52 tff(61,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(62,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(63,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[62])).
% 16.06/10.52 tff(64,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')).
% 16.06/10.52 tff(65,plain,
% 16.06/10.52 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[64, 63])).
% 16.06/10.52 tff(66,plain,
% 16.06/10.52 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[65, 61])).
% 16.06/10.52 tff(67,plain,(
% 16.06/10.52 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 16.06/10.52 inference(skolemize,[status(sab)],[66])).
% 16.06/10.52 tff(68,plain,
% 16.06/10.52 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[67, 60])).
% 16.06/10.52 tff(69,plain,
% 16.06/10.52 (((~![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(70,plain,
% 16.06/10.52 ((~![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))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(71,plain,
% 16.06/10.52 ((~![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)),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[70, 69])).
% 16.06/10.52 tff(72,plain,
% 16.06/10.52 (~node20(c_e_h_2, c_l, s0)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[71, 68, 58])).
% 16.06/10.52 tff(73,plain,
% 16.06/10.52 (^[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))))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(74,plain,
% 16.06/10.52 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[73])).
% 16.06/10.52 tff(75,plain,
% 16.06/10.52 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(76,plain,
% 16.06/10.52 (^[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))))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(77,plain,
% 16.06/10.52 (![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)))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[76])).
% 16.06/10.52 tff(78,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')).
% 16.06/10.52 tff(79,plain,
% 16.06/10.52 (![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)))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[78, 77])).
% 16.06/10.52 tff(80,plain,
% 16.06/10.52 (![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)))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[79, 75])).
% 16.06/10.52 tff(81,plain,(
% 16.06/10.52 ![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)))),
% 16.06/10.52 inference(skolemize,[status(sab)],[80])).
% 16.06/10.52 tff(82,plain,
% 16.06/10.52 (![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)))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[81, 74])).
% 16.06/10.52 tff(83,plain,
% 16.06/10.52 (((~![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_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) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1)))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(84,plain,
% 16.06/10.52 ((~![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_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)))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(85,plain,
% 16.06/10.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[84, 83])).
% 16.06/10.52 tff(86,plain,
% 16.06/10.52 ($false),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[85, 82, 72, 13, 1])).
% 16.06/10.52 tff(87,plain,((~node21(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,[]))).
% 16.06/10.52 tff(88,plain,
% 16.06/10.52 (~node21(c_e_h_2, c_l, s0, s1)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[87, 1])).
% 16.06/10.52 tff(89,plain,
% 16.06/10.52 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(90,plain,
% 16.06/10.52 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[89])).
% 16.06/10.52 tff(91,plain,
% 16.06/10.52 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(92,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound11')).
% 16.06/10.52 tff(93,plain,
% 16.06/10.52 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[92, 91])).
% 16.06/10.52 tff(94,plain,(
% 16.06/10.52 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 16.06/10.52 inference(skolemize,[status(sab)],[93])).
% 16.06/10.52 tff(95,plain,
% 16.06/10.52 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[94, 90])).
% 16.06/10.52 tff(96,plain,
% 16.06/10.52 (succ(s0, s1) <=> succ(s0, s1)),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(97,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 16.06/10.52 tff(98,plain,
% 16.06/10.52 (succ(s0, s1)),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[97, 96])).
% 16.06/10.52 tff(99,plain,
% 16.06/10.52 (((~![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(100,plain,
% 16.06/10.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(101,plain,
% 16.06/10.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[100, 99])).
% 16.06/10.52 tff(102,plain,
% 16.06/10.52 (trans(s0, s1)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[101, 98, 95])).
% 16.06/10.52 tff(103,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(104,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[103])).
% 16.06/10.52 tff(105,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(106,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(107,plain,
% 16.06/10.52 (![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))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[106])).
% 16.06/10.52 tff(108,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')).
% 16.06/10.52 tff(109,plain,
% 16.06/10.52 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[108, 107])).
% 16.06/10.52 tff(110,plain,
% 16.06/10.52 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[109, 105])).
% 16.06/10.52 tff(111,plain,(
% 16.06/10.52 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 16.06/10.52 inference(skolemize,[status(sab)],[110])).
% 16.06/10.52 tff(112,plain,
% 16.06/10.52 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[111, 104])).
% 16.06/10.52 tff(113,plain,
% 16.06/10.52 (((~![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_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))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(114,plain,
% 16.06/10.52 ((~![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_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1))),
% 16.06/10.52 inference(quant_inst,[status(thm)],[])).
% 16.06/10.52 tff(115,plain,
% 16.06/10.52 ((~![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_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1)),
% 16.06/10.52 inference(modus_ponens,[status(thm)],[114, 113])).
% 16.06/10.52 tff(116,plain,
% 16.06/10.52 (node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[115, 112, 102])).
% 16.06/10.52 tff(117,plain,
% 16.06/10.52 (node22(c_e_h_2, c_l, s0, s1)),
% 16.06/10.52 inference(unit_resolution,[status(thm)],[116, 88])).
% 16.06/10.52 tff(118,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(119,plain,
% 16.06/10.52 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 16.06/10.52 inference(quant_intro,[status(thm)],[118])).
% 16.06/10.52 tff(120,plain,
% 16.06/10.52 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 16.06/10.52 inference(rewrite,[status(thm)],[])).
% 16.06/10.52 tff(121,plain,
% 16.06/10.52 (^[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)))),
% 16.06/10.52 inference(bind,[status(th)],[])).
% 16.06/10.52 tff(122,plain,
% 16.06/10.52 (![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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[121])).
% 16.06/10.53 tff(123,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')).
% 16.06/10.53 tff(124,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[123, 122])).
% 16.06/10.53 tff(125,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[124, 120])).
% 16.06/10.53 tff(126,plain,(
% 16.06/10.53 ![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))),
% 16.06/10.53 inference(skolemize,[status(sab)],[125])).
% 16.06/10.53 tff(127,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[126, 119])).
% 16.06/10.53 tff(128,plain,
% 16.06/10.53 (((~![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_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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(129,plain,
% 16.06/10.53 ((~![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_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))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(130,plain,
% 16.06/10.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0)),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[129, 128])).
% 16.06/10.53 tff(131,plain,
% 16.06/10.53 ($false),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[130, 127, 117, 12, 1])).
% 16.06/10.53 tff(132,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.53 tff(133,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s2)), introduced(assumption)).
% 16.06/10.53 tff(134,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s0)), introduced(assumption)).
% 16.06/10.53 tff(135,plain,
% 16.06/10.53 (^[I0: $i, I1: $i] : refl((~m_or_h_gate_v_out(I0, I1, s0)) <=> (~m_or_h_gate_v_out(I0, I1, s0)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(136,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[135])).
% 16.06/10.53 tff(137,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(138,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')).
% 16.06/10.53 tff(139,plain,
% 16.06/10.53 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[138, 137])).
% 16.06/10.53 tff(140,plain,(
% 16.06/10.53 ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 16.06/10.53 inference(skolemize,[status(sab)],[139])).
% 16.06/10.53 tff(141,plain,
% 16.06/10.53 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[140, 136])).
% 16.06/10.53 tff(142,plain,
% 16.06/10.53 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(143,plain,
% 16.06/10.53 ($false),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[142, 141, 134])).
% 16.06/10.53 tff(144,plain,(~m_or_h_gate_v_out(c_e_h_1, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.53 tff(145,plain,
% 16.06/10.53 (^[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)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(146,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[145])).
% 16.06/10.53 tff(147,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(148,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')).
% 16.06/10.53 tff(149,plain,
% 16.06/10.53 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[148, 147])).
% 16.06/10.53 tff(150,plain,(
% 16.06/10.53 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 16.06/10.53 inference(skolemize,[status(sab)],[149])).
% 16.06/10.53 tff(151,plain,
% 16.06/10.53 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[150, 146])).
% 16.06/10.53 tff(152,plain,
% 16.06/10.53 (((~![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(153,plain,
% 16.06/10.53 ((~![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))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(154,plain,
% 16.06/10.53 ((~![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)),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[153, 152])).
% 16.06/10.53 tff(155,plain,
% 16.06/10.53 (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[154, 151, 144])).
% 16.06/10.53 tff(156,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s1)), introduced(assumption)).
% 16.06/10.53 tff(157,assumption,(node15(c_e_h_1, c_h, s0, s1)), introduced(assumption)).
% 16.06/10.53 tff(158,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s0)), introduced(assumption)).
% 16.06/10.53 tff(159,plain,
% 16.06/10.53 (^[I0: $i, I1: $i] : refl((~m_c_h_element_v_out(I0, I1, s0)) <=> (~m_c_h_element_v_out(I0, I1, s0)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(160,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[159])).
% 16.06/10.53 tff(161,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(162,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')).
% 16.06/10.53 tff(163,plain,
% 16.06/10.53 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[162, 161])).
% 16.06/10.53 tff(164,plain,(
% 16.06/10.53 ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 16.06/10.53 inference(skolemize,[status(sab)],[163])).
% 16.06/10.53 tff(165,plain,
% 16.06/10.53 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[164, 160])).
% 16.06/10.53 tff(166,plain,
% 16.06/10.53 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(167,plain,
% 16.06/10.53 ($false),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[166, 165, 158])).
% 16.06/10.53 tff(168,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.53 tff(169,plain,
% 16.06/10.53 (^[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)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(170,plain,
% 16.06/10.53 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[169])).
% 16.06/10.53 tff(171,plain,
% 16.06/10.53 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(172,plain,
% 16.06/10.53 (^[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)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(173,plain,
% 16.06/10.53 (![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)) | (~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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[172])).
% 16.06/10.53 tff(174,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')).
% 16.06/10.53 tff(175,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[174, 173])).
% 16.06/10.53 tff(176,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[175, 171])).
% 16.06/10.53 tff(177,plain,(
% 16.06/10.53 ![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))),
% 16.06/10.53 inference(skolemize,[status(sab)],[176])).
% 16.06/10.53 tff(178,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[177, 170])).
% 16.06/10.53 tff(179,plain,
% 16.06/10.53 (((~![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_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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(180,plain,
% 16.06/10.53 ((~![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_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(181,plain,
% 16.06/10.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0)),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[180, 179])).
% 16.06/10.53 tff(182,plain,
% 16.06/10.53 ($false),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[181, 178, 156, 168, 157])).
% 16.06/10.53 tff(183,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,[]))).
% 16.06/10.53 tff(184,plain,
% 16.06/10.53 (~node15(c_e_h_1, c_h, s0, s1)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[183, 156])).
% 16.06/10.53 tff(185,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s0)), introduced(assumption)).
% 16.06/10.53 tff(186,plain,
% 16.06/10.53 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(187,plain,
% 16.06/10.53 ($false),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[186, 141, 185])).
% 16.06/10.53 tff(188,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.53 tff(189,plain,
% 16.06/10.53 (^[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)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(190,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[189])).
% 16.06/10.53 tff(191,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(192,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')).
% 16.06/10.53 tff(193,plain,
% 16.06/10.53 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[192, 191])).
% 16.06/10.53 tff(194,plain,(
% 16.06/10.53 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 16.06/10.53 inference(skolemize,[status(sab)],[193])).
% 16.06/10.53 tff(195,plain,
% 16.06/10.53 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[194, 190])).
% 16.06/10.53 tff(196,plain,
% 16.06/10.53 (((~![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(197,plain,
% 16.06/10.53 ((~![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))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(198,plain,
% 16.06/10.53 ((~![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)),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[197, 196])).
% 16.06/10.53 tff(199,plain,
% 16.06/10.53 (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[198, 195, 188])).
% 16.06/10.53 tff(200,plain,
% 16.06/10.53 (^[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)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(201,plain,
% 16.06/10.53 (![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)) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[200])).
% 16.06/10.53 tff(202,plain,
% 16.06/10.53 (![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)) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(203,plain,
% 16.06/10.53 (^[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)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(204,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[203])).
% 16.06/10.53 tff(205,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')).
% 16.06/10.53 tff(206,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[205, 204])).
% 16.06/10.53 tff(207,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[206, 202])).
% 16.06/10.53 tff(208,plain,(
% 16.06/10.53 ![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))),
% 16.06/10.53 inference(skolemize,[status(sab)],[207])).
% 16.06/10.53 tff(209,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[208, 201])).
% 16.06/10.53 tff(210,plain,
% 16.06/10.53 (((~![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_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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(211,plain,
% 16.06/10.53 ((~![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_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))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(212,plain,
% 16.06/10.53 ((~![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_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)),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[211, 210])).
% 16.06/10.53 tff(213,plain,
% 16.06/10.53 ((~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[212, 209, 199])).
% 16.06/10.53 tff(214,plain,
% 16.06/10.53 (~node16(c_e_h_1, c_h, s0)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[213, 155])).
% 16.06/10.53 tff(215,plain,
% 16.06/10.53 (^[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)))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(216,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[215])).
% 16.06/10.53 tff(217,plain,
% 16.06/10.53 (![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(218,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')).
% 16.06/10.53 tff(219,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[218, 217])).
% 16.06/10.53 tff(220,plain,(
% 16.06/10.53 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 16.06/10.53 inference(skolemize,[status(sab)],[219])).
% 16.06/10.53 tff(221,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[220, 216])).
% 16.06/10.53 tff(222,plain,
% 16.06/10.53 (((~![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))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(223,plain,
% 16.06/10.53 ((~![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))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(224,plain,
% 16.06/10.53 ((~![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)),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[223, 222])).
% 16.06/10.53 tff(225,plain,
% 16.06/10.53 (node19(c_e_h_1, c_h, s0, s1)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[224, 221, 102])).
% 16.06/10.53 tff(226,plain,
% 16.06/10.53 (^[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))))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(227,plain,
% 16.06/10.53 (![Y: $i, I0: $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)))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[226])).
% 16.06/10.53 tff(228,plain,
% 16.06/10.53 (![Y: $i, I0: $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)))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(229,plain,
% 16.06/10.53 (^[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)))))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(230,plain,
% 16.06/10.53 (![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)))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[229])).
% 16.06/10.53 tff(231,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')).
% 16.06/10.53 tff(232,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[231, 230])).
% 16.06/10.53 tff(233,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[232, 228])).
% 16.06/10.53 tff(234,plain,(
% 16.06/10.53 ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.53 inference(skolemize,[status(sab)],[233])).
% 16.06/10.53 tff(235,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[234, 227])).
% 16.06/10.53 tff(236,plain,
% 16.06/10.53 (((~![Y: $i, I0: $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, s0, s1)) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, 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)))) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(237,plain,
% 16.06/10.53 ((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))) <=> ((~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(238,plain,
% 16.06/10.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | ((~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0)))),
% 16.06/10.53 inference(monotonicity,[status(thm)],[237])).
% 16.06/10.53 tff(239,plain,
% 16.06/10.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0))),
% 16.06/10.53 inference(transitivity,[status(thm)],[238, 236])).
% 16.06/10.53 tff(240,plain,
% 16.06/10.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(241,plain,
% 16.06/10.53 ((~![Y: $i, I0: $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, s0, s1)) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0)),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[240, 239])).
% 16.06/10.53 tff(242,plain,
% 16.06/10.53 (node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[241, 235, 225])).
% 16.06/10.53 tff(243,plain,
% 16.06/10.53 (node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[242, 214])).
% 16.06/10.53 tff(244,plain,
% 16.06/10.53 (node14(c_e_h_1, c_h, s0, s1)),
% 16.06/10.53 inference(unit_resolution,[status(thm)],[243, 184])).
% 16.06/10.53 tff(245,plain,
% 16.06/10.53 (^[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))))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(246,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[245])).
% 16.06/10.53 tff(247,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(248,plain,
% 16.06/10.53 (^[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))))),
% 16.06/10.53 inference(bind,[status(th)],[])).
% 16.06/10.53 tff(249,plain,
% 16.06/10.53 (![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)))),
% 16.06/10.53 inference(quant_intro,[status(thm)],[248])).
% 16.06/10.53 tff(250,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')).
% 16.06/10.53 tff(251,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[250, 249])).
% 16.06/10.53 tff(252,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[251, 247])).
% 16.06/10.53 tff(253,plain,(
% 16.06/10.53 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 16.06/10.53 inference(skolemize,[status(sab)],[252])).
% 16.06/10.53 tff(254,plain,
% 16.06/10.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 16.06/10.53 inference(modus_ponens,[status(thm)],[253, 246])).
% 16.06/10.53 tff(255,plain,
% 16.06/10.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, 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, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~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_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(256,plain,
% 16.06/10.53 (((~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_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 16.06/10.53 inference(rewrite,[status(thm)],[])).
% 16.06/10.53 tff(257,plain,
% 16.06/10.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1))))),
% 16.06/10.53 inference(monotonicity,[status(thm)],[256])).
% 16.06/10.53 tff(258,plain,
% 16.06/10.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 16.06/10.53 inference(transitivity,[status(thm)],[257, 255])).
% 16.06/10.53 tff(259,plain,
% 16.06/10.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.06/10.53 inference(quant_inst,[status(thm)],[])).
% 16.06/10.53 tff(260,plain,
% 16.06/10.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[259, 258])).
% 16.06/10.54 tff(261,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[260, 254, 156, 244, 155])).
% 16.06/10.54 tff(262,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(263,plain,
% 16.06/10.54 (^[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)))),
% 16.06/10.54 inference(bind,[status(th)],[])).
% 16.06/10.54 tff(264,plain,
% 16.06/10.54 (![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))),
% 16.06/10.54 inference(quant_intro,[status(thm)],[263])).
% 16.06/10.54 tff(265,plain,
% 16.06/10.54 (![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(266,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')).
% 16.06/10.54 tff(267,plain,
% 16.06/10.54 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[266, 265])).
% 16.06/10.54 tff(268,plain,(
% 16.06/10.54 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 16.06/10.54 inference(skolemize,[status(sab)],[267])).
% 16.06/10.54 tff(269,plain,
% 16.06/10.54 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[268, 264])).
% 16.06/10.54 tff(270,plain,
% 16.06/10.54 (((~![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(271,plain,
% 16.06/10.54 ((~![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))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(272,plain,
% 16.06/10.54 ((~![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)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[271, 270])).
% 16.06/10.54 tff(273,plain,
% 16.06/10.54 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[272, 269, 262])).
% 16.06/10.54 tff(274,plain,
% 16.06/10.54 (^[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)))),
% 16.06/10.54 inference(bind,[status(th)],[])).
% 16.06/10.54 tff(275,plain,
% 16.06/10.54 (![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))),
% 16.06/10.54 inference(quant_intro,[status(thm)],[274])).
% 16.06/10.54 tff(276,plain,
% 16.06/10.54 (![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(277,plain,
% 16.06/10.54 (^[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)))),
% 16.06/10.54 inference(bind,[status(th)],[])).
% 16.06/10.54 tff(278,plain,
% 16.06/10.54 (![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))),
% 16.06/10.54 inference(quant_intro,[status(thm)],[277])).
% 16.06/10.54 tff(279,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')).
% 16.06/10.54 tff(280,plain,
% 16.06/10.54 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[279, 278])).
% 16.06/10.54 tff(281,plain,
% 16.06/10.54 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[280, 276])).
% 16.06/10.54 tff(282,plain,(
% 16.06/10.54 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 16.06/10.54 inference(skolemize,[status(sab)],[281])).
% 16.06/10.54 tff(283,plain,
% 16.06/10.54 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[282, 275])).
% 16.06/10.54 tff(284,plain,
% 16.06/10.54 (((~![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_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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(285,plain,
% 16.06/10.54 ((~![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_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(286,plain,
% 16.06/10.54 ((~![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_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[285, 284])).
% 16.06/10.54 tff(287,plain,
% 16.06/10.54 (~node20(c_e_h_1, c_i, s1)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[286, 283, 273])).
% 16.06/10.54 tff(288,assumption,(~node20(c_e_h_1, c_i, s1)), introduced(assumption)).
% 16.06/10.54 tff(289,assumption,(node21(c_e_h_1, c_i, s1, s2)), introduced(assumption)).
% 16.06/10.54 tff(290,plain,
% 16.06/10.54 (((~![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_i, s1) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, 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) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(291,plain,
% 16.06/10.54 ((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))) <=> (node20(c_e_h_1, c_i, s1) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(292,plain,
% 16.06/10.54 (((~![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_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) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))))),
% 16.06/10.54 inference(monotonicity,[status(thm)],[291])).
% 16.06/10.54 tff(293,plain,
% 16.06/10.54 (((~![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_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) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)))),
% 16.06/10.54 inference(transitivity,[status(thm)],[292, 290])).
% 16.06/10.54 tff(294,plain,
% 16.06/10.54 ((~![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_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(295,plain,
% 16.06/10.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s1) | (~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[294, 293])).
% 16.06/10.54 tff(296,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[295, 82, 289, 133, 288])).
% 16.06/10.54 tff(297,plain,((~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | node20(c_e_h_1, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(298,plain,
% 16.06/10.54 ((~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[297, 287])).
% 16.06/10.54 tff(299,plain,
% 16.06/10.54 (~node21(c_e_h_1, c_i, s1, s2)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[298, 133])).
% 16.06/10.54 tff(300,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s1)), introduced(assumption)).
% 16.06/10.54 tff(301,assumption,(node22(c_e_h_1, c_i, s0, s1)), introduced(assumption)).
% 16.06/10.54 tff(302,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s0)), introduced(assumption)).
% 16.06/10.54 tff(303,plain,
% 16.06/10.54 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(304,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[303, 9, 302])).
% 16.06/10.54 tff(305,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(306,plain,
% 16.06/10.54 (((~![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_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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(307,plain,
% 16.06/10.54 ((~![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_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(308,plain,
% 16.06/10.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[307, 306])).
% 16.06/10.54 tff(309,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[308, 127, 305, 301, 300])).
% 16.06/10.54 tff(310,plain,((~node22(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,[]))).
% 16.06/10.54 tff(311,plain,
% 16.06/10.54 (~node22(c_e_h_1, c_i, s0, s1)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[310, 300])).
% 16.06/10.54 tff(312,plain,
% 16.06/10.54 (((~![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(313,plain,
% 16.06/10.54 ((~![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))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(314,plain,
% 16.06/10.54 ((~![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)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[313, 312])).
% 16.06/10.54 tff(315,plain,
% 16.06/10.54 (node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[314, 112, 102])).
% 16.06/10.54 tff(316,plain,
% 16.06/10.54 (node21(c_e_h_1, c_i, s0, s1)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[315, 311])).
% 16.06/10.54 tff(317,plain,
% 16.06/10.54 (((~![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(318,plain,
% 16.06/10.54 ((~![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))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(319,plain,
% 16.06/10.54 ((~![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)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[318, 317])).
% 16.06/10.54 tff(320,plain,
% 16.06/10.54 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[319, 269, 168])).
% 16.06/10.54 tff(321,plain,
% 16.06/10.54 (((~![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_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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(322,plain,
% 16.06/10.54 ((~![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_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(323,plain,
% 16.06/10.54 ((~![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_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[322, 321])).
% 16.06/10.54 tff(324,plain,
% 16.06/10.54 (~node20(c_e_h_1, c_i, s0)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[323, 283, 320])).
% 16.06/10.54 tff(325,plain,
% 16.06/10.54 (((~![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_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, 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)))) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(326,plain,
% 16.06/10.54 ((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))) <=> (node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(327,plain,
% 16.06/10.54 (((~![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_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) | (~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1))))),
% 16.06/10.54 inference(monotonicity,[status(thm)],[326])).
% 16.06/10.54 tff(328,plain,
% 16.06/10.54 (((~![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_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) | (~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)))),
% 16.06/10.54 inference(transitivity,[status(thm)],[327, 325])).
% 16.06/10.54 tff(329,plain,
% 16.06/10.54 ((~![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_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(330,plain,
% 16.06/10.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[329, 328])).
% 16.06/10.54 tff(331,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[330, 82, 324, 316, 300])).
% 16.06/10.54 tff(332,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(333,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s1)), introduced(assumption)).
% 16.06/10.54 tff(334,assumption,(node22(c_e_h_1, c_i, s1, s2)), introduced(assumption)).
% 16.06/10.54 tff(335,plain,
% 16.06/10.54 (((~![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_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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(336,plain,
% 16.06/10.54 ((~![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_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(337,plain,
% 16.06/10.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[336, 335])).
% 16.06/10.54 tff(338,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[337, 127, 334, 133, 333])).
% 16.06/10.54 tff(339,plain,((~node22(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(340,plain,
% 16.06/10.54 ((~node22(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[339, 332])).
% 16.06/10.54 tff(341,plain,
% 16.06/10.54 (~node22(c_e_h_1, c_i, s1, s2)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[340, 133])).
% 16.06/10.54 tff(342,plain,
% 16.06/10.54 (succ(s1, s2) <=> succ(s1, s2)),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(343,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 16.06/10.54 tff(344,plain,
% 16.06/10.54 (succ(s1, s2)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[343, 342])).
% 16.06/10.54 tff(345,plain,
% 16.06/10.54 (((~![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(346,plain,
% 16.06/10.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(347,plain,
% 16.06/10.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[346, 345])).
% 16.06/10.54 tff(348,plain,
% 16.06/10.54 (trans(s1, s2)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[347, 344, 95])).
% 16.06/10.54 tff(349,plain,
% 16.06/10.54 (((~![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(350,plain,
% 16.06/10.54 ((~![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))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(351,plain,
% 16.06/10.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[350, 349])).
% 16.06/10.54 tff(352,plain,
% 16.06/10.54 (node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[351, 112, 348])).
% 16.06/10.54 tff(353,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[352, 341, 299])).
% 16.06/10.54 tff(354,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(355,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s2)), introduced(assumption)).
% 16.06/10.54 tff(356,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s1)), introduced(assumption)).
% 16.06/10.54 tff(357,assumption,(node15(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 16.06/10.54 tff(358,plain,
% 16.06/10.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(359,plain,
% 16.06/10.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(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))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(360,plain,
% 16.06/10.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[359, 358])).
% 16.06/10.54 tff(361,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[360, 178, 355, 356, 357])).
% 16.06/10.54 tff(362,plain,((~node15(c_e_h_1, c_h, s1, s2)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(363,plain,
% 16.06/10.54 (~node15(c_e_h_1, c_h, s1, s2)),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[362, 355, 356])).
% 16.06/10.54 tff(364,assumption,(~node15(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 16.06/10.54 tff(365,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s1)), introduced(assumption)).
% 16.06/10.54 tff(366,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s0)), introduced(assumption)).
% 16.06/10.54 tff(367,plain,
% 16.06/10.54 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 16.06/10.54 inference(quant_inst,[status(thm)],[])).
% 16.06/10.54 tff(368,plain,
% 16.06/10.54 ($false),
% 16.06/10.54 inference(unit_resolution,[status(thm)],[367, 9, 366])).
% 16.06/10.54 tff(369,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.54 tff(370,plain,
% 16.06/10.54 (^[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)))),
% 16.06/10.54 inference(bind,[status(th)],[])).
% 16.06/10.54 tff(371,plain,
% 16.06/10.54 (![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))),
% 16.06/10.54 inference(quant_intro,[status(thm)],[370])).
% 16.06/10.54 tff(372,plain,
% 16.06/10.54 (![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))),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(373,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')).
% 16.06/10.54 tff(374,plain,
% 16.06/10.54 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[373, 372])).
% 16.06/10.54 tff(375,plain,(
% 16.06/10.54 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 16.06/10.54 inference(skolemize,[status(sab)],[374])).
% 16.06/10.54 tff(376,plain,
% 16.06/10.54 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 16.06/10.54 inference(modus_ponens,[status(thm)],[375, 371])).
% 16.06/10.54 tff(377,plain,
% 16.06/10.54 (m_cell_v_left(c_e_h_3, c_e_h_1) <=> m_cell_v_left(c_e_h_3, c_e_h_1)),
% 16.06/10.54 inference(rewrite,[status(thm)],[])).
% 16.06/10.54 tff(378,axiom,(m_cell_v_left(c_e_h_3, c_e_h_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_7')).
% 16.06/10.55 tff(379,plain,
% 16.06/10.55 (m_cell_v_left(c_e_h_3, c_e_h_1)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[378, 377])).
% 16.06/10.55 tff(380,plain,
% 16.06/10.55 (((~![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, 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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(381,plain,
% 16.06/10.55 ((~![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, s0))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(382,plain,
% 16.06/10.55 ((~![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, s0)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[381, 380])).
% 16.06/10.55 tff(383,plain,
% 16.06/10.55 (node3(c_e_h_3, c_e_h_1, s0)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[382, 379, 376])).
% 16.06/10.55 tff(384,plain,
% 16.06/10.55 (^[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)))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(385,plain,
% 16.06/10.55 (![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)) <=> ![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))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[384])).
% 16.06/10.55 tff(386,plain,
% 16.06/10.55 (![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)) <=> ![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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(387,plain,
% 16.06/10.55 (^[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)))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(388,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[387])).
% 16.06/10.55 tff(389,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')).
% 16.06/10.55 tff(390,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[389, 388])).
% 16.06/10.55 tff(391,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[390, 386])).
% 16.06/10.55 tff(392,plain,(
% 16.06/10.55 ![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))),
% 16.06/10.55 inference(skolemize,[status(sab)],[391])).
% 16.06/10.55 tff(393,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[392, 385])).
% 16.06/10.55 tff(394,plain,
% 16.06/10.55 (((~![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, 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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(395,plain,
% 16.06/10.55 ((~![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, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(396,plain,
% 16.06/10.55 ((~![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, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[395, 394])).
% 16.06/10.55 tff(397,plain,
% 16.06/10.55 ((~m_cell_v_ack(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[396, 393, 383])).
% 16.06/10.55 tff(398,plain,
% 16.06/10.55 (~m_cell_v_ack(c_e_h_1, s0)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[397, 369])).
% 16.06/10.55 tff(399,plain,
% 16.06/10.55 (^[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)))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(400,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[399])).
% 16.06/10.55 tff(401,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(402,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')).
% 16.06/10.55 tff(403,plain,
% 16.06/10.55 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[402, 401])).
% 16.06/10.55 tff(404,plain,(
% 16.06/10.55 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 16.06/10.55 inference(skolemize,[status(sab)],[403])).
% 16.06/10.55 tff(405,plain,
% 16.06/10.55 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[404, 400])).
% 16.06/10.55 tff(406,plain,
% 16.06/10.55 (((~![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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(407,plain,
% 16.06/10.55 ((~![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))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(408,plain,
% 16.06/10.55 ((~![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)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[407, 406])).
% 16.06/10.55 tff(409,plain,
% 16.06/10.55 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[408, 405, 398])).
% 16.06/10.55 tff(410,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s0)), introduced(assumption)).
% 16.06/10.55 tff(411,plain,
% 16.06/10.55 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(412,plain,
% 16.06/10.55 ($false),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[411, 9, 410])).
% 16.06/10.55 tff(413,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.55 tff(414,plain,
% 16.06/10.55 (^[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)))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(415,plain,
% 16.06/10.55 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[414])).
% 16.06/10.55 tff(416,plain,
% 16.06/10.55 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(417,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')).
% 16.06/10.55 tff(418,plain,
% 16.06/10.55 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[417, 416])).
% 16.06/10.55 tff(419,plain,(
% 16.06/10.55 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 16.06/10.55 inference(skolemize,[status(sab)],[418])).
% 16.06/10.55 tff(420,plain,
% 16.06/10.55 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[419, 415])).
% 16.06/10.55 tff(421,plain,
% 16.06/10.55 (((~![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, 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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(422,plain,
% 16.06/10.55 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(423,plain,
% 16.06/10.55 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[422, 421])).
% 16.06/10.55 tff(424,plain,
% 16.06/10.55 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[423, 420, 413])).
% 16.06/10.55 tff(425,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s1)), introduced(assumption)).
% 16.06/10.55 tff(426,assumption,(node6(c_e_h_1, c_j, s0, s1)), introduced(assumption)).
% 16.06/10.55 tff(427,plain,
% 16.06/10.55 (^[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)))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(428,plain,
% 16.06/10.55 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[427])).
% 16.06/10.55 tff(429,plain,
% 16.06/10.55 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(430,plain,
% 16.06/10.55 (^[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)))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(431,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[430])).
% 16.06/10.55 tff(432,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')).
% 16.06/10.55 tff(433,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[432, 431])).
% 16.06/10.55 tff(434,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[433, 429])).
% 16.06/10.55 tff(435,plain,(
% 16.06/10.55 ![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))),
% 16.06/10.55 inference(skolemize,[status(sab)],[434])).
% 16.06/10.55 tff(436,plain,
% 16.06/10.55 (![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))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[435, 428])).
% 16.06/10.55 tff(437,plain,
% 16.06/10.55 (((~![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, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~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, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(438,plain,
% 16.06/10.55 (((~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, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(439,plain,
% 16.06/10.55 (((~![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, 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, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1))))),
% 16.06/10.55 inference(monotonicity,[status(thm)],[438])).
% 16.06/10.55 tff(440,plain,
% 16.06/10.55 (((~![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, 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, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 16.06/10.55 inference(transitivity,[status(thm)],[439, 437])).
% 16.06/10.55 tff(441,plain,
% 16.06/10.55 ((~![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, 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))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(442,plain,
% 16.06/10.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~node6(c_e_h_1, c_j, s0, s1))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[441, 440])).
% 16.06/10.55 tff(443,plain,
% 16.06/10.55 ($false),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[442, 436, 425, 426, 188])).
% 16.06/10.55 tff(444,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,[]))).
% 16.06/10.55 tff(445,plain,
% 16.06/10.55 (~node6(c_e_h_1, c_j, s0, s1)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[444, 425])).
% 16.06/10.55 tff(446,plain,
% 16.06/10.55 (^[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))))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(447,plain,
% 16.06/10.55 (![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)))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[446])).
% 16.06/10.55 tff(448,plain,
% 16.06/10.55 (![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)))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(449,plain,
% 16.06/10.55 (^[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))))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(450,plain,
% 16.06/10.55 (![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)))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[449])).
% 16.06/10.55 tff(451,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')).
% 16.06/10.55 tff(452,plain,
% 16.06/10.55 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[451, 450])).
% 16.06/10.55 tff(453,plain,
% 16.06/10.55 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[452, 448])).
% 16.06/10.55 tff(454,plain,(
% 16.06/10.55 ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 16.06/10.55 inference(skolemize,[status(sab)],[453])).
% 16.06/10.55 tff(455,plain,
% 16.06/10.55 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[454, 447])).
% 16.06/10.55 tff(456,plain,
% 16.06/10.55 (((~![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_1, c_j, s0, s1) | node5(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)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(457,plain,
% 16.06/10.55 ((node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(458,plain,
% 16.06/10.55 (((~![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)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1)))),
% 16.06/10.55 inference(monotonicity,[status(thm)],[457])).
% 16.06/10.55 tff(459,plain,
% 16.06/10.55 (((~![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)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1))),
% 16.06/10.55 inference(transitivity,[status(thm)],[458, 456])).
% 16.06/10.55 tff(460,plain,
% 16.06/10.55 ((~![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)))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(461,plain,
% 16.06/10.55 ((~![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_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[460, 459])).
% 16.06/10.55 tff(462,plain,
% 16.06/10.55 (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[461, 455, 102])).
% 16.06/10.55 tff(463,plain,
% 16.06/10.55 (node5(c_e_h_1, c_j, s0, s1)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[462, 445])).
% 16.06/10.55 tff(464,plain,
% 16.06/10.55 (^[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))))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(465,plain,
% 16.06/10.55 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[464])).
% 16.06/10.55 tff(466,plain,
% 16.06/10.55 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(467,plain,
% 16.06/10.55 (^[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)))))),
% 16.06/10.55 inference(bind,[status(th)],[])).
% 16.06/10.55 tff(468,plain,
% 16.06/10.55 (![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)))),
% 16.06/10.55 inference(quant_intro,[status(thm)],[467])).
% 16.06/10.55 tff(469,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')).
% 16.06/10.55 tff(470,plain,
% 16.06/10.55 (![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)))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[469, 468])).
% 16.06/10.55 tff(471,plain,
% 16.06/10.55 (![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)))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[470, 466])).
% 16.06/10.55 tff(472,plain,(
% 16.06/10.55 ![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)))),
% 16.06/10.55 inference(skolemize,[status(sab)],[471])).
% 16.06/10.55 tff(473,plain,
% 16.06/10.55 (![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)))),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[472, 465])).
% 16.06/10.55 tff(474,plain,
% 16.06/10.55 (((~![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, 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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(475,plain,
% 16.06/10.55 ((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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(476,plain,
% 16.06/10.55 (((~![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, 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)))),
% 16.06/10.55 inference(monotonicity,[status(thm)],[475])).
% 16.06/10.55 tff(477,plain,
% 16.06/10.55 (((~![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, 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))),
% 16.06/10.55 inference(transitivity,[status(thm)],[476, 474])).
% 16.06/10.55 tff(478,plain,
% 16.06/10.55 ((~![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, 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)))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(479,plain,
% 16.06/10.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[478, 477])).
% 16.06/10.55 tff(480,plain,
% 16.06/10.55 ($false),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[479, 473, 425, 463, 424, 409])).
% 16.06/10.55 tff(481,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.55 tff(482,plain,
% 16.06/10.55 (((~![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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(483,plain,
% 16.06/10.55 ((~![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))),
% 16.06/10.55 inference(quant_inst,[status(thm)],[])).
% 16.06/10.55 tff(484,plain,
% 16.06/10.55 ((~![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)),
% 16.06/10.55 inference(modus_ponens,[status(thm)],[483, 482])).
% 16.06/10.55 tff(485,plain,
% 16.06/10.55 (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 16.06/10.55 inference(unit_resolution,[status(thm)],[484, 195, 481])).
% 16.06/10.55 tff(486,plain,
% 16.06/10.55 (((~![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_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))),
% 16.06/10.55 inference(rewrite,[status(thm)],[])).
% 16.06/10.55 tff(487,plain,
% 16.06/10.55 ((~![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_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))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(488,plain,
% 16.06/10.56 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | 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)),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[487, 486])).
% 16.06/10.56 tff(489,plain,
% 16.06/10.56 ((~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[488, 209, 485])).
% 16.06/10.56 tff(490,plain,
% 16.06/10.56 (~node16(c_e_h_1, c_h, s1)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[489, 365])).
% 16.06/10.56 tff(491,assumption,(node14(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 16.06/10.56 tff(492,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(493,plain,
% 16.06/10.56 (((~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)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(494,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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))))),
% 16.06/10.56 inference(monotonicity,[status(thm)],[493])).
% 16.06/10.56 tff(495,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.06/10.56 inference(transitivity,[status(thm)],[494, 492])).
% 16.06/10.56 tff(496,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(497,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[496, 495])).
% 16.06/10.56 tff(498,plain,
% 16.06/10.56 ($false),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[497, 254, 355, 491, 365])).
% 16.06/10.56 tff(499,plain,((~node14(c_e_h_1, c_h, s1, 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)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.56 tff(500,plain,
% 16.06/10.56 (~node14(c_e_h_1, c_h, s1, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[499, 365, 355])).
% 16.06/10.56 tff(501,plain,
% 16.06/10.56 (((~![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))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(502,plain,
% 16.06/10.56 ((~![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))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(503,plain,
% 16.06/10.56 ((~![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)),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[502, 501])).
% 16.06/10.56 tff(504,plain,
% 16.06/10.56 (node19(c_e_h_1, c_h, s1, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[503, 221, 348])).
% 16.06/10.56 tff(505,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node14(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)))) | node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node14(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(506,plain,
% 16.06/10.56 ((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))) <=> (node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node14(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(507,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | (node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node14(c_e_h_1, c_h, s1, s2)))),
% 16.06/10.56 inference(monotonicity,[status(thm)],[506])).
% 16.06/10.56 tff(508,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node14(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(transitivity,[status(thm)],[507, 505])).
% 16.06/10.56 tff(509,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(510,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node14(c_e_h_1, c_h, s1, s2)),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[509, 508])).
% 16.06/10.56 tff(511,plain,
% 16.06/10.56 (node16(c_e_h_1, c_h, s1) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[510, 235, 504])).
% 16.06/10.56 tff(512,plain,
% 16.06/10.56 ($false),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[511, 500, 490, 364])).
% 16.06/10.56 tff(513,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s1) | node15(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,[]))).
% 16.06/10.56 tff(514,plain,
% 16.06/10.56 (m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[513, 363, 355])).
% 16.06/10.56 tff(515,plain,
% 16.06/10.56 (^[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))))),
% 16.06/10.56 inference(bind,[status(th)],[])).
% 16.06/10.56 tff(516,plain,
% 16.06/10.56 (![I0: $i, X: $i, 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)))),
% 16.06/10.56 inference(quant_intro,[status(thm)],[515])).
% 16.06/10.56 tff(517,plain,
% 16.06/10.56 (![I0: $i, X: $i, 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)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(518,plain,
% 16.06/10.56 (^[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))))),
% 16.06/10.56 inference(bind,[status(th)],[])).
% 16.06/10.56 tff(519,plain,
% 16.06/10.56 (![I0: $i, X: $i, 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)))),
% 16.06/10.56 inference(quant_intro,[status(thm)],[518])).
% 16.06/10.56 tff(520,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')).
% 16.06/10.56 tff(521,plain,
% 16.06/10.56 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[520, 519])).
% 16.06/10.56 tff(522,plain,
% 16.06/10.56 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[521, 517])).
% 16.06/10.56 tff(523,plain,(
% 16.06/10.56 ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 16.06/10.56 inference(skolemize,[status(sab)],[522])).
% 16.06/10.56 tff(524,plain,
% 16.06/10.56 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[523, 516])).
% 16.06/10.56 tff(525,plain,
% 16.06/10.56 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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, s1) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(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_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(526,plain,
% 16.06/10.56 (((~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))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(527,plain,
% 16.06/10.56 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1))))),
% 16.06/10.56 inference(monotonicity,[status(thm)],[526])).
% 16.06/10.56 tff(528,plain,
% 16.06/10.56 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)))),
% 16.06/10.56 inference(transitivity,[status(thm)],[527, 525])).
% 16.06/10.56 tff(529,plain,
% 16.06/10.56 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(530,plain,
% 16.06/10.56 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, 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, s1) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[529, 528])).
% 16.06/10.56 tff(531,plain,
% 16.06/10.56 ((~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1))),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[530, 524, 485])).
% 16.06/10.56 tff(532,plain,
% 16.06/10.56 (~node17(c_e_h_1, c_h, s1)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[531, 514])).
% 16.06/10.56 tff(533,plain,
% 16.06/10.56 (^[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))))),
% 16.06/10.56 inference(bind,[status(th)],[])).
% 16.06/10.56 tff(534,plain,
% 16.06/10.56 (![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)))),
% 16.06/10.56 inference(quant_intro,[status(thm)],[533])).
% 16.06/10.56 tff(535,plain,
% 16.06/10.56 (![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)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(536,plain,
% 16.06/10.56 (^[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))))),
% 16.06/10.56 inference(bind,[status(th)],[])).
% 16.06/10.56 tff(537,plain,
% 16.06/10.56 (![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)))),
% 16.06/10.56 inference(quant_intro,[status(thm)],[536])).
% 16.06/10.56 tff(538,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')).
% 16.06/10.56 tff(539,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[538, 537])).
% 16.06/10.56 tff(540,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[539, 535])).
% 16.06/10.56 tff(541,plain,(
% 16.06/10.56 ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.56 inference(skolemize,[status(sab)],[540])).
% 16.06/10.56 tff(542,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[541, 534])).
% 16.06/10.56 tff(543,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, 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) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(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)))) | node17(c_e_h_1, c_h, s1) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(544,plain,
% 16.06/10.56 ((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))) <=> (node17(c_e_h_1, c_h, s1) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(545,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, 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)))) | (node17(c_e_h_1, c_h, s1) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2)))),
% 16.06/10.56 inference(monotonicity,[status(thm)],[544])).
% 16.06/10.56 tff(546,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, 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)))) | node17(c_e_h_1, c_h, s1) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(transitivity,[status(thm)],[545, 543])).
% 16.06/10.56 tff(547,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, 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)))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(548,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, 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) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2)),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[547, 546])).
% 16.06/10.56 tff(549,plain,
% 16.06/10.56 (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[548, 542, 504])).
% 16.06/10.56 tff(550,plain,
% 16.06/10.56 (node18(c_e_h_1, c_h, s1, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[549, 532])).
% 16.06/10.56 tff(551,plain,
% 16.06/10.56 (^[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))))),
% 16.06/10.56 inference(bind,[status(th)],[])).
% 16.06/10.56 tff(552,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.06/10.56 inference(quant_intro,[status(thm)],[551])).
% 16.06/10.56 tff(553,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(554,plain,
% 16.06/10.56 (^[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))))),
% 16.06/10.56 inference(bind,[status(th)],[])).
% 16.06/10.56 tff(555,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.06/10.56 inference(quant_intro,[status(thm)],[554])).
% 16.06/10.56 tff(556,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')).
% 16.06/10.56 tff(557,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[556, 555])).
% 16.06/10.56 tff(558,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[557, 553])).
% 16.06/10.56 tff(559,plain,(
% 16.06/10.56 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 16.06/10.56 inference(skolemize,[status(sab)],[558])).
% 16.06/10.56 tff(560,plain,
% 16.06/10.56 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[559, 552])).
% 16.06/10.56 tff(561,plain,
% 16.06/10.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(562,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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)))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(563,plain,
% 16.06/10.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2))),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[562, 561])).
% 16.06/10.56 tff(564,plain,
% 16.06/10.56 ($false),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[563, 560, 355, 356, 550])).
% 16.06/10.56 tff(565,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.56 tff(566,plain,
% 16.06/10.56 (~m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[565, 262])).
% 16.06/10.56 tff(567,plain,
% 16.06/10.56 (((~![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))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(568,plain,
% 16.06/10.56 ((~![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))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(569,plain,
% 16.06/10.56 ((~![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)),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[568, 567])).
% 16.06/10.56 tff(570,plain,
% 16.06/10.56 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[569, 269, 566])).
% 16.06/10.56 tff(571,plain,
% 16.06/10.56 (((~![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_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))),
% 16.06/10.56 inference(rewrite,[status(thm)],[])).
% 16.06/10.56 tff(572,plain,
% 16.06/10.56 ((~![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_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))),
% 16.06/10.56 inference(quant_inst,[status(thm)],[])).
% 16.06/10.56 tff(573,plain,
% 16.06/10.56 ((~![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_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 16.06/10.56 inference(modus_ponens,[status(thm)],[572, 571])).
% 16.06/10.56 tff(574,plain,
% 16.06/10.56 (~node20(c_e_h_1, c_i, s2)),
% 16.06/10.56 inference(unit_resolution,[status(thm)],[573, 283, 570])).
% 16.06/10.56 tff(575,assumption,(~node20(c_e_h_1, c_i, s2)), introduced(assumption)).
% 16.06/10.56 tff(576,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s2)), introduced(assumption)).
% 16.06/10.56 tff(577,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s3)), introduced(assumption)).
% 16.06/10.56 tff(578,assumption,(node22(c_e_h_1, c_i, s2, s3)), introduced(assumption)).
% 16.06/10.57 tff(579,plain,
% 16.06/10.57 (((~![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_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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(580,plain,
% 16.06/10.57 ((~![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_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(581,plain,
% 16.06/10.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[580, 579])).
% 16.06/10.57 tff(582,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[581, 127, 577, 576, 578])).
% 16.06/10.57 tff(583,plain,((~node22(c_e_h_1, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(584,plain,
% 16.06/10.57 (~node22(c_e_h_1, c_i, s2, s3)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[583, 577, 576])).
% 16.06/10.57 tff(585,plain,
% 16.06/10.57 (succ(s2, s3) <=> succ(s2, s3)),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(586,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 16.06/10.57 tff(587,plain,
% 16.06/10.57 (succ(s2, s3)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[586, 585])).
% 16.06/10.57 tff(588,plain,
% 16.06/10.57 (((~![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(589,plain,
% 16.06/10.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(590,plain,
% 16.06/10.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[589, 588])).
% 16.06/10.57 tff(591,plain,
% 16.06/10.57 (trans(s2, s3)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[590, 587, 95])).
% 16.06/10.57 tff(592,plain,
% 16.06/10.57 (((~![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(593,plain,
% 16.06/10.57 ((~![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))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(594,plain,
% 16.06/10.57 ((~![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)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[593, 592])).
% 16.06/10.57 tff(595,plain,
% 16.06/10.57 (node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[594, 112, 591])).
% 16.06/10.57 tff(596,plain,
% 16.06/10.57 (node21(c_e_h_1, c_i, s2, s3)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[595, 584])).
% 16.06/10.57 tff(597,plain,
% 16.06/10.57 (((~![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_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)))) | 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)))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(598,plain,
% 16.06/10.57 ((~![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_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(599,plain,
% 16.06/10.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[598, 597])).
% 16.06/10.57 tff(600,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[599, 82, 577, 596, 575])).
% 16.06/10.57 tff(601,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(602,plain,
% 16.06/10.57 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[601, 574])).
% 16.06/10.57 tff(603,plain,
% 16.06/10.57 (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[602, 354])).
% 16.06/10.57 tff(604,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s3)), introduced(assumption)).
% 16.06/10.57 tff(605,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s3)), introduced(assumption)).
% 16.06/10.57 tff(606,plain,
% 16.06/10.57 (^[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)))),
% 16.06/10.57 inference(bind,[status(th)],[])).
% 16.06/10.57 tff(607,plain,
% 16.06/10.57 (![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))),
% 16.06/10.57 inference(quant_intro,[status(thm)],[606])).
% 16.06/10.57 tff(608,plain,
% 16.06/10.57 (![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(609,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')).
% 16.06/10.57 tff(610,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[609, 608])).
% 16.06/10.57 tff(611,plain,(
% 16.06/10.57 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 16.06/10.57 inference(skolemize,[status(sab)],[610])).
% 16.06/10.57 tff(612,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[611, 607])).
% 16.06/10.57 tff(613,plain,
% 16.06/10.57 (((~![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(614,plain,
% 16.06/10.57 ((~![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))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(615,plain,
% 16.06/10.57 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[614, 613])).
% 16.06/10.57 tff(616,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[615, 612, 605, 604])).
% 16.06/10.57 tff(617,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(618,plain,
% 16.06/10.57 (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[617, 603])).
% 16.06/10.57 tff(619,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 16.06/10.57 tff(620,assumption,(node18(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 16.06/10.57 tff(621,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s1)), introduced(assumption)).
% 16.06/10.57 tff(622,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s0)), introduced(assumption)).
% 16.06/10.57 tff(623,plain,
% 16.06/10.57 (^[I0: $i, I1: $i] : refl((~m_mutex_h_half_v_out(I0, I1, s0)) <=> (~m_mutex_h_half_v_out(I0, I1, s0)))),
% 16.06/10.57 inference(bind,[status(th)],[])).
% 16.06/10.57 tff(624,plain,
% 16.06/10.57 (![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))),
% 16.06/10.57 inference(quant_intro,[status(thm)],[623])).
% 16.06/10.57 tff(625,plain,
% 16.06/10.57 (![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(626,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')).
% 16.06/10.57 tff(627,plain,
% 16.06/10.57 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[626, 625])).
% 16.06/10.57 tff(628,plain,(
% 16.06/10.57 ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 16.06/10.57 inference(skolemize,[status(sab)],[627])).
% 16.06/10.57 tff(629,plain,
% 16.06/10.57 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[628, 624])).
% 16.06/10.57 tff(630,plain,
% 16.06/10.57 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(631,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[630, 629, 622])).
% 16.06/10.57 tff(632,plain,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(633,plain,
% 16.06/10.57 (^[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)))),
% 16.06/10.57 inference(bind,[status(th)],[])).
% 16.06/10.57 tff(634,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 16.06/10.57 inference(quant_intro,[status(thm)],[633])).
% 16.06/10.57 tff(635,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(636,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')).
% 16.06/10.57 tff(637,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[636, 635])).
% 16.06/10.57 tff(638,plain,(
% 16.06/10.57 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 16.06/10.57 inference(skolemize,[status(sab)],[637])).
% 16.06/10.57 tff(639,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[638, 634])).
% 16.06/10.57 tff(640,plain,
% 16.06/10.57 (((~![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, 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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(641,plain,
% 16.06/10.57 ((~![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, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(642,plain,
% 16.06/10.57 ((~![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, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[641, 640])).
% 16.06/10.57 tff(643,plain,
% 16.06/10.57 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s0)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[642, 639, 632])).
% 16.06/10.57 tff(644,plain,
% 16.06/10.57 (((~![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, 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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(645,plain,
% 16.06/10.57 ((~![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, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(646,plain,
% 16.06/10.57 ((~![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, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[645, 644])).
% 16.06/10.57 tff(647,plain,
% 16.06/10.57 (~node20(c_e_h_1, c_c, s0)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[646, 283, 643])).
% 16.06/10.57 tff(648,assumption,(node21(c_e_h_1, c_c, s0, s1)), introduced(assumption)).
% 16.06/10.57 tff(649,plain,
% 16.06/10.57 (((~![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_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1)) | node20(c_e_h_1, c_c, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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)) | (~node21(c_e_h_1, c_c, s0, s1)) | node20(c_e_h_1, c_c, s0))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(650,plain,
% 16.06/10.57 ((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)) | (~node21(c_e_h_1, c_c, s0, s1)) | node20(c_e_h_1, c_c, s0))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(651,plain,
% 16.06/10.57 (((~![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_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)) | (~node21(c_e_h_1, c_c, s0, s1)) | node20(c_e_h_1, c_c, s0)))),
% 16.06/10.57 inference(monotonicity,[status(thm)],[650])).
% 16.06/10.57 tff(652,plain,
% 16.06/10.57 (((~![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_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)) | (~node21(c_e_h_1, c_c, s0, s1)) | node20(c_e_h_1, c_c, s0))),
% 16.06/10.57 inference(transitivity,[status(thm)],[651, 649])).
% 16.06/10.57 tff(653,plain,
% 16.06/10.57 ((~![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_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(654,plain,
% 16.06/10.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1)) | node20(c_e_h_1, c_c, s0)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[653, 652])).
% 16.06/10.57 tff(655,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[654, 82, 648, 647, 621])).
% 16.06/10.57 tff(656,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,[]))).
% 16.06/10.57 tff(657,plain,
% 16.06/10.57 (~node21(c_e_h_1, c_c, s0, s1)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[656, 621])).
% 16.06/10.57 tff(658,plain,
% 16.06/10.57 (((~![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(659,plain,
% 16.06/10.57 ((~![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))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(660,plain,
% 16.06/10.57 ((~![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)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[659, 658])).
% 16.06/10.57 tff(661,plain,
% 16.06/10.57 (node21(c_e_h_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[660, 112, 102])).
% 16.06/10.57 tff(662,plain,
% 16.06/10.57 (node22(c_e_h_1, c_c, s0, s1)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[661, 657])).
% 16.06/10.57 tff(663,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s0)), introduced(assumption)).
% 16.06/10.57 tff(664,plain,
% 16.06/10.57 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(665,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[664, 9, 663])).
% 16.06/10.57 tff(666,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(667,plain,
% 16.06/10.57 (((~![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, 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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(668,plain,
% 16.06/10.57 ((~![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, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(669,plain,
% 16.06/10.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[668, 667])).
% 16.06/10.57 tff(670,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[669, 127, 666, 662, 621])).
% 16.06/10.57 tff(671,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(672,plain,
% 16.06/10.57 (^[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)))),
% 16.06/10.57 inference(bind,[status(th)],[])).
% 16.06/10.57 tff(673,plain,
% 16.06/10.57 (![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))),
% 16.06/10.57 inference(quant_intro,[status(thm)],[672])).
% 16.06/10.57 tff(674,plain,
% 16.06/10.57 (![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(675,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')).
% 16.06/10.57 tff(676,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[675, 674])).
% 16.06/10.57 tff(677,plain,(
% 16.06/10.57 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 16.06/10.57 inference(skolemize,[status(sab)],[676])).
% 16.06/10.57 tff(678,plain,
% 16.06/10.57 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[677, 673])).
% 16.06/10.57 tff(679,plain,
% 16.06/10.57 (((~![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, s1)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(680,plain,
% 16.06/10.57 ((~![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, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(681,plain,
% 16.06/10.57 ((~![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, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[680, 679])).
% 16.06/10.57 tff(682,plain,
% 16.06/10.57 (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[681, 678, 671])).
% 16.06/10.57 tff(683,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s1)), introduced(assumption)).
% 16.06/10.57 tff(684,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s2)), introduced(assumption)).
% 16.06/10.57 tff(685,assumption,(node18(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 16.06/10.57 tff(686,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s1)), introduced(assumption)).
% 16.06/10.57 tff(687,assumption,(node15(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 16.06/10.57 tff(688,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s0)), introduced(assumption)).
% 16.06/10.57 tff(689,plain,
% 16.06/10.57 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(690,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[689, 165, 688])).
% 16.06/10.57 tff(691,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(692,plain,
% 16.06/10.57 (((~![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_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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(693,plain,
% 16.06/10.57 ((~![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_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(694,plain,
% 16.06/10.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[693, 692])).
% 16.06/10.57 tff(695,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[694, 178, 691, 686, 687])).
% 16.06/10.57 tff(696,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,[]))).
% 16.06/10.57 tff(697,plain,
% 16.06/10.57 (~node15(c_e_h_1, c_e, s0, s1)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[696, 686])).
% 16.06/10.57 tff(698,plain,
% 16.06/10.57 (((~![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))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(699,plain,
% 16.06/10.57 ((~![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))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(700,plain,
% 16.06/10.57 ((~![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)),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[699, 698])).
% 16.06/10.57 tff(701,plain,
% 16.06/10.57 (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[700, 678, 666])).
% 16.06/10.57 tff(702,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s0)), introduced(assumption)).
% 16.06/10.57 tff(703,assumption,(node14(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 16.06/10.57 tff(704,plain,
% 16.06/10.57 (((~![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_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)))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(705,plain,
% 16.06/10.57 (((~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)))),
% 16.06/10.57 inference(rewrite,[status(thm)],[])).
% 16.06/10.57 tff(706,plain,
% 16.06/10.57 (((~![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_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))))),
% 16.06/10.57 inference(monotonicity,[status(thm)],[705])).
% 16.06/10.57 tff(707,plain,
% 16.06/10.57 (((~![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_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)))),
% 16.06/10.57 inference(transitivity,[status(thm)],[706, 704])).
% 16.06/10.57 tff(708,plain,
% 16.06/10.57 ((~![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_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)))),
% 16.06/10.57 inference(quant_inst,[status(thm)],[])).
% 16.06/10.57 tff(709,plain,
% 16.06/10.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1))),
% 16.06/10.57 inference(modus_ponens,[status(thm)],[708, 707])).
% 16.06/10.57 tff(710,plain,
% 16.06/10.57 ($false),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[709, 254, 686, 703, 702])).
% 16.06/10.57 tff(711,plain,((~node14(c_e_h_1, c_e, s0, 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)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.57 tff(712,plain,
% 16.06/10.57 ((~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[711, 701])).
% 16.06/10.57 tff(713,plain,
% 16.06/10.57 (~node14(c_e_h_1, c_e, s0, s1)),
% 16.06/10.57 inference(unit_resolution,[status(thm)],[712, 686])).
% 16.06/10.57 tff(714,plain,
% 16.06/10.57 (((~![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, 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_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(715,plain,
% 16.06/10.58 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(716,plain,
% 16.06/10.58 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[715, 714])).
% 16.06/10.58 tff(717,plain,
% 16.06/10.58 (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[716, 612, 305])).
% 16.06/10.58 tff(718,plain,
% 16.06/10.58 (((~![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_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))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(719,plain,
% 16.06/10.58 ((~![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_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))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(720,plain,
% 16.06/10.58 ((~![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_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)),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[719, 718])).
% 16.06/10.58 tff(721,plain,
% 16.06/10.58 ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[720, 209, 701])).
% 16.06/10.58 tff(722,plain,
% 16.06/10.58 (~node16(c_e_h_1, c_e, s0)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[721, 717])).
% 16.06/10.58 tff(723,plain,
% 16.06/10.58 (((~![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))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(724,plain,
% 16.06/10.58 ((~![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))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(725,plain,
% 16.06/10.58 ((~![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)),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[724, 723])).
% 16.06/10.58 tff(726,plain,
% 16.06/10.58 (node19(c_e_h_1, c_e, s0, s1)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[725, 221, 102])).
% 16.06/10.58 tff(727,plain,
% 16.06/10.58 (((~![Y: $i, I0: $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, s0, s1) | node14(c_e_h_1, c_e, s0, s1) | (~node19(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)))) | node15(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)) | node16(c_e_h_1, c_e, s0))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(728,plain,
% 16.06/10.58 ((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))) <=> (node15(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)) | node16(c_e_h_1, c_e, s0))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(729,plain,
% 16.06/10.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | (node15(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)) | node16(c_e_h_1, c_e, s0)))),
% 16.06/10.58 inference(monotonicity,[status(thm)],[728])).
% 16.06/10.58 tff(730,plain,
% 16.06/10.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | node15(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)) | node16(c_e_h_1, c_e, s0))),
% 16.06/10.58 inference(transitivity,[status(thm)],[729, 727])).
% 16.06/10.58 tff(731,plain,
% 16.06/10.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(732,plain,
% 16.06/10.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s0, s1) | node14(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node16(c_e_h_1, c_e, s0)),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[731, 730])).
% 16.06/10.58 tff(733,plain,
% 16.06/10.58 (node15(c_e_h_1, c_e, s0, s1) | node14(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[732, 235, 726])).
% 16.06/10.58 tff(734,plain,
% 16.06/10.58 (node15(c_e_h_1, c_e, s0, s1) | node14(c_e_h_1, c_e, s0, s1)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[733, 722])).
% 16.06/10.58 tff(735,plain,
% 16.06/10.58 ($false),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[734, 713, 697])).
% 16.06/10.58 tff(736,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.58 tff(737,plain,
% 16.06/10.58 (((~![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_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)))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(738,plain,
% 16.06/10.58 (((~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)))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(739,plain,
% 16.06/10.58 (((~![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_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))))),
% 16.06/10.58 inference(monotonicity,[status(thm)],[738])).
% 16.06/10.58 tff(740,plain,
% 16.06/10.58 (((~![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_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)))),
% 16.06/10.58 inference(transitivity,[status(thm)],[739, 737])).
% 16.06/10.58 tff(741,plain,
% 16.06/10.58 ((~![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_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(742,plain,
% 16.06/10.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node18(c_e_h_1, c_e, s1, s2))),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[741, 740])).
% 16.06/10.58 tff(743,plain,
% 16.06/10.58 ($false),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[742, 560, 684, 736, 685])).
% 16.06/10.58 tff(744,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,[]))).
% 16.06/10.58 tff(745,plain,
% 16.06/10.58 (~node18(c_e_h_1, c_e, s1, s2)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[744, 684])).
% 16.06/10.58 tff(746,plain,
% 16.06/10.58 (((~![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_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))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(747,plain,
% 16.06/10.58 ((~![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_e, s1, s2))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(748,plain,
% 16.06/10.58 ((~![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_e, s1, s2)),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[747, 746])).
% 16.06/10.58 tff(749,plain,
% 16.06/10.58 (node19(c_e_h_1, c_e, s1, s2)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[748, 221, 348])).
% 16.06/10.58 tff(750,plain,
% 16.06/10.58 (((~![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_e, s1, s2)) | node17(c_e_h_1, c_e, s1) | 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)))) | (~node19(c_e_h_1, c_e, s1, s2)) | node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(751,plain,
% 16.06/10.58 ((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))) <=> ((~node19(c_e_h_1, c_e, s1, s2)) | node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(752,plain,
% 16.06/10.58 (((~![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_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)))) | ((~node19(c_e_h_1, c_e, s1, s2)) | node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2)))),
% 16.06/10.58 inference(monotonicity,[status(thm)],[751])).
% 16.06/10.58 tff(753,plain,
% 16.06/10.58 (((~![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_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)))) | (~node19(c_e_h_1, c_e, s1, s2)) | node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2))),
% 16.06/10.58 inference(transitivity,[status(thm)],[752, 750])).
% 16.06/10.58 tff(754,plain,
% 16.06/10.58 ((~![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_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(755,plain,
% 16.06/10.58 ((~![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_e, s1, s2)) | node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2)),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[754, 753])).
% 16.06/10.58 tff(756,plain,
% 16.06/10.58 (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[755, 542, 749])).
% 16.06/10.58 tff(757,plain,
% 16.06/10.58 (node17(c_e_h_1, c_e, s1)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[756, 745])).
% 16.06/10.58 tff(758,plain,
% 16.06/10.58 (^[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))))),
% 16.06/10.58 inference(bind,[status(th)],[])).
% 16.06/10.58 tff(759,plain,
% 16.06/10.58 (![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))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 16.06/10.58 inference(quant_intro,[status(thm)],[758])).
% 16.06/10.58 tff(760,plain,
% 16.06/10.58 (![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))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(761,plain,
% 16.06/10.58 (^[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)))))),
% 16.06/10.58 inference(bind,[status(th)],[])).
% 16.06/10.58 tff(762,plain,
% 16.06/10.58 (![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))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 16.06/10.58 inference(quant_intro,[status(thm)],[761])).
% 16.06/10.58 tff(763,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')).
% 16.06/10.58 tff(764,plain,
% 16.06/10.58 (![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)))),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[763, 762])).
% 16.06/10.58 tff(765,plain,
% 16.06/10.58 (![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)))),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[764, 760])).
% 16.06/10.58 tff(766,plain,(
% 16.06/10.58 ![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)))),
% 16.06/10.58 inference(skolemize,[status(sab)],[765])).
% 16.06/10.58 tff(767,plain,
% 16.06/10.58 (![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)))),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[766, 759])).
% 16.06/10.58 tff(768,plain,
% 16.06/10.58 (((~![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_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_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)))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(769,plain,
% 16.06/10.58 ((~![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_e, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(770,plain,
% 16.06/10.58 ((~![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_e, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1))),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[769, 768])).
% 16.06/10.58 tff(771,plain,
% 16.06/10.58 (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))),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[770, 767, 757])).
% 16.06/10.58 tff(772,plain,
% 16.06/10.58 (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[771, 683])).
% 16.06/10.58 tff(773,assumption,(node15(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 16.06/10.58 tff(774,plain,
% 16.06/10.58 (((~![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_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))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(775,plain,
% 16.06/10.58 ((~![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_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 16.06/10.58 inference(quant_inst,[status(thm)],[])).
% 16.06/10.58 tff(776,plain,
% 16.06/10.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 16.06/10.58 inference(modus_ponens,[status(thm)],[775, 774])).
% 16.06/10.58 tff(777,plain,
% 16.06/10.58 ($false),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[776, 178, 684, 736, 773])).
% 16.06/10.58 tff(778,plain,((~node15(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,[]))).
% 16.06/10.58 tff(779,plain,
% 16.06/10.58 (~node15(c_e_h_1, c_e, s1, s2)),
% 16.06/10.58 inference(unit_resolution,[status(thm)],[778, 684])).
% 16.06/10.58 tff(780,assumption,(node14(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 16.06/10.58 tff(781,plain,
% 16.06/10.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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)))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(782,plain,
% 16.06/10.58 (((~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)))),
% 16.06/10.58 inference(rewrite,[status(thm)],[])).
% 16.06/10.58 tff(783,plain,
% 16.06/10.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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))))),
% 16.06/10.58 inference(monotonicity,[status(thm)],[782])).
% 16.06/10.58 tff(784,plain,
% 16.06/10.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.06/10.59 inference(transitivity,[status(thm)],[783, 781])).
% 16.06/10.59 tff(785,plain,
% 16.06/10.59 ((~![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_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)))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(786,plain,
% 16.06/10.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~node14(c_e_h_1, c_e, s1, s2))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[785, 784])).
% 16.06/10.59 tff(787,plain,
% 16.06/10.59 ($false),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[786, 254, 684, 780, 683])).
% 16.06/10.59 tff(788,plain,((~node14(c_e_h_1, c_e, s1, 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)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.59 tff(789,plain,
% 16.06/10.59 (~node14(c_e_h_1, c_e, s1, s2)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[788, 683, 684])).
% 16.06/10.59 tff(790,plain,
% 16.06/10.59 (((~![Y: $i, I0: $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, s1, s2)) | 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))) <=> ((~![Y: $i, I0: $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, s1, s2)) | 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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(791,plain,
% 16.06/10.59 ((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))) <=> ((~node19(c_e_h_1, c_e, s1, s2)) | 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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(792,plain,
% 16.06/10.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | ((~node19(c_e_h_1, c_e, s1, s2)) | 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)))),
% 16.06/10.59 inference(monotonicity,[status(thm)],[791])).
% 16.06/10.59 tff(793,plain,
% 16.06/10.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))) | (~node19(c_e_h_1, c_e, s1, s2)) | 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))),
% 16.06/10.59 inference(transitivity,[status(thm)],[792, 790])).
% 16.06/10.59 tff(794,plain,
% 16.06/10.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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)))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(795,plain,
% 16.06/10.59 ((~![Y: $i, I0: $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, s1, s2)) | 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)),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[794, 793])).
% 16.06/10.59 tff(796,plain,
% 16.06/10.59 (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)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[795, 235, 749])).
% 16.06/10.59 tff(797,plain,
% 16.06/10.59 (node16(c_e_h_1, c_e, s1)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[796, 789, 779])).
% 16.06/10.59 tff(798,plain,
% 16.06/10.59 (((~![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_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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(799,plain,
% 16.06/10.59 ((~![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_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))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(800,plain,
% 16.06/10.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[799, 798])).
% 16.06/10.59 tff(801,plain,
% 16.06/10.59 ($false),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[800, 209, 797, 683, 772])).
% 16.06/10.59 tff(802,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 16.06/10.59 tff(803,plain,
% 16.06/10.59 (~m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[802, 682])).
% 16.06/10.59 tff(804,plain,
% 16.06/10.59 (((~![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_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~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, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(805,plain,
% 16.06/10.59 (((~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))) <=> (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, s3)) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(806,plain,
% 16.06/10.59 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3))))),
% 16.06/10.59 inference(monotonicity,[status(thm)],[805])).
% 16.06/10.59 tff(807,plain,
% 16.06/10.59 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 16.06/10.59 inference(transitivity,[status(thm)],[806, 804])).
% 16.06/10.59 tff(808,plain,
% 16.06/10.59 ((~![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_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(809,plain,
% 16.06/10.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[808, 807])).
% 16.06/10.59 tff(810,plain,
% 16.06/10.59 ($false),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[809, 560, 803, 620, 619])).
% 16.06/10.59 tff(811,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,[]))).
% 16.06/10.59 tff(812,plain,
% 16.06/10.59 (~node18(c_e_h_1, c_e, s2, s3)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[811, 619])).
% 16.06/10.59 tff(813,plain,
% 16.06/10.59 (((~![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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(814,plain,
% 16.06/10.59 ((~![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))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(815,plain,
% 16.06/10.59 ((~![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)),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[814, 813])).
% 16.06/10.59 tff(816,plain,
% 16.06/10.59 (node19(c_e_h_1, c_e, s2, s3)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[815, 221, 591])).
% 16.06/10.59 tff(817,plain,
% 16.06/10.59 (((~![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_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)))) | 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)))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(818,plain,
% 16.06/10.59 ((~![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_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(819,plain,
% 16.06/10.59 ((~![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_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[818, 817])).
% 16.06/10.59 tff(820,plain,
% 16.06/10.59 (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[819, 542, 816])).
% 16.06/10.59 tff(821,plain,
% 16.06/10.59 (node17(c_e_h_1, c_e, s2)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[820, 812])).
% 16.06/10.59 tff(822,assumption,(node15(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 16.06/10.59 tff(823,plain,
% 16.06/10.59 (((~![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_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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(824,plain,
% 16.06/10.59 ((~![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_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(825,plain,
% 16.06/10.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[824, 823])).
% 16.06/10.59 tff(826,plain,
% 16.06/10.59 ($false),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[825, 178, 803, 822, 619])).
% 16.06/10.59 tff(827,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,[]))).
% 16.06/10.59 tff(828,plain,
% 16.06/10.59 (~node15(c_e_h_1, c_e, s2, s3)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[827, 619])).
% 16.06/10.59 tff(829,assumption,(m_user_v_req(c_e_h_1, c_u, s0)), introduced(assumption)).
% 16.06/10.59 tff(830,plain,
% 16.06/10.59 (^[I0: $i, I1: $i] : refl((~m_user_v_req(I0, I1, s0)) <=> (~m_user_v_req(I0, I1, s0)))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(831,plain,
% 16.06/10.59 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[830])).
% 16.06/10.59 tff(832,plain,
% 16.06/10.59 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(833,axiom,(![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_user_1')).
% 16.06/10.59 tff(834,plain,
% 16.06/10.59 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[833, 832])).
% 16.06/10.59 tff(835,plain,(
% 16.06/10.59 ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 16.06/10.59 inference(skolemize,[status(sab)],[834])).
% 16.06/10.59 tff(836,plain,
% 16.06/10.59 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[835, 831])).
% 16.06/10.59 tff(837,plain,
% 16.06/10.59 ((~![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))) | (~m_user_v_req(c_e_h_1, c_u, s0))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(838,plain,
% 16.06/10.59 ($false),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[837, 836, 829])).
% 16.06/10.59 tff(839,plain,(~m_user_v_req(c_e_h_1, c_u, s0)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.59 tff(840,plain,
% 16.06/10.59 (^[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)))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(841,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[840])).
% 16.06/10.59 tff(842,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(843,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')).
% 16.06/10.59 tff(844,plain,
% 16.06/10.59 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[843, 842])).
% 16.06/10.59 tff(845,plain,(
% 16.06/10.59 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 16.06/10.59 inference(skolemize,[status(sab)],[844])).
% 16.06/10.59 tff(846,plain,
% 16.06/10.59 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[845, 841])).
% 16.06/10.59 tff(847,plain,
% 16.06/10.59 (((~![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, 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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(848,plain,
% 16.06/10.59 ((~![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, s0)) | m_user_v_req(c_e_h_1, c_u, s0))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(849,plain,
% 16.06/10.59 ((~![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, s0)) | m_user_v_req(c_e_h_1, c_u, s0)),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[848, 847])).
% 16.06/10.59 tff(850,plain,
% 16.06/10.59 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s0)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[849, 846, 839])).
% 16.06/10.59 tff(851,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s1)), introduced(assumption)).
% 16.06/10.59 tff(852,assumption,(node13(c_e_h_1, c_a, s0, s1)), introduced(assumption)).
% 16.06/10.59 tff(853,plain,
% 16.06/10.59 (^[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)))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(854,plain,
% 16.06/10.59 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[853])).
% 16.06/10.59 tff(855,plain,
% 16.06/10.59 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(856,plain,
% 16.06/10.59 (^[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)))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(857,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[856])).
% 16.06/10.59 tff(858,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')).
% 16.06/10.59 tff(859,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[858, 857])).
% 16.06/10.59 tff(860,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[859, 855])).
% 16.06/10.59 tff(861,plain,(
% 16.06/10.59 ![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))),
% 16.06/10.59 inference(skolemize,[status(sab)],[860])).
% 16.06/10.59 tff(862,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[861, 854])).
% 16.06/10.59 tff(863,plain,
% 16.06/10.59 (((~![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, 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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(864,plain,
% 16.06/10.59 ((~![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, s1)) | (~node13(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(865,plain,
% 16.06/10.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)) | (~node13(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0)),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[864, 863])).
% 16.06/10.59 tff(866,plain,
% 16.06/10.59 ($false),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[865, 862, 852, 632, 851])).
% 16.06/10.59 tff(867,plain,((~node13(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,[]))).
% 16.06/10.59 tff(868,plain,
% 16.06/10.59 (~node13(c_e_h_1, c_a, s0, s1)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[867, 851])).
% 16.06/10.59 tff(869,plain,
% 16.06/10.59 (^[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)))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(870,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[869])).
% 16.06/10.59 tff(871,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(872,plain,
% 16.06/10.59 (^[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)))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(873,plain,
% 16.06/10.59 (![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))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[872])).
% 16.06/10.59 tff(874,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')).
% 16.06/10.59 tff(875,plain,
% 16.06/10.59 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[874, 873])).
% 16.06/10.59 tff(876,plain,
% 16.06/10.59 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[875, 871])).
% 16.06/10.59 tff(877,plain,(
% 16.06/10.59 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 16.06/10.59 inference(skolemize,[status(sab)],[876])).
% 16.06/10.59 tff(878,plain,
% 16.06/10.59 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[877, 870])).
% 16.06/10.59 tff(879,plain,
% 16.06/10.59 (((~![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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(880,plain,
% 16.06/10.59 ((~![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))),
% 16.06/10.59 inference(quant_inst,[status(thm)],[])).
% 16.06/10.59 tff(881,plain,
% 16.06/10.59 ((~![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)),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[880, 879])).
% 16.06/10.59 tff(882,plain,
% 16.06/10.59 (node12(c_e_h_1, c_a, s0, s1) | node13(c_e_h_1, c_a, s0, s1)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[881, 878, 102])).
% 16.06/10.59 tff(883,plain,
% 16.06/10.59 (node12(c_e_h_1, c_a, s0, s1)),
% 16.06/10.59 inference(unit_resolution,[status(thm)],[882, 868])).
% 16.06/10.59 tff(884,plain,
% 16.06/10.59 (^[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))))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(885,plain,
% 16.06/10.59 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[884])).
% 16.06/10.59 tff(886,plain,
% 16.06/10.59 (![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))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(887,plain,
% 16.06/10.59 (^[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))))),
% 16.06/10.59 inference(bind,[status(th)],[])).
% 16.06/10.59 tff(888,plain,
% 16.06/10.59 (![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)))),
% 16.06/10.59 inference(quant_intro,[status(thm)],[887])).
% 16.06/10.59 tff(889,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')).
% 16.06/10.59 tff(890,plain,
% 16.06/10.59 (![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)))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[889, 888])).
% 16.06/10.59 tff(891,plain,
% 16.06/10.59 (![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)))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[890, 886])).
% 16.06/10.59 tff(892,plain,(
% 16.06/10.59 ![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)))),
% 16.06/10.59 inference(skolemize,[status(sab)],[891])).
% 16.06/10.59 tff(893,plain,
% 16.06/10.59 (![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)))),
% 16.06/10.59 inference(modus_ponens,[status(thm)],[892, 885])).
% 16.06/10.59 tff(894,plain,
% 16.06/10.59 (((~![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)))) | ((~node12(c_e_h_1, c_a, s0, s1)) | (~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))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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_out(c_e_h_1, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(895,plain,
% 16.06/10.59 (((~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))) <=> ((~node12(c_e_h_1, c_a, s0, s1)) | (~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))),
% 16.06/10.59 inference(rewrite,[status(thm)],[])).
% 16.06/10.59 tff(896,plain,
% 16.06/10.59 (((~![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)))) | ((~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)))) | ((~node12(c_e_h_1, c_a, s0, s1)) | (~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)))),
% 16.06/10.59 inference(monotonicity,[status(thm)],[895])).
% 16.06/10.59 tff(897,plain,
% 16.06/10.59 (((~![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)))) | ((~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)))) | (~node12(c_e_h_1, c_a, s0, s1)) | (~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))),
% 16.06/10.60 inference(transitivity,[status(thm)],[896, 894])).
% 16.06/10.60 tff(898,plain,
% 16.06/10.60 ((~![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, 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)))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(899,plain,
% 16.06/10.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[898, 897])).
% 16.06/10.60 tff(900,plain,
% 16.06/10.60 ($false),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[899, 893, 883, 851, 850])).
% 16.06/10.60 tff(901,plain,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.60 tff(902,plain,
% 16.06/10.60 (((~![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))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(903,plain,
% 16.06/10.60 ((~![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))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(904,plain,
% 16.06/10.60 ((~![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)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[903, 902])).
% 16.06/10.60 tff(905,plain,
% 16.06/10.60 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s1)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[904, 639, 901])).
% 16.06/10.60 tff(906,plain,
% 16.06/10.60 (((~![I0: $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))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(907,plain,
% 16.06/10.60 ((~![I0: $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))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(908,plain,
% 16.06/10.60 ((~![I0: $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)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[907, 906])).
% 16.06/10.60 tff(909,plain,
% 16.06/10.60 (~node20(c_e_h_1, c_c, s1)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[908, 283, 905])).
% 16.06/10.60 tff(910,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s2)), introduced(assumption)).
% 16.06/10.60 tff(911,assumption,(node22(c_e_h_1, c_c, s1, s2)), introduced(assumption)).
% 16.06/10.60 tff(912,plain,
% 16.06/10.60 (((~![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_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))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(913,plain,
% 16.06/10.60 ((~![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_c, s2)) | (~node22(c_e_h_1, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(914,plain,
% 16.06/10.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node22(c_e_h_1, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[913, 912])).
% 16.06/10.60 tff(915,plain,
% 16.06/10.60 ($false),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[914, 127, 911, 671, 910])).
% 16.06/10.60 tff(916,plain,((~node22(c_e_h_1, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2))), inference(lemma,lemma(discharge,[]))).
% 16.06/10.60 tff(917,plain,
% 16.06/10.60 (~node22(c_e_h_1, c_c, s1, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[916, 910])).
% 16.06/10.60 tff(918,plain,
% 16.06/10.60 (((~![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))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(919,plain,
% 16.06/10.60 ((~![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))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(920,plain,
% 16.06/10.60 ((~![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)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[919, 918])).
% 16.06/10.60 tff(921,plain,
% 16.06/10.60 (node21(c_e_h_1, c_c, s1, s2) | node22(c_e_h_1, c_c, s1, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[920, 112, 348])).
% 16.06/10.60 tff(922,plain,
% 16.06/10.60 (node21(c_e_h_1, c_c, s1, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[921, 917])).
% 16.06/10.60 tff(923,plain,
% 16.06/10.60 (((~![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_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)))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(924,plain,
% 16.06/10.60 ((~![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_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)))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(925,plain,
% 16.06/10.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node21(c_e_h_1, c_c, s1, s2))),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[924, 923])).
% 16.06/10.60 tff(926,plain,
% 16.06/10.60 ($false),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[925, 82, 922, 910, 909])).
% 16.06/10.60 tff(927,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.60 tff(928,plain,
% 16.06/10.60 (((~![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, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))) <=> ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(929,plain,
% 16.06/10.60 ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(930,plain,
% 16.06/10.60 ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[929, 928])).
% 16.06/10.60 tff(931,plain,
% 16.06/10.60 (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[930, 678, 927])).
% 16.06/10.60 tff(932,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s2)), introduced(assumption)).
% 16.06/10.60 tff(933,assumption,(node14(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 16.06/10.60 tff(934,plain,
% 16.06/10.60 (((~![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_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))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(935,plain,
% 16.06/10.60 (((~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))) <=> ((~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))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(936,plain,
% 16.06/10.60 (((~![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_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)))) | ((~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)))),
% 16.06/10.60 inference(monotonicity,[status(thm)],[935])).
% 16.06/10.60 tff(937,plain,
% 16.06/10.60 (((~![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_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)))) | (~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))),
% 16.06/10.60 inference(transitivity,[status(thm)],[936, 934])).
% 16.06/10.60 tff(938,plain,
% 16.06/10.60 ((~![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_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)))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(939,plain,
% 16.06/10.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[938, 937])).
% 16.06/10.60 tff(940,plain,
% 16.06/10.60 ($false),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[939, 254, 933, 619, 932])).
% 16.06/10.60 tff(941,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,[]))).
% 16.06/10.60 tff(942,plain,
% 16.06/10.60 (~node14(c_e_h_1, c_e, s2, s3)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[941, 619, 931])).
% 16.06/10.60 tff(943,plain,
% 16.06/10.60 (((~![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_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node15(c_e_h_1, c_e, s2, s3) | node14(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)))) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node15(c_e_h_1, c_e, s2, s3) | node14(c_e_h_1, c_e, s2, s3))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(944,plain,
% 16.06/10.60 ((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))) <=> (node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node15(c_e_h_1, c_e, s2, s3) | node14(c_e_h_1, c_e, s2, s3))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(945,plain,
% 16.06/10.60 (((~![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_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)))) | (node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node15(c_e_h_1, c_e, s2, s3) | node14(c_e_h_1, c_e, s2, s3)))),
% 16.06/10.60 inference(monotonicity,[status(thm)],[944])).
% 16.06/10.60 tff(946,plain,
% 16.06/10.60 (((~![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_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)))) | node16(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node15(c_e_h_1, c_e, s2, s3) | node14(c_e_h_1, c_e, s2, s3))),
% 16.06/10.60 inference(transitivity,[status(thm)],[945, 943])).
% 16.06/10.60 tff(947,plain,
% 16.06/10.60 ((~![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_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)))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(948,plain,
% 16.06/10.60 ((~![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_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node15(c_e_h_1, c_e, s2, s3) | node14(c_e_h_1, c_e, s2, s3)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[947, 946])).
% 16.06/10.60 tff(949,plain,
% 16.06/10.60 (node16(c_e_h_1, c_e, s2) | node15(c_e_h_1, c_e, s2, s3) | node14(c_e_h_1, c_e, s2, s3)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[948, 235, 816])).
% 16.06/10.60 tff(950,plain,
% 16.06/10.60 (node16(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[949, 942, 828])).
% 16.06/10.60 tff(951,assumption,(node17(c_e_h_1, c_e, s2)), introduced(assumption)).
% 16.06/10.60 tff(952,assumption,(node16(c_e_h_1, c_e, s2)), introduced(assumption)).
% 16.06/10.60 tff(953,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s2)), introduced(assumption)).
% 16.06/10.60 tff(954,plain,
% 16.06/10.60 (((~![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_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)))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(955,plain,
% 16.06/10.60 (((~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)))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(956,plain,
% 16.06/10.60 (((~![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_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))))),
% 16.06/10.60 inference(monotonicity,[status(thm)],[955])).
% 16.06/10.60 tff(957,plain,
% 16.06/10.60 (((~![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_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)))),
% 16.06/10.60 inference(transitivity,[status(thm)],[956, 954])).
% 16.06/10.60 tff(958,plain,
% 16.06/10.60 ((~![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_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(959,plain,
% 16.06/10.60 ((~![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_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))),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[958, 957])).
% 16.06/10.60 tff(960,plain,
% 16.06/10.60 (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))),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[959, 524, 951])).
% 16.06/10.60 tff(961,plain,
% 16.06/10.60 (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[960, 953])).
% 16.06/10.60 tff(962,plain,
% 16.06/10.60 (((~![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_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))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(963,plain,
% 16.06/10.60 ((~![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_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))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(964,plain,
% 16.06/10.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[963, 962])).
% 16.06/10.60 tff(965,plain,
% 16.06/10.60 (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[964, 209, 952])).
% 16.06/10.60 tff(966,plain,
% 16.06/10.60 ($false),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[965, 961, 953])).
% 16.06/10.60 tff(967,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node16(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 16.06/10.60 tff(968,plain,
% 16.06/10.60 (m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[967, 952, 951])).
% 16.06/10.60 tff(969,plain,
% 16.06/10.60 (((~![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_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_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)))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(970,plain,
% 16.06/10.60 ((~![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_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)))),
% 16.06/10.60 inference(quant_inst,[status(thm)],[])).
% 16.06/10.60 tff(971,plain,
% 16.06/10.60 ((~![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_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2))),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[970, 969])).
% 16.06/10.60 tff(972,plain,
% 16.06/10.60 (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))),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[971, 767, 951])).
% 16.06/10.60 tff(973,plain,
% 16.06/10.60 (m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 16.06/10.60 inference(unit_resolution,[status(thm)],[972, 968])).
% 16.06/10.60 tff(974,plain,
% 16.06/10.60 (^[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))))),
% 16.06/10.60 inference(bind,[status(th)],[])).
% 16.06/10.60 tff(975,plain,
% 16.06/10.60 (![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))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 16.06/10.60 inference(quant_intro,[status(thm)],[974])).
% 16.06/10.60 tff(976,plain,
% 16.06/10.60 (![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))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(977,plain,
% 16.06/10.60 (^[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))))),
% 16.06/10.60 inference(bind,[status(th)],[])).
% 16.06/10.60 tff(978,plain,
% 16.06/10.60 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~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)))),
% 16.06/10.60 inference(quant_intro,[status(thm)],[977])).
% 16.06/10.60 tff(979,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')).
% 16.06/10.60 tff(980,plain,
% 16.06/10.60 (![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)))),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[979, 978])).
% 16.06/10.60 tff(981,plain,
% 16.06/10.60 (![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)))),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[980, 976])).
% 16.06/10.60 tff(982,plain,(
% 16.06/10.60 ![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)))),
% 16.06/10.60 inference(skolemize,[status(sab)],[981])).
% 16.06/10.60 tff(983,plain,
% 16.06/10.60 (![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)))),
% 16.06/10.60 inference(modus_ponens,[status(thm)],[982, 975])).
% 16.06/10.60 tff(984,plain,
% 16.06/10.60 (((~![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)))) | ((~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)) | (~node16(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)))) | (~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)) | (~node16(c_e_h_1, c_e, s2)))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(985,plain,
% 16.06/10.60 (((~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))) <=> ((~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)) | (~node16(c_e_h_1, c_e, s2)))),
% 16.06/10.60 inference(rewrite,[status(thm)],[])).
% 16.06/10.60 tff(986,plain,
% 16.06/10.60 (((~![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_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)))) | ((~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)) | (~node16(c_e_h_1, c_e, s2))))),
% 16.06/10.61 inference(monotonicity,[status(thm)],[985])).
% 16.06/10.61 tff(987,plain,
% 16.06/10.61 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~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)))) | (~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)) | (~node16(c_e_h_1, c_e, s2)))),
% 16.06/10.61 inference(transitivity,[status(thm)],[986, 984])).
% 16.06/10.61 tff(988,plain,
% 16.06/10.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~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)))),
% 16.06/10.61 inference(quant_inst,[status(thm)],[])).
% 16.06/10.61 tff(989,plain,
% 16.06/10.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~node16(c_e_h_1, c_e, s2))),
% 16.06/10.61 inference(modus_ponens,[status(thm)],[988, 987])).
% 16.06/10.61 tff(990,plain,
% 16.06/10.61 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[989, 983, 952])).
% 16.06/10.61 tff(991,plain,
% 16.06/10.61 ($false),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[990, 973, 968])).
% 16.06/10.61 tff(992,plain,((~node16(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 16.06/10.61 tff(993,plain,
% 16.06/10.61 ($false),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[992, 950, 821])).
% 16.06/10.61 tff(994,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 16.06/10.61 tff(995,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 16.06/10.61 tff(996,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 16.06/10.61 tff(997,assumption,(node18(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 16.06/10.61 tff(998,plain,
% 16.06/10.61 (((~![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_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~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)) | m_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) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(999,plain,
% 16.06/10.61 (((~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))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1000,plain,
% 16.06/10.61 (((~![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_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, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))))),
% 16.06/10.61 inference(monotonicity,[status(thm)],[999])).
% 16.06/10.61 tff(1001,plain,
% 16.06/10.61 (((~![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_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, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 16.06/10.61 inference(transitivity,[status(thm)],[1000, 998])).
% 16.06/10.61 tff(1002,plain,
% 16.06/10.61 ((~![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_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))),
% 16.06/10.61 inference(quant_inst,[status(thm)],[])).
% 16.06/10.61 tff(1003,plain,
% 16.06/10.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 16.06/10.61 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 16.06/10.61 tff(1004,plain,
% 16.06/10.61 ($false),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1003, 560, 995, 997, 996])).
% 16.06/10.61 tff(1005,plain,((~node18(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,[]))).
% 16.06/10.61 tff(1006,plain,
% 16.06/10.61 (~node18(c_e_h_1, c_e, s3, s4)),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1005, 995, 996])).
% 16.06/10.61 tff(1007,plain,
% 16.06/10.61 (succ(s3, s4) <=> succ(s3, s4)),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1008,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 16.06/10.61 tff(1009,plain,
% 16.06/10.61 (succ(s3, s4)),
% 16.06/10.61 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 16.06/10.61 tff(1010,plain,
% 16.06/10.61 (((~![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))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1011,plain,
% 16.06/10.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 16.06/10.61 inference(quant_inst,[status(thm)],[])).
% 16.06/10.61 tff(1012,plain,
% 16.06/10.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 16.06/10.61 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 16.06/10.61 tff(1013,plain,
% 16.06/10.61 (trans(s3, s4)),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1012, 1009, 95])).
% 16.06/10.61 tff(1014,plain,
% 16.06/10.61 (((~![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))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1015,plain,
% 16.06/10.61 ((~![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))),
% 16.06/10.61 inference(quant_inst,[status(thm)],[])).
% 16.06/10.61 tff(1016,plain,
% 16.06/10.61 ((~![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)),
% 16.06/10.61 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 16.06/10.61 tff(1017,plain,
% 16.06/10.61 (node19(c_e_h_1, c_e, s3, s4)),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1016, 221, 1013])).
% 16.06/10.61 tff(1018,plain,
% 16.06/10.61 (((~![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, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(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)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1019,plain,
% 16.06/10.61 ((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))) <=> ((~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1020,plain,
% 16.06/10.61 (((~![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_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)))) | ((~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)))),
% 16.06/10.61 inference(monotonicity,[status(thm)],[1019])).
% 16.06/10.61 tff(1021,plain,
% 16.06/10.61 (((~![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_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)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4))),
% 16.06/10.61 inference(transitivity,[status(thm)],[1020, 1018])).
% 16.06/10.61 tff(1022,plain,
% 16.06/10.61 ((~![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_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 16.06/10.61 inference(quant_inst,[status(thm)],[])).
% 16.06/10.61 tff(1023,plain,
% 16.06/10.61 ((~![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, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)),
% 16.06/10.61 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 16.06/10.61 tff(1024,plain,
% 16.06/10.61 (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1023, 542, 1017])).
% 16.06/10.61 tff(1025,plain,
% 16.06/10.61 (node17(c_e_h_1, c_e, s3)),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1024, 1006])).
% 16.06/10.61 tff(1026,assumption,(node15(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 16.06/10.61 tff(1027,plain,
% 16.06/10.61 (((~![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_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))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1028,plain,
% 16.06/10.61 ((~![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_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 16.06/10.61 inference(quant_inst,[status(thm)],[])).
% 16.06/10.61 tff(1029,plain,
% 16.06/10.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 16.06/10.61 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 16.06/10.61 tff(1030,plain,
% 16.06/10.61 ($false),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1029, 178, 995, 1026, 996])).
% 16.06/10.61 tff(1031,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,[]))).
% 16.06/10.61 tff(1032,plain,
% 16.06/10.61 (~node15(c_e_h_1, c_e, s3, s4)),
% 16.06/10.61 inference(unit_resolution,[status(thm)],[1031, 995, 996])).
% 16.06/10.61 tff(1033,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s3)), introduced(assumption)).
% 16.06/10.61 tff(1034,assumption,(node14(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 16.06/10.61 tff(1035,plain,
% 16.06/10.61 (((~![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_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)))) | (~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)))),
% 16.06/10.61 inference(rewrite,[status(thm)],[])).
% 16.06/10.61 tff(1036,plain,
% 16.06/10.61 ((~![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_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)))),
% 16.15/10.61 inference(quant_inst,[status(thm)],[])).
% 16.15/10.61 tff(1037,plain,
% 16.15/10.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 16.15/10.61 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 16.15/10.61 tff(1038,plain,
% 16.15/10.61 ($false),
% 16.15/10.61 inference(unit_resolution,[status(thm)],[1037, 254, 995, 1034, 1033])).
% 16.15/10.61 tff(1039,plain,((~node14(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_in1(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.61 tff(1040,plain,
% 16.15/10.61 (~node14(c_e_h_1, c_e, s3, s4)),
% 16.15/10.61 inference(unit_resolution,[status(thm)],[1039, 995, 1033])).
% 16.15/10.61 tff(1041,plain,
% 16.15/10.61 (((~![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_e, s3, s4)) | 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))) <=> ((~![Y: $i, I0: $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, s3, s4)) | 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))),
% 16.15/10.61 inference(rewrite,[status(thm)],[])).
% 16.15/10.61 tff(1042,plain,
% 16.15/10.61 ((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))) <=> ((~node19(c_e_h_1, c_e, s3, s4)) | 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))),
% 16.15/10.61 inference(rewrite,[status(thm)],[])).
% 16.15/10.61 tff(1043,plain,
% 16.15/10.61 (((~![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)))) | (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)))) | ((~node19(c_e_h_1, c_e, s3, s4)) | 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)))),
% 16.15/10.61 inference(monotonicity,[status(thm)],[1042])).
% 16.15/10.61 tff(1044,plain,
% 16.15/10.61 (((~![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)))) | (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)))) | (~node19(c_e_h_1, c_e, s3, s4)) | 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))),
% 16.15/10.61 inference(transitivity,[status(thm)],[1043, 1041])).
% 16.15/10.61 tff(1045,plain,
% 16.15/10.61 ((~![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)))) | (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)))),
% 16.15/10.61 inference(quant_inst,[status(thm)],[])).
% 16.15/10.61 tff(1046,plain,
% 16.15/10.61 ((~![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_e, s3, s4)) | 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)),
% 16.15/10.61 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 16.15/10.61 tff(1047,plain,
% 16.15/10.61 (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)),
% 16.15/10.61 inference(unit_resolution,[status(thm)],[1046, 235, 1017])).
% 16.15/10.61 tff(1048,plain,
% 16.15/10.61 (node16(c_e_h_1, c_e, s3)),
% 16.15/10.61 inference(unit_resolution,[status(thm)],[1047, 1040, 1032])).
% 16.15/10.61 tff(1049,assumption,(node17(c_e_h_1, c_e, s3)), introduced(assumption)).
% 16.15/10.61 tff(1050,assumption,(node16(c_e_h_1, c_e, s3)), introduced(assumption)).
% 16.15/10.61 tff(1051,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s3)), introduced(assumption)).
% 16.15/10.61 tff(1052,plain,
% 16.15/10.61 (((~![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_e, s3)) | m_c_h_element_v_in2(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)))) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 16.15/10.61 inference(rewrite,[status(thm)],[])).
% 16.15/10.61 tff(1053,plain,
% 16.15/10.61 (((~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))) <=> ((~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 16.15/10.61 inference(rewrite,[status(thm)],[])).
% 16.15/10.61 tff(1054,plain,
% 16.15/10.61 (((~![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_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)))) | ((~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))))),
% 16.15/10.61 inference(monotonicity,[status(thm)],[1053])).
% 16.15/10.61 tff(1055,plain,
% 16.15/10.61 (((~![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_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)))) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 16.15/10.61 inference(transitivity,[status(thm)],[1054, 1052])).
% 16.15/10.61 tff(1056,plain,
% 16.15/10.61 ((~![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_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)))),
% 16.15/10.61 inference(quant_inst,[status(thm)],[])).
% 16.15/10.61 tff(1057,plain,
% 16.15/10.61 ((~![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_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 16.15/10.61 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 16.15/10.61 tff(1058,plain,
% 16.15/10.61 (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 16.15/10.61 inference(unit_resolution,[status(thm)],[1057, 524, 1049])).
% 16.15/10.61 tff(1059,plain,
% 16.15/10.61 (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 16.15/10.61 inference(unit_resolution,[status(thm)],[1058, 1051])).
% 16.15/10.61 tff(1060,plain,
% 16.15/10.61 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | 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))),
% 16.15/10.61 inference(rewrite,[status(thm)],[])).
% 16.15/10.61 tff(1061,plain,
% 16.15/10.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | 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))),
% 16.15/10.61 inference(quant_inst,[status(thm)],[])).
% 16.15/10.61 tff(1062,plain,
% 16.15/10.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 16.15/10.61 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 16.15/10.61 tff(1063,plain,
% 16.15/10.61 (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 16.15/10.61 inference(unit_resolution,[status(thm)],[1062, 209, 1050])).
% 16.15/10.62 tff(1064,plain,
% 16.15/10.62 ($false),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1063, 1059, 1051])).
% 16.15/10.62 tff(1065,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node16(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.62 tff(1066,plain,
% 16.15/10.62 (m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1065, 1050, 1049])).
% 16.15/10.62 tff(1067,plain,
% 16.15/10.62 (((~![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_e, s3)) | (~m_c_h_element_v_in2(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)))) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1068,plain,
% 16.15/10.62 ((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))) <=> ((~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1069,plain,
% 16.15/10.62 (((~![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_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)))) | ((~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 16.15/10.62 inference(monotonicity,[status(thm)],[1068])).
% 16.15/10.62 tff(1070,plain,
% 16.15/10.62 (((~![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_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)))) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 16.15/10.62 inference(transitivity,[status(thm)],[1069, 1067])).
% 16.15/10.62 tff(1071,plain,
% 16.15/10.62 ((~![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_e, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1072,plain,
% 16.15/10.62 ((~![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_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 16.15/10.62 tff(1073,plain,
% 16.15/10.62 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1072, 767, 1049])).
% 16.15/10.62 tff(1074,plain,
% 16.15/10.62 (m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1073, 1066])).
% 16.15/10.62 tff(1075,plain,
% 16.15/10.62 (((~![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)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(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)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3)))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1076,plain,
% 16.15/10.62 (((~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))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3)))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1077,plain,
% 16.15/10.62 (((~![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_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)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3))))),
% 16.15/10.62 inference(monotonicity,[status(thm)],[1076])).
% 16.15/10.62 tff(1078,plain,
% 16.15/10.62 (((~![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_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)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3)))),
% 16.15/10.62 inference(transitivity,[status(thm)],[1077, 1075])).
% 16.15/10.62 tff(1079,plain,
% 16.15/10.62 ((~![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_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)))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1080,plain,
% 16.15/10.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 16.15/10.62 tff(1081,plain,
% 16.15/10.62 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1080, 983, 1050])).
% 16.15/10.62 tff(1082,plain,
% 16.15/10.62 ($false),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1081, 1074, 1066])).
% 16.15/10.62 tff(1083,plain,((~node16(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.62 tff(1084,plain,
% 16.15/10.62 ($false),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1083, 1048, 1025])).
% 16.15/10.62 tff(1085,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.62 tff(1086,plain,
% 16.15/10.62 (m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1085, 995, 994])).
% 16.15/10.62 tff(1087,plain,
% 16.15/10.62 (~node18(c_e_h_1, c_e, s3, s4)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1005, 995, 994])).
% 16.15/10.62 tff(1088,plain,
% 16.15/10.62 (node17(c_e_h_1, c_e, s3)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1024, 1087])).
% 16.15/10.62 tff(1089,plain,
% 16.15/10.62 ((~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1057, 524, 1051])).
% 16.15/10.62 tff(1090,plain,
% 16.15/10.62 ($false),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1089, 1088, 1086])).
% 16.15/10.62 tff(1091,plain,((~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,[]))).
% 16.15/10.62 tff(1092,plain,
% 16.15/10.62 (~m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1091, 618])).
% 16.15/10.62 tff(1093,plain,
% 16.15/10.62 (^[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)))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1094,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1093])).
% 16.15/10.62 tff(1095,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1096,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')).
% 16.15/10.62 tff(1097,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 16.15/10.62 tff(1098,plain,(
% 16.15/10.62 ![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))),
% 16.15/10.62 inference(skolemize,[status(sab)],[1097])).
% 16.15/10.62 tff(1099,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1098, 1094])).
% 16.15/10.62 tff(1100,plain,
% 16.15/10.62 (((~![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1101,plain,
% 16.15/10.62 ((~![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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1102,plain,
% 16.15/10.62 ((~![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)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 16.15/10.62 tff(1103,plain,
% 16.15/10.62 (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)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1102, 1099])).
% 16.15/10.62 tff(1104,plain,
% 16.15/10.62 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1103, 1092])).
% 16.15/10.62 tff(1105,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)), introduced(assumption)).
% 16.15/10.62 tff(1106,plain,
% 16.15/10.62 (((~![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1107,plain,
% 16.15/10.62 ((~![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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1108,plain,
% 16.15/10.62 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 16.15/10.62 tff(1109,plain,
% 16.15/10.62 ($false),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1108, 1099, 996, 1105])).
% 16.15/10.62 tff(1110,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,[]))).
% 16.15/10.62 tff(1111,plain,
% 16.15/10.62 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1110, 994])).
% 16.15/10.62 tff(1112,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 16.15/10.62 tff(1113,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 16.15/10.62 tff(1114,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), introduced(assumption)).
% 16.15/10.62 tff(1115,plain,
% 16.15/10.62 (((~![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1116,plain,
% 16.15/10.62 ((~![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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1117,plain,
% 16.15/10.62 ((~![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)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 16.15/10.62 tff(1118,plain,
% 16.15/10.62 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1117, 1099, 691])).
% 16.15/10.62 tff(1119,assumption,(node10(c_e_h_1, c_n, s0, s1)), introduced(assumption)).
% 16.15/10.62 tff(1120,assumption,(m_cell_v_token(c_e_h_1, s0)), introduced(assumption)).
% 16.15/10.62 tff(1121,plain,
% 16.15/10.62 (^[X: $i] : refl((~m_cell_v_token(c_e_h_1, X)) <=> (~m_cell_v_token(c_e_h_1, X)))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1122,plain,
% 16.15/10.62 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1121])).
% 16.15/10.62 tff(1123,plain,
% 16.15/10.62 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1124,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_1, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_3')).
% 16.15/10.62 tff(1125,plain,
% 16.15/10.62 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 16.15/10.62 tff(1126,plain,(
% 16.15/10.62 ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 16.15/10.62 inference(skolemize,[status(sab)],[1125])).
% 16.15/10.62 tff(1127,plain,
% 16.15/10.62 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1126, 1122])).
% 16.15/10.62 tff(1128,plain,
% 16.15/10.62 ((~![X: $i] : (~m_cell_v_token(c_e_h_1, X))) | (~m_cell_v_token(c_e_h_1, s0))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1129,plain,
% 16.15/10.62 ($false),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1128, 1127, 1120])).
% 16.15/10.62 tff(1130,plain,(~m_cell_v_token(c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.62 tff(1131,plain,
% 16.15/10.62 (((~![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1132,plain,
% 16.15/10.62 ((~![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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1133,plain,
% 16.15/10.62 ((~![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)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 16.15/10.62 tff(1134,plain,
% 16.15/10.62 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1133, 31, 1130])).
% 16.15/10.62 tff(1135,plain,
% 16.15/10.62 (((~![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1136,plain,
% 16.15/10.62 ((~![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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1137,plain,
% 16.15/10.62 ((~![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)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 16.15/10.62 tff(1138,plain,
% 16.15/10.62 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1137, 42, 1134])).
% 16.15/10.62 tff(1139,plain,
% 16.15/10.62 (^[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)))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1140,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1139])).
% 16.15/10.62 tff(1141,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1142,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')).
% 16.15/10.62 tff(1143,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 16.15/10.62 tff(1144,plain,(
% 16.15/10.62 ![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))),
% 16.15/10.62 inference(skolemize,[status(sab)],[1143])).
% 16.15/10.62 tff(1145,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1144, 1140])).
% 16.15/10.62 tff(1146,plain,
% 16.15/10.62 (((~![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1147,plain,
% 16.15/10.62 ((~![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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1148,plain,
% 16.15/10.62 ((~![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)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 16.15/10.62 tff(1149,plain,
% 16.15/10.62 (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)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1148, 1145])).
% 16.15/10.62 tff(1150,plain,
% 16.15/10.62 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1149, 1138])).
% 16.15/10.62 tff(1151,plain,
% 16.15/10.62 (^[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)))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1152,plain,
% 16.15/10.62 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1151])).
% 16.15/10.62 tff(1153,plain,
% 16.15/10.62 (![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)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1154,plain,
% 16.15/10.62 (^[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))))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1155,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1154])).
% 16.15/10.62 tff(1156,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')).
% 16.15/10.62 tff(1157,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 16.15/10.62 tff(1158,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1157, 1153])).
% 16.15/10.62 tff(1159,plain,(
% 16.15/10.62 ![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))),
% 16.15/10.62 inference(skolemize,[status(sab)],[1158])).
% 16.15/10.62 tff(1160,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1159, 1152])).
% 16.15/10.62 tff(1161,plain,
% 16.15/10.62 (((~![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_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(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_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1162,plain,
% 16.15/10.62 (((~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_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1163,plain,
% 16.15/10.62 (((~![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_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_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1))))),
% 16.15/10.62 inference(monotonicity,[status(thm)],[1162])).
% 16.15/10.62 tff(1164,plain,
% 16.15/10.62 (((~![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_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_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 16.15/10.62 inference(transitivity,[status(thm)],[1163, 1161])).
% 16.15/10.62 tff(1165,plain,
% 16.15/10.62 ((~![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_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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1166,plain,
% 16.15/10.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 16.15/10.62 tff(1167,plain,
% 16.15/10.62 ($false),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1166, 1160, 1150, 1119, 1118, 1114])).
% 16.15/10.62 tff(1168,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,[]))).
% 16.15/10.62 tff(1169,plain,
% 16.15/10.62 (~node10(c_e_h_1, c_n, s0, s1)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1168, 1114])).
% 16.15/10.62 tff(1170,plain,
% 16.15/10.62 (^[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)))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1171,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1170])).
% 16.15/10.62 tff(1172,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1173,plain,
% 16.15/10.62 (^[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)))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1174,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1173])).
% 16.15/10.62 tff(1175,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')).
% 16.15/10.62 tff(1176,plain,
% 16.15/10.62 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 16.15/10.62 tff(1177,plain,
% 16.15/10.62 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1176, 1172])).
% 16.15/10.62 tff(1178,plain,(
% 16.15/10.62 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 16.15/10.62 inference(skolemize,[status(sab)],[1177])).
% 16.15/10.62 tff(1179,plain,
% 16.15/10.62 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1178, 1171])).
% 16.15/10.62 tff(1180,plain,
% 16.15/10.62 (((~![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1181,plain,
% 16.15/10.62 ((~![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))),
% 16.15/10.62 inference(quant_inst,[status(thm)],[])).
% 16.15/10.62 tff(1182,plain,
% 16.15/10.62 ((~![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)),
% 16.15/10.62 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 16.15/10.62 tff(1183,plain,
% 16.15/10.62 (node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1182, 1179, 102])).
% 16.15/10.62 tff(1184,plain,
% 16.15/10.62 (node11(c_e_h_1, c_n, s0, s1)),
% 16.15/10.62 inference(unit_resolution,[status(thm)],[1183, 1169])).
% 16.15/10.62 tff(1185,plain,
% 16.15/10.62 (^[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)))),
% 16.15/10.62 inference(bind,[status(th)],[])).
% 16.15/10.62 tff(1186,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(quant_intro,[status(thm)],[1185])).
% 16.15/10.62 tff(1187,plain,
% 16.15/10.62 (![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))),
% 16.15/10.62 inference(rewrite,[status(thm)],[])).
% 16.15/10.62 tff(1188,plain,
% 16.15/10.62 (^[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)))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1189,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1188])).
% 16.15/10.63 tff(1190,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')).
% 16.15/10.63 tff(1191,plain,
% 16.15/10.63 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 16.15/10.63 tff(1192,plain,
% 16.15/10.63 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1191, 1187])).
% 16.15/10.63 tff(1193,plain,(
% 16.15/10.63 ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 16.15/10.63 inference(skolemize,[status(sab)],[1192])).
% 16.15/10.63 tff(1194,plain,
% 16.15/10.63 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1193, 1186])).
% 16.15/10.63 tff(1195,plain,
% 16.15/10.63 (((~![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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1196,plain,
% 16.15/10.63 ((~![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))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1197,plain,
% 16.15/10.63 ((~![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)),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 16.15/10.63 tff(1198,plain,
% 16.15/10.63 (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)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1197, 1194])).
% 16.15/10.63 tff(1199,plain,
% 16.15/10.63 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1198, 1130])).
% 16.15/10.63 tff(1200,plain,
% 16.15/10.63 (^[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)))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1201,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1200])).
% 16.15/10.63 tff(1202,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1203,plain,
% 16.15/10.63 (^[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)))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1204,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1203])).
% 16.15/10.63 tff(1205,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')).
% 16.15/10.63 tff(1206,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 16.15/10.63 tff(1207,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1206, 1202])).
% 16.15/10.63 tff(1208,plain,(
% 16.15/10.63 ![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))),
% 16.15/10.63 inference(skolemize,[status(sab)],[1207])).
% 16.15/10.63 tff(1209,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1208, 1201])).
% 16.15/10.63 tff(1210,plain,
% 16.15/10.63 (((~![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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1211,plain,
% 16.15/10.63 ((~![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))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1212,plain,
% 16.15/10.63 ((~![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)),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 16.15/10.63 tff(1213,plain,
% 16.15/10.63 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1212, 1209, 1199])).
% 16.15/10.63 tff(1214,plain,
% 16.15/10.63 (^[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))))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1215,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1214])).
% 16.15/10.63 tff(1216,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1217,plain,
% 16.15/10.63 (^[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)))))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1218,plain,
% 16.15/10.63 (![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)))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1217])).
% 16.15/10.63 tff(1219,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')).
% 16.15/10.63 tff(1220,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 16.15/10.63 tff(1221,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1220, 1216])).
% 16.15/10.63 tff(1222,plain,(
% 16.15/10.63 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 16.15/10.63 inference(skolemize,[status(sab)],[1221])).
% 16.15/10.63 tff(1223,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1222, 1215])).
% 16.15/10.63 tff(1224,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1225,plain,
% 16.15/10.63 ((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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1226,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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))))),
% 16.15/10.63 inference(monotonicity,[status(thm)],[1225])).
% 16.15/10.63 tff(1227,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.63 inference(transitivity,[status(thm)],[1226, 1224])).
% 16.15/10.63 tff(1228,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1229,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 16.15/10.63 tff(1230,plain,
% 16.15/10.63 ($false),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1229, 1223, 1213, 1184, 1114])).
% 16.15/10.63 tff(1231,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.63 tff(1232,assumption,(node11(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 16.15/10.63 tff(1233,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1234,plain,
% 16.15/10.63 ((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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1235,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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))))),
% 16.15/10.63 inference(monotonicity,[status(thm)],[1234])).
% 16.15/10.63 tff(1236,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.63 inference(transitivity,[status(thm)],[1235, 1233])).
% 16.15/10.63 tff(1237,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1238,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 16.15/10.63 tff(1239,plain,
% 16.15/10.63 ($false),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1238, 1223, 1113, 1232, 1231])).
% 16.15/10.63 tff(1240,plain,((~node11(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,[]))).
% 16.15/10.63 tff(1241,plain,
% 16.15/10.63 (~node11(c_e_h_1, c_n, s1, s2)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1240, 1113])).
% 16.15/10.63 tff(1242,plain,
% 16.15/10.63 (((~![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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1243,plain,
% 16.15/10.63 ((~![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))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1244,plain,
% 16.15/10.63 ((~![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)),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 16.15/10.63 tff(1245,plain,
% 16.15/10.63 (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)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1244, 1099])).
% 16.15/10.63 tff(1246,plain,
% 16.15/10.63 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1245, 736])).
% 16.15/10.63 tff(1247,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), introduced(assumption)).
% 16.15/10.63 tff(1248,assumption,(node11(c_e_h_1, c_m, s0, s1)), introduced(assumption)).
% 16.15/10.63 tff(1249,plain,
% 16.15/10.63 (^[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)))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1250,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_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))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1249])).
% 16.15/10.63 tff(1251,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1252,plain,
% 16.15/10.63 (^[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)))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1253,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1252])).
% 16.15/10.63 tff(1254,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')).
% 16.15/10.63 tff(1255,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 16.15/10.63 tff(1256,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1255, 1251])).
% 16.15/10.63 tff(1257,plain,(
% 16.15/10.63 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 16.15/10.63 inference(skolemize,[status(sab)],[1256])).
% 16.15/10.63 tff(1258,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1257, 1250])).
% 16.15/10.63 tff(1259,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1260,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1261,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 16.15/10.63 tff(1262,plain,
% 16.15/10.63 ($false),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1261, 1258, 1138, 1248, 1247])).
% 16.15/10.63 tff(1263,plain,((~node11(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,[]))).
% 16.15/10.63 tff(1264,plain,
% 16.15/10.63 (~node11(c_e_h_1, c_m, s0, s1)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1263, 1247])).
% 16.15/10.63 tff(1265,plain,
% 16.15/10.63 (((~![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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1266,plain,
% 16.15/10.63 ((~![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))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1267,plain,
% 16.15/10.63 ((~![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)),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 16.15/10.63 tff(1268,plain,
% 16.15/10.63 (node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1267, 1179, 102])).
% 16.15/10.63 tff(1269,plain,
% 16.15/10.63 (node10(c_e_h_1, c_m, s0, s1)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1268, 1264])).
% 16.15/10.63 tff(1270,plain,
% 16.15/10.63 (^[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))))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1271,plain,
% 16.15/10.63 (![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)))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1270])).
% 16.15/10.63 tff(1272,plain,
% 16.15/10.63 (![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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1273,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')).
% 16.15/10.63 tff(1274,plain,
% 16.15/10.63 (![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)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 16.15/10.63 tff(1275,plain,(
% 16.15/10.63 ![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)))),
% 16.15/10.63 inference(skolemize,[status(sab)],[1274])).
% 16.15/10.63 tff(1276,plain,
% 16.15/10.63 (![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)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1275, 1271])).
% 16.15/10.63 tff(1277,plain,
% 16.15/10.63 (((~![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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1278,plain,
% 16.15/10.63 ((~![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)))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1279,plain,
% 16.15/10.63 ((~![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))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 16.15/10.63 tff(1280,plain,
% 16.15/10.63 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1279, 1276, 1213])).
% 16.15/10.63 tff(1281,plain,
% 16.15/10.63 (^[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)))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1282,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1281])).
% 16.15/10.63 tff(1283,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1284,plain,
% 16.15/10.63 (^[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)))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1285,plain,
% 16.15/10.63 (![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))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1284])).
% 16.15/10.63 tff(1286,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')).
% 16.15/10.63 tff(1287,plain,
% 16.15/10.63 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 16.15/10.63 tff(1288,plain,
% 16.15/10.63 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1287, 1283])).
% 16.15/10.63 tff(1289,plain,(
% 16.15/10.63 ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 16.15/10.63 inference(skolemize,[status(sab)],[1288])).
% 16.15/10.63 tff(1290,plain,
% 16.15/10.63 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1289, 1282])).
% 16.15/10.63 tff(1291,plain,
% 16.15/10.63 (((~![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))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1292,plain,
% 16.15/10.63 ((~![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))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1293,plain,
% 16.15/10.63 ((~![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)),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 16.15/10.63 tff(1294,plain,
% 16.15/10.63 (~node9(c_e_h_1, c_m, s0)),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1293, 1290, 1280])).
% 16.15/10.63 tff(1295,plain,
% 16.15/10.63 (^[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))))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1296,plain,
% 16.15/10.63 (![Y: $i, I0: $i, 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)))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1295])).
% 16.15/10.63 tff(1297,plain,
% 16.15/10.63 (![Y: $i, I0: $i, 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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1298,plain,
% 16.15/10.63 (^[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))))),
% 16.15/10.63 inference(bind,[status(th)],[])).
% 16.15/10.63 tff(1299,plain,
% 16.15/10.63 (![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)))),
% 16.15/10.63 inference(quant_intro,[status(thm)],[1298])).
% 16.15/10.63 tff(1300,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')).
% 16.15/10.63 tff(1301,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 16.15/10.63 tff(1302,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1301, 1297])).
% 16.15/10.63 tff(1303,plain,(
% 16.15/10.63 ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 16.15/10.63 inference(skolemize,[status(sab)],[1302])).
% 16.15/10.63 tff(1304,plain,
% 16.15/10.63 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1303, 1296])).
% 16.15/10.63 tff(1305,plain,
% 16.15/10.63 (((~![Y: $i, I0: $i, 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)))),
% 16.15/10.63 inference(rewrite,[status(thm)],[])).
% 16.15/10.63 tff(1306,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, 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)))),
% 16.15/10.63 inference(quant_inst,[status(thm)],[])).
% 16.15/10.63 tff(1307,plain,
% 16.15/10.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1))),
% 16.15/10.63 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 16.15/10.63 tff(1308,plain,
% 16.15/10.63 ($false),
% 16.15/10.63 inference(unit_resolution,[status(thm)],[1307, 1304, 1294, 1269, 1247])).
% 16.15/10.64 tff(1309,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.64 tff(1310,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1311,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1312,plain,
% 16.15/10.64 ((~![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)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 16.15/10.64 tff(1313,plain,
% 16.15/10.64 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1312, 1145, 1309])).
% 16.15/10.64 tff(1314,assumption,(node10(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 16.15/10.64 tff(1315,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)), introduced(assumption)).
% 16.15/10.64 tff(1316,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~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_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1317,plain,
% 16.15/10.64 (((~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_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1318,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))))),
% 16.15/10.64 inference(monotonicity,[status(thm)],[1317])).
% 16.15/10.64 tff(1319,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 16.15/10.64 inference(transitivity,[status(thm)],[1318, 1316])).
% 16.15/10.64 tff(1320,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1321,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 16.15/10.64 tff(1322,plain,
% 16.15/10.64 ($false),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1321, 1160, 1113, 1315, 1314, 1313])).
% 16.15/10.64 tff(1323,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) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.64 tff(1324,plain,
% 16.15/10.64 ((~node10(c_e_h_1, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1323, 1246])).
% 16.15/10.64 tff(1325,plain,
% 16.15/10.64 (~node10(c_e_h_1, c_n, s1, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1324, 1113])).
% 16.15/10.64 tff(1326,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1327,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1328,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 16.15/10.64 tff(1329,plain,
% 16.15/10.64 (node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1328, 1179, 348])).
% 16.15/10.64 tff(1330,plain,
% 16.15/10.64 ($false),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1329, 1325, 1241])).
% 16.15/10.64 tff(1331,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.64 tff(1332,plain,
% 16.15/10.64 (((~![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)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1333,plain,
% 16.15/10.64 ((~![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)))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1334,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 16.15/10.64 tff(1335,plain,
% 16.15/10.64 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1334, 1276, 1331])).
% 16.15/10.64 tff(1336,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1337,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1338,plain,
% 16.15/10.64 ((~![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)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 16.15/10.64 tff(1339,plain,
% 16.15/10.64 (~node9(c_e_h_1, c_m, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1338, 1290, 1335])).
% 16.15/10.64 tff(1340,assumption,(node10(c_e_h_1, c_m, s2, s3)), introduced(assumption)).
% 16.15/10.64 tff(1341,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, 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) | (~node10(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, 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)))) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1342,plain,
% 16.15/10.64 ((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))) <=> (node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1343,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, 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)))) | (node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))))),
% 16.15/10.64 inference(monotonicity,[status(thm)],[1342])).
% 16.15/10.64 tff(1344,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, 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)))) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)))),
% 16.15/10.64 inference(transitivity,[status(thm)],[1343, 1341])).
% 16.15/10.64 tff(1345,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, 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)))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1346,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 16.15/10.64 tff(1347,plain,
% 16.15/10.64 ($false),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1346, 1304, 1340, 1339, 1112])).
% 16.15/10.64 tff(1348,plain,((~node10(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,[]))).
% 16.15/10.64 tff(1349,plain,
% 16.15/10.64 (~node10(c_e_h_1, c_m, s2, s3)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1348, 1112])).
% 16.15/10.64 tff(1350,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1351,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1352,plain,
% 16.15/10.64 ((~![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)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 16.15/10.64 tff(1353,plain,
% 16.15/10.64 (node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1352, 1179, 591])).
% 16.15/10.64 tff(1354,plain,
% 16.15/10.64 (node11(c_e_h_1, c_m, s2, s3)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1353, 1349])).
% 16.15/10.64 tff(1355,plain,
% 16.15/10.64 (((~![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)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1356,plain,
% 16.15/10.64 ((~![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)))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1357,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 16.15/10.64 tff(1358,plain,
% 16.15/10.64 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1357, 1276, 1231])).
% 16.15/10.64 tff(1359,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1360,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1361,plain,
% 16.15/10.64 ((~![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)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 16.15/10.64 tff(1362,plain,
% 16.15/10.64 (~node9(c_e_h_1, c_m, s1)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1361, 1290, 1358])).
% 16.15/10.64 tff(1363,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), introduced(assumption)).
% 16.15/10.64 tff(1364,assumption,(node11(c_e_h_1, c_m, s1, s2)), introduced(assumption)).
% 16.15/10.64 tff(1365,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1366,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1367,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 16.15/10.64 tff(1368,plain,
% 16.15/10.64 ($false),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1367, 1258, 1363, 1364, 1309])).
% 16.15/10.64 tff(1369,plain,((~node11(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,[]))).
% 16.15/10.64 tff(1370,plain,
% 16.15/10.64 (~node11(c_e_h_1, c_m, s1, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1369, 1363])).
% 16.15/10.64 tff(1371,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1372,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1373,plain,
% 16.15/10.64 ((~![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)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 16.15/10.64 tff(1374,plain,
% 16.15/10.64 (node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1373, 1179, 348])).
% 16.15/10.64 tff(1375,plain,
% 16.15/10.64 (node10(c_e_h_1, c_m, s1, s2)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1374, 1370])).
% 16.15/10.64 tff(1376,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, 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, s2)) | node9(c_e_h_1, c_m, s1) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1377,plain,
% 16.15/10.64 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1378,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2))))),
% 16.15/10.64 inference(monotonicity,[status(thm)],[1377])).
% 16.15/10.64 tff(1379,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 16.15/10.64 inference(transitivity,[status(thm)],[1378, 1376])).
% 16.15/10.64 tff(1380,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, 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)))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1381,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1) | (~node10(c_e_h_1, c_m, s1, s2))),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 16.15/10.64 tff(1382,plain,
% 16.15/10.64 ($false),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1381, 1304, 1363, 1375, 1362])).
% 16.15/10.64 tff(1383,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.64 tff(1384,plain,
% 16.15/10.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1385,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1386,plain,
% 16.15/10.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 16.15/10.64 tff(1387,plain,
% 16.15/10.64 ($false),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1386, 1258, 1383, 1354, 1112])).
% 16.15/10.64 tff(1388,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.64 tff(1389,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.64 inference(rewrite,[status(thm)],[])).
% 16.15/10.64 tff(1390,plain,
% 16.15/10.64 ((~![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))),
% 16.15/10.64 inference(quant_inst,[status(thm)],[])).
% 16.15/10.64 tff(1391,plain,
% 16.15/10.64 ((~![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)),
% 16.15/10.64 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 16.15/10.64 tff(1392,plain,
% 16.15/10.64 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)),
% 16.15/10.64 inference(unit_resolution,[status(thm)],[1391, 1145, 1388])).
% 16.15/10.64 tff(1393,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)), introduced(assumption)).
% 16.15/10.64 tff(1394,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)), introduced(assumption)).
% 16.15/10.64 tff(1395,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 16.15/10.64 tff(1396,plain,
% 16.15/10.64 (((~![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))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1397,plain,
% 16.15/10.65 ((~![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, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1398,plain,
% 16.15/10.65 ((~![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, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 16.15/10.65 tff(1399,plain,
% 16.15/10.65 (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)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1398, 1145])).
% 16.15/10.65 tff(1400,plain,
% 16.15/10.65 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1399, 1383])).
% 16.15/10.65 tff(1401,plain,
% 16.15/10.65 (((~![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))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1402,plain,
% 16.15/10.65 ((~![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))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1403,plain,
% 16.15/10.65 ((~![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)),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 16.15/10.65 tff(1404,plain,
% 16.15/10.65 (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)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1403, 1099])).
% 16.15/10.65 tff(1405,plain,
% 16.15/10.65 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1404, 803])).
% 16.15/10.65 tff(1406,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), introduced(assumption)).
% 16.15/10.65 tff(1407,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 16.15/10.65 tff(1408,assumption,(node11(c_e_h_1, c_n, s2, s3)), introduced(assumption)).
% 16.15/10.65 tff(1409,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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, s3) | (~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, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1410,plain,
% 16.15/10.65 ((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, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1411,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3))))),
% 16.15/10.65 inference(monotonicity,[status(thm)],[1410])).
% 16.15/10.65 tff(1412,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 16.15/10.65 inference(transitivity,[status(thm)],[1411, 1409])).
% 16.15/10.65 tff(1413,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1414,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3))),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 16.15/10.65 tff(1415,plain,
% 16.15/10.65 ($false),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1414, 1223, 1407, 1408, 1406])).
% 16.15/10.65 tff(1416,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.65 tff(1417,plain,
% 16.15/10.65 (~node11(c_e_h_1, c_n, s2, s3)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1416, 1406, 1407])).
% 16.15/10.65 tff(1418,plain,
% 16.15/10.65 (((~![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))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1419,plain,
% 16.15/10.65 ((~![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))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1420,plain,
% 16.15/10.65 ((~![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)),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 16.15/10.65 tff(1421,plain,
% 16.15/10.65 (node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1420, 1179, 591])).
% 16.15/10.65 tff(1422,plain,
% 16.15/10.65 (node10(c_e_h_1, c_n, s2, s3)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1421, 1417])).
% 16.15/10.65 tff(1423,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)), introduced(assumption)).
% 16.15/10.65 tff(1424,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)), introduced(assumption)).
% 16.15/10.65 tff(1425,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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, s2)) | 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)) | (~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_in2(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_in1(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1426,plain,
% 16.15/10.65 (((~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_in2(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_in1(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1427,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_in2(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_in1(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3))))),
% 16.15/10.65 inference(monotonicity,[status(thm)],[1426])).
% 16.15/10.65 tff(1428,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_in2(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_in1(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 16.15/10.65 inference(transitivity,[status(thm)],[1427, 1425])).
% 16.15/10.65 tff(1429,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1430,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3))),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 16.15/10.65 tff(1431,plain,
% 16.15/10.65 ($false),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1430, 1160, 1424, 1423, 1422, 1406])).
% 16.15/10.65 tff(1432,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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, s2))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.65 tff(1433,plain,
% 16.15/10.65 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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))),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1432, 1331])).
% 16.15/10.65 tff(1434,plain,
% 16.15/10.65 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2))),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1433, 1405])).
% 16.15/10.65 tff(1435,plain,
% 16.15/10.65 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1434, 1400])).
% 16.15/10.65 tff(1436,assumption,(node11(c_e_h_1, c_n, s3, s4)), introduced(assumption)).
% 16.15/10.65 tff(1437,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1438,plain,
% 16.15/10.65 ((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)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1439,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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))))),
% 16.15/10.65 inference(monotonicity,[status(thm)],[1438])).
% 16.15/10.65 tff(1440,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.65 inference(transitivity,[status(thm)],[1439, 1437])).
% 16.15/10.65 tff(1441,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1442,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4))),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 16.15/10.65 tff(1443,plain,
% 16.15/10.65 ($false),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1442, 1223, 1436, 1435, 1395])).
% 16.15/10.65 tff(1444,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,[]))).
% 16.15/10.65 tff(1445,plain,
% 16.15/10.65 (~node11(c_e_h_1, c_n, s3, s4)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1444, 1395])).
% 16.15/10.65 tff(1446,plain,
% 16.15/10.65 (((~![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))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1447,plain,
% 16.15/10.65 ((~![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))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1448,plain,
% 16.15/10.65 ((~![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)),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 16.15/10.65 tff(1449,plain,
% 16.15/10.65 (node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1448, 1179, 1013])).
% 16.15/10.65 tff(1450,plain,
% 16.15/10.65 (node10(c_e_h_1, c_n, s3, s4)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1449, 1445])).
% 16.15/10.65 tff(1451,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~node10(c_e_h_1, c_n, s3, s4)) | (~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) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1452,plain,
% 16.15/10.65 (((~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) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1453,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3))))),
% 16.15/10.65 inference(monotonicity,[status(thm)],[1452])).
% 16.15/10.65 tff(1454,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)))),
% 16.15/10.65 inference(transitivity,[status(thm)],[1453, 1451])).
% 16.15/10.65 tff(1455,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1456,plain,
% 16.15/10.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3))),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 16.15/10.65 tff(1457,plain,
% 16.15/10.65 ($false),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1456, 1160, 1450, 1395, 1394, 1393])).
% 16.15/10.65 tff(1458,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, 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))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.65 tff(1459,plain,
% 16.15/10.65 (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))),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1458, 1392])).
% 16.15/10.65 tff(1460,plain,
% 16.15/10.65 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1459, 1111])).
% 16.15/10.65 tff(1461,assumption,(node9(c_e_h_1, c_m, s3)), introduced(assumption)).
% 16.15/10.65 tff(1462,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)), introduced(assumption)).
% 16.15/10.65 tff(1463,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), introduced(assumption)).
% 16.15/10.65 tff(1464,plain,
% 16.15/10.65 (((~![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)))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1465,plain,
% 16.15/10.65 ((~![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)))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1466,plain,
% 16.15/10.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 16.15/10.65 tff(1467,plain,
% 16.15/10.65 ($false),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1466, 1276, 1463, 1462])).
% 16.15/10.65 tff(1468,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.65 tff(1469,plain,
% 16.15/10.65 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1468, 1435])).
% 16.15/10.65 tff(1470,plain,
% 16.15/10.65 (((~![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))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.65 tff(1471,plain,
% 16.15/10.65 ((~![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))),
% 16.15/10.65 inference(quant_inst,[status(thm)],[])).
% 16.15/10.65 tff(1472,plain,
% 16.15/10.65 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)),
% 16.15/10.65 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 16.15/10.65 tff(1473,plain,
% 16.15/10.65 ($false),
% 16.15/10.65 inference(unit_resolution,[status(thm)],[1472, 1290, 1469, 1461])).
% 16.15/10.65 tff(1474,plain,(~node9(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.65 tff(1475,assumption,(~node9(c_e_h_1, c_m, s3)), introduced(assumption)).
% 16.15/10.65 tff(1476,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 16.15/10.65 tff(1477,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 16.15/10.65 tff(1478,assumption,(node11(c_e_h_1, c_m, s3, s4)), introduced(assumption)).
% 16.15/10.65 tff(1479,plain,
% 16.15/10.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.65 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1480,plain,
% 16.15/10.66 ((~![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_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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1481,plain,
% 16.15/10.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 16.15/10.66 tff(1482,plain,
% 16.15/10.66 ($false),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1481, 1258, 1477, 1478, 1476])).
% 16.15/10.66 tff(1483,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,[]))).
% 16.15/10.66 tff(1484,plain,
% 16.15/10.66 (~node11(c_e_h_1, c_m, s3, s4)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1483, 1477, 1476])).
% 16.15/10.66 tff(1485,plain,
% 16.15/10.66 (((~![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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1486,plain,
% 16.15/10.66 ((~![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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1487,plain,
% 16.15/10.66 ((~![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)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 16.15/10.66 tff(1488,plain,
% 16.15/10.66 (node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1487, 1179, 1013])).
% 16.15/10.66 tff(1489,plain,
% 16.15/10.66 (node10(c_e_h_1, c_m, s3, s4)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1488, 1484])).
% 16.15/10.66 tff(1490,plain,
% 16.15/10.66 (((~![Y: $i, I0: $i, 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)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1491,plain,
% 16.15/10.66 ((~![Y: $i, I0: $i, 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)))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1492,plain,
% 16.15/10.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4))),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 16.15/10.66 tff(1493,plain,
% 16.15/10.66 ($false),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1492, 1304, 1477, 1489, 1475])).
% 16.15/10.66 tff(1494,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | node9(c_e_h_1, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.66 tff(1495,plain,
% 16.15/10.66 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | node9(c_e_h_1, c_m, s3)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1494, 1388])).
% 16.15/10.66 tff(1496,plain,
% 16.15/10.66 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1495, 1474])).
% 16.15/10.66 tff(1497,plain,
% 16.15/10.66 (((~![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, 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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1498,plain,
% 16.15/10.66 ((~![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, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1499,plain,
% 16.15/10.66 ((~![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, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 16.15/10.66 tff(1500,plain,
% 16.15/10.66 (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)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1499, 1145])).
% 16.15/10.66 tff(1501,plain,
% 16.15/10.66 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1500, 1496])).
% 16.15/10.66 tff(1502,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 16.15/10.66 tff(1503,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 16.15/10.66 tff(1504,assumption,(node11(c_e_h_1, c_n, s4, s5)), introduced(assumption)).
% 16.15/10.66 tff(1505,plain,
% 16.15/10.66 (((~![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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1506,plain,
% 16.15/10.66 ((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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1507,plain,
% 16.15/10.66 (((~![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, 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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5))))),
% 16.15/10.66 inference(monotonicity,[status(thm)],[1506])).
% 16.15/10.66 tff(1508,plain,
% 16.15/10.66 (((~![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, 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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 16.15/10.66 inference(transitivity,[status(thm)],[1507, 1505])).
% 16.15/10.66 tff(1509,plain,
% 16.15/10.66 ((~![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, 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)))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1510,plain,
% 16.15/10.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5))),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 16.15/10.66 tff(1511,plain,
% 16.15/10.66 ($false),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1510, 1223, 1503, 1504, 1502])).
% 16.15/10.66 tff(1512,plain,((~node11(c_e_h_1, c_n, s4, 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, s4))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.66 tff(1513,plain,
% 16.15/10.66 (~node11(c_e_h_1, c_n, s4, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1512, 1503, 1502])).
% 16.15/10.66 tff(1514,plain,
% 16.15/10.66 (succ(s4, s5) <=> succ(s4, s5)),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1515,axiom,(succ(s4, s5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 16.15/10.66 tff(1516,plain,
% 16.15/10.66 (succ(s4, s5)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 16.15/10.66 tff(1517,plain,
% 16.15/10.66 (((~![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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1518,plain,
% 16.15/10.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1519,plain,
% 16.15/10.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 16.15/10.66 tff(1520,plain,
% 16.15/10.66 (trans(s4, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1519, 1516, 95])).
% 16.15/10.66 tff(1521,plain,
% 16.15/10.66 (((~![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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1522,plain,
% 16.15/10.66 ((~![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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1523,plain,
% 16.15/10.66 ((~![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)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 16.15/10.66 tff(1524,plain,
% 16.15/10.66 (node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1523, 1179, 1520])).
% 16.15/10.66 tff(1525,plain,
% 16.15/10.66 (node10(c_e_h_1, c_n, s4, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1524, 1513])).
% 16.15/10.66 tff(1526,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)), introduced(assumption)).
% 16.15/10.66 tff(1527,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), introduced(assumption)).
% 16.15/10.66 tff(1528,plain,
% 16.15/10.66 (((~![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_n, s4, s5)) | 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_in2(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))) | (~node10(c_e_h_1, c_n, s4, s5)) | 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_in2(c_e_h_1, c_n, s4)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1529,plain,
% 16.15/10.66 (((~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)) <=> ((~node10(c_e_h_1, c_n, s4, s5)) | 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_in2(c_e_h_1, c_n, s4)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1530,plain,
% 16.15/10.66 (((~![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_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))) | ((~node10(c_e_h_1, c_n, s4, s5)) | 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_in2(c_e_h_1, c_n, s4))))),
% 16.15/10.66 inference(monotonicity,[status(thm)],[1529])).
% 16.15/10.66 tff(1531,plain,
% 16.15/10.66 (((~![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_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))) | (~node10(c_e_h_1, c_n, s4, s5)) | 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_in2(c_e_h_1, c_n, s4)))),
% 16.15/10.66 inference(transitivity,[status(thm)],[1530, 1528])).
% 16.15/10.66 tff(1532,plain,
% 16.15/10.66 ((~![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_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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1533,plain,
% 16.15/10.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_1, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4))),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 16.15/10.66 tff(1534,plain,
% 16.15/10.66 ($false),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1533, 1160, 1527, 1526, 1503, 1525])).
% 16.15/10.66 tff(1535,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_in2(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,[]))).
% 16.15/10.66 tff(1536,plain,
% 16.15/10.66 (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))),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1535, 1501])).
% 16.15/10.66 tff(1537,plain,
% 16.15/10.66 (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))),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1536, 1460])).
% 16.15/10.66 tff(1538,plain,
% 16.15/10.66 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1537, 1104])).
% 16.15/10.66 tff(1539,plain,
% 16.15/10.66 (((~![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, 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)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1540,plain,
% 16.15/10.66 ((~![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, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1541,plain,
% 16.15/10.66 ((~![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, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 16.15/10.66 tff(1542,plain,
% 16.15/10.66 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1541, 1276, 1538])).
% 16.15/10.66 tff(1543,plain,
% 16.15/10.66 (((~![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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1544,plain,
% 16.15/10.66 ((~![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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1545,plain,
% 16.15/10.66 ((~![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)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 16.15/10.66 tff(1546,plain,
% 16.15/10.66 (~node9(c_e_h_1, c_m, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1545, 1290, 1542])).
% 16.15/10.66 tff(1547,assumption,(node9(c_e_h_1, c_m, s4)), introduced(assumption)).
% 16.15/10.66 tff(1548,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)), introduced(assumption)).
% 16.15/10.66 tff(1549,plain,
% 16.15/10.66 (((~![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, 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)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1550,plain,
% 16.15/10.66 ((~![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, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1551,plain,
% 16.15/10.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 16.15/10.66 tff(1552,plain,
% 16.15/10.66 ($false),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1551, 1276, 1548, 1502])).
% 16.15/10.66 tff(1553,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.66 tff(1554,plain,
% 16.15/10.66 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1553, 1460])).
% 16.15/10.66 tff(1555,plain,
% 16.15/10.66 (((~![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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1556,plain,
% 16.15/10.66 ((~![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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1557,plain,
% 16.15/10.66 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 16.15/10.66 tff(1558,plain,
% 16.15/10.66 ($false),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1557, 1290, 1554, 1547])).
% 16.15/10.66 tff(1559,plain,(~node9(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.66 tff(1560,assumption,(~node9(c_e_h_1, c_m, s4)), introduced(assumption)).
% 16.15/10.66 tff(1561,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 16.15/10.66 tff(1562,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 16.15/10.66 tff(1563,assumption,(node11(c_e_h_1, c_m, s4, s5)), introduced(assumption)).
% 16.15/10.66 tff(1564,plain,
% 16.15/10.66 (((~![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_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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1565,plain,
% 16.15/10.66 ((~![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_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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1566,plain,
% 16.15/10.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 16.15/10.66 tff(1567,plain,
% 16.15/10.66 ($false),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1566, 1258, 1561, 1562, 1563])).
% 16.15/10.66 tff(1568,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,[]))).
% 16.15/10.66 tff(1569,plain,
% 16.15/10.66 (~node11(c_e_h_1, c_m, s4, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1568, 1562, 1561])).
% 16.15/10.66 tff(1570,plain,
% 16.15/10.66 (((~![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))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.66 tff(1571,plain,
% 16.15/10.66 ((~![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))),
% 16.15/10.66 inference(quant_inst,[status(thm)],[])).
% 16.15/10.66 tff(1572,plain,
% 16.15/10.66 ((~![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)),
% 16.15/10.66 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 16.15/10.66 tff(1573,plain,
% 16.15/10.66 (node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1572, 1179, 1520])).
% 16.15/10.66 tff(1574,plain,
% 16.15/10.66 (node10(c_e_h_1, c_m, s4, s5)),
% 16.15/10.66 inference(unit_resolution,[status(thm)],[1573, 1569])).
% 16.15/10.66 tff(1575,plain,
% 16.15/10.66 (((~![Y: $i, I0: $i, 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, s5)) | node9(c_e_h_1, c_m, s4) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4) | (~node10(c_e_h_1, c_m, s4, s5)))),
% 16.15/10.66 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1576,plain,
% 16.15/10.67 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4) | (~node10(c_e_h_1, c_m, s4, s5)))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1577,plain,
% 16.15/10.67 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4) | (~node10(c_e_h_1, c_m, s4, s5))))),
% 16.15/10.67 inference(monotonicity,[status(thm)],[1576])).
% 16.15/10.67 tff(1578,plain,
% 16.15/10.67 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4) | (~node10(c_e_h_1, c_m, s4, s5)))),
% 16.15/10.67 inference(transitivity,[status(thm)],[1577, 1575])).
% 16.15/10.67 tff(1579,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, 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)))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1580,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4) | (~node10(c_e_h_1, c_m, s4, s5))),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 16.15/10.67 tff(1581,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1580, 1304, 1562, 1574, 1560])).
% 16.15/10.67 tff(1582,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.67 tff(1583,plain,
% 16.15/10.67 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1582, 1496])).
% 16.15/10.67 tff(1584,plain,
% 16.15/10.67 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1583, 1559])).
% 16.15/10.67 tff(1585,assumption,(~node9(c_e_h_1, c_m, s5)), introduced(assumption)).
% 16.15/10.67 tff(1586,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 16.15/10.67 tff(1587,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 16.15/10.67 tff(1588,assumption,(node11(c_e_h_1, c_m, s5, s6)), introduced(assumption)).
% 16.15/10.67 tff(1589,plain,
% 16.15/10.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1590,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1591,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 16.15/10.67 tff(1592,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1591, 1258, 1587, 1586, 1588])).
% 16.15/10.67 tff(1593,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,[]))).
% 16.15/10.67 tff(1594,plain,
% 16.15/10.67 (~node11(c_e_h_1, c_m, s5, s6)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1593, 1587, 1586])).
% 16.15/10.67 tff(1595,plain,
% 16.15/10.67 (succ(s5, s6) <=> succ(s5, s6)),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1596,axiom,(succ(s5, s6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 16.15/10.67 tff(1597,plain,
% 16.15/10.67 (succ(s5, s6)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 16.15/10.67 tff(1598,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1599,plain,
% 16.15/10.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1600,plain,
% 16.15/10.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 16.15/10.67 tff(1601,plain,
% 16.15/10.67 (trans(s5, s6)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1600, 1597, 95])).
% 16.15/10.67 tff(1602,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1603,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1604,plain,
% 16.15/10.67 ((~![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)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 16.15/10.67 tff(1605,plain,
% 16.15/10.67 (node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1604, 1179, 1601])).
% 16.15/10.67 tff(1606,plain,
% 16.15/10.67 (node10(c_e_h_1, c_m, s5, s6)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1605, 1594])).
% 16.15/10.67 tff(1607,plain,
% 16.15/10.67 (((~![Y: $i, I0: $i, 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, s6)) | node9(c_e_h_1, c_m, s5) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1608,plain,
% 16.15/10.67 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1609,plain,
% 16.15/10.67 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6))))),
% 16.15/10.67 inference(monotonicity,[status(thm)],[1608])).
% 16.15/10.67 tff(1610,plain,
% 16.15/10.67 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 16.15/10.67 inference(transitivity,[status(thm)],[1609, 1607])).
% 16.15/10.67 tff(1611,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, 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)))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1612,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6))),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 16.15/10.67 tff(1613,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1612, 1304, 1587, 1606, 1585])).
% 16.15/10.67 tff(1614,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,[]))).
% 16.15/10.67 tff(1615,plain,
% 16.15/10.67 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1614, 1584])).
% 16.15/10.67 tff(1616,plain,
% 16.15/10.67 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1615, 1546])).
% 16.15/10.67 tff(1617,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s6)), introduced(assumption)).
% 16.15/10.67 tff(1618,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 16.15/10.67 tff(1619,plain,
% 16.15/10.67 (^[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)))),
% 16.15/10.67 inference(bind,[status(th)],[])).
% 16.15/10.67 tff(1620,plain,
% 16.15/10.67 (![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))),
% 16.15/10.67 inference(quant_intro,[status(thm)],[1619])).
% 16.15/10.67 tff(1621,plain,
% 16.15/10.67 (![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1622,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')).
% 16.15/10.67 tff(1623,plain,
% 16.15/10.67 (![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))),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 16.15/10.67 tff(1624,plain,(
% 16.15/10.67 ![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))),
% 16.15/10.67 inference(skolemize,[status(sab)],[1623])).
% 16.15/10.67 tff(1625,plain,
% 16.15/10.67 (![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))),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1624, 1620])).
% 16.15/10.67 tff(1626,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1627,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1628,plain,
% 16.15/10.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 16.15/10.67 tff(1629,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1628, 1625, 1618, 1617])).
% 16.15/10.67 tff(1630,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.67 tff(1631,plain,
% 16.15/10.67 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1630, 1616])).
% 16.15/10.67 tff(1632,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)), introduced(assumption)).
% 16.15/10.67 tff(1633,assumption,(node20(c_e_h_1, c_r, s6)), introduced(assumption)).
% 16.15/10.67 tff(1634,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1635,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1636,plain,
% 16.15/10.67 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 16.15/10.67 tff(1637,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1636, 68, 1633, 1632])).
% 16.15/10.67 tff(1638,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s6) | (~node20(c_e_h_1, c_r, s6))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.67 tff(1639,plain,
% 16.15/10.67 (~node20(c_e_h_1, c_r, s6)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1638, 1631])).
% 16.15/10.67 tff(1640,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 16.15/10.67 tff(1641,assumption,(node22(c_e_h_1, c_r, s1, s2)), introduced(assumption)).
% 16.15/10.67 tff(1642,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s1)), introduced(assumption)).
% 16.15/10.67 tff(1643,assumption,(node21(c_e_h_1, c_r, s0, s1)), introduced(assumption)).
% 16.15/10.67 tff(1644,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1645,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1646,plain,
% 16.15/10.67 ((~![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)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 16.15/10.67 tff(1647,plain,
% 16.15/10.67 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1646, 1625, 1138])).
% 16.15/10.67 tff(1648,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1649,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1650,plain,
% 16.15/10.67 ((~![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)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 16.15/10.67 tff(1651,plain,
% 16.15/10.67 (~node20(c_e_h_1, c_r, s0)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1650, 68, 1647])).
% 16.15/10.67 tff(1652,plain,
% 16.15/10.67 (((~![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_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)))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1653,plain,
% 16.15/10.67 ((~![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_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1654,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1))),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 16.15/10.67 tff(1655,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1654, 82, 1651, 1643, 1642])).
% 16.15/10.67 tff(1656,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,[]))).
% 16.15/10.67 tff(1657,plain,
% 16.15/10.67 (~node21(c_e_h_1, c_r, s0, s1)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1656, 1642])).
% 16.15/10.67 tff(1658,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1659,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1660,plain,
% 16.15/10.67 ((~![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)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 16.15/10.67 tff(1661,plain,
% 16.15/10.67 (node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1660, 112, 102])).
% 16.15/10.67 tff(1662,plain,
% 16.15/10.67 (node22(c_e_h_1, c_r, s0, s1)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1661, 1657])).
% 16.15/10.67 tff(1663,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s0)), introduced(assumption)).
% 16.15/10.67 tff(1664,plain,
% 16.15/10.67 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1665,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1664, 9, 1663])).
% 16.15/10.67 tff(1666,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.67 tff(1667,plain,
% 16.15/10.67 (((~![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_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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1668,plain,
% 16.15/10.67 ((~![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_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1669,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 16.15/10.67 tff(1670,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1669, 127, 1666, 1662, 1642])).
% 16.15/10.67 tff(1671,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.67 tff(1672,plain,
% 16.15/10.67 (((~![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_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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1673,plain,
% 16.15/10.67 ((~![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_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1674,plain,
% 16.15/10.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 16.15/10.67 tff(1675,plain,
% 16.15/10.67 ($false),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1674, 127, 1671, 1641, 1640])).
% 16.15/10.67 tff(1676,plain,((~node22(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,[]))).
% 16.15/10.67 tff(1677,plain,
% 16.15/10.67 (~node22(c_e_h_1, c_r, s1, s2)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1676, 1640])).
% 16.15/10.67 tff(1678,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1679,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.67 tff(1680,plain,
% 16.15/10.67 ((~![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)),
% 16.15/10.67 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 16.15/10.67 tff(1681,plain,
% 16.15/10.67 (node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1680, 112, 348])).
% 16.15/10.67 tff(1682,plain,
% 16.15/10.67 (node21(c_e_h_1, c_r, s1, s2)),
% 16.15/10.67 inference(unit_resolution,[status(thm)],[1681, 1677])).
% 16.15/10.67 tff(1683,plain,
% 16.15/10.67 (((~![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))),
% 16.15/10.67 inference(rewrite,[status(thm)],[])).
% 16.15/10.67 tff(1684,plain,
% 16.15/10.67 ((~![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))),
% 16.15/10.67 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1685,plain,
% 16.15/10.68 ((~![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)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 16.15/10.68 tff(1686,plain,
% 16.15/10.68 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1685, 1625, 1309])).
% 16.15/10.68 tff(1687,plain,
% 16.15/10.68 (((~![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_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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1688,plain,
% 16.15/10.68 ((~![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_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1689,plain,
% 16.15/10.68 ((~![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_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 16.15/10.68 tff(1690,plain,
% 16.15/10.68 (~node20(c_e_h_1, c_r, s1)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1689, 68, 1686])).
% 16.15/10.68 tff(1691,plain,
% 16.15/10.68 (((~![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_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, 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) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1692,plain,
% 16.15/10.68 ((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))) <=> (node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1693,plain,
% 16.15/10.68 (((~![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_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) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2))))),
% 16.15/10.68 inference(monotonicity,[status(thm)],[1692])).
% 16.15/10.68 tff(1694,plain,
% 16.15/10.68 (((~![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_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) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)))),
% 16.15/10.68 inference(transitivity,[status(thm)],[1693, 1691])).
% 16.15/10.68 tff(1695,plain,
% 16.15/10.68 ((~![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_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1696,plain,
% 16.15/10.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 16.15/10.68 tff(1697,plain,
% 16.15/10.68 ($false),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1696, 82, 1690, 1682, 1640])).
% 16.15/10.68 tff(1698,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.68 tff(1699,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 16.15/10.68 tff(1700,assumption,(node21(c_e_h_1, c_r, s2, s3)), introduced(assumption)).
% 16.15/10.68 tff(1701,plain,
% 16.15/10.68 (^[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)))),
% 16.15/10.68 inference(bind,[status(th)],[])).
% 16.15/10.68 tff(1702,plain,
% 16.15/10.68 (![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))),
% 16.15/10.68 inference(quant_intro,[status(thm)],[1701])).
% 16.15/10.68 tff(1703,plain,
% 16.15/10.68 (![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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1704,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')).
% 16.15/10.68 tff(1705,plain,
% 16.15/10.68 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 16.15/10.68 tff(1706,plain,(
% 16.15/10.68 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 16.15/10.68 inference(skolemize,[status(sab)],[1705])).
% 16.15/10.68 tff(1707,plain,
% 16.15/10.68 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1706, 1702])).
% 16.15/10.68 tff(1708,plain,
% 16.15/10.68 (((~![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, s2)) | m_c_h_element_v_out(c_e_h_1, 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_1, c_r, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1709,plain,
% 16.15/10.68 ((~![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, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1710,plain,
% 16.15/10.68 ((~![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, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 16.15/10.68 tff(1711,plain,
% 16.15/10.68 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s2)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1710, 1707, 803])).
% 16.15/10.68 tff(1712,plain,
% 16.15/10.68 (((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, 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_1, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s2))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1713,plain,
% 16.15/10.68 ((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s2))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1714,plain,
% 16.15/10.68 ((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s2)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 16.15/10.68 tff(1715,plain,
% 16.15/10.68 (~node20(c_e_h_1, c_r, s2)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1714, 283, 1711])).
% 16.15/10.68 tff(1716,plain,
% 16.15/10.68 (((~![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_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)))) | 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)))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1717,plain,
% 16.15/10.68 ((~![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_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1718,plain,
% 16.15/10.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3))),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 16.15/10.68 tff(1719,plain,
% 16.15/10.68 ($false),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1718, 82, 1715, 1699, 1700])).
% 16.15/10.68 tff(1720,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,[]))).
% 16.15/10.68 tff(1721,plain,
% 16.15/10.68 (~node21(c_e_h_1, c_r, s2, s3)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1720, 1699])).
% 16.15/10.68 tff(1722,plain,
% 16.15/10.68 (((~![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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1723,plain,
% 16.15/10.68 ((~![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))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1724,plain,
% 16.15/10.68 ((~![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)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 16.15/10.68 tff(1725,plain,
% 16.15/10.68 (node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1724, 112, 591])).
% 16.15/10.68 tff(1726,plain,
% 16.15/10.68 (node22(c_e_h_1, c_r, s2, s3)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1725, 1721])).
% 16.15/10.68 tff(1727,plain,
% 16.15/10.68 (((~![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_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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1728,plain,
% 16.15/10.68 ((~![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_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1729,plain,
% 16.15/10.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 16.15/10.68 tff(1730,plain,
% 16.15/10.68 ($false),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1729, 127, 1699, 1726, 1698])).
% 16.15/10.68 tff(1731,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.68 tff(1732,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 16.15/10.68 tff(1733,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 16.15/10.68 tff(1734,plain,
% 16.15/10.68 (((~![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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1735,plain,
% 16.15/10.68 ((~![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))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1736,plain,
% 16.15/10.68 ((~![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)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 16.15/10.68 tff(1737,plain,
% 16.15/10.68 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1736, 1625, 1388])).
% 16.15/10.68 tff(1738,plain,
% 16.15/10.68 (((~![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_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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1739,plain,
% 16.15/10.68 ((~![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_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1740,plain,
% 16.15/10.68 ((~![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_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1739, 1738])).
% 16.15/10.68 tff(1741,plain,
% 16.15/10.68 (~node20(c_e_h_1, c_r, s3)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1740, 68, 1737])).
% 16.15/10.68 tff(1742,assumption,(node21(c_e_h_1, c_r, s3, s4)), introduced(assumption)).
% 16.15/10.68 tff(1743,plain,
% 16.15/10.68 (((~![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_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1744,plain,
% 16.15/10.68 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1745,plain,
% 16.15/10.68 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4))))),
% 16.15/10.68 inference(monotonicity,[status(thm)],[1744])).
% 16.15/10.68 tff(1746,plain,
% 16.15/10.68 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 16.15/10.68 inference(transitivity,[status(thm)],[1745, 1743])).
% 16.15/10.68 tff(1747,plain,
% 16.15/10.68 ((~![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_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1748,plain,
% 16.15/10.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4))),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 16.15/10.68 tff(1749,plain,
% 16.15/10.68 ($false),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1748, 82, 1742, 1741, 1732])).
% 16.15/10.68 tff(1750,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,[]))).
% 16.15/10.68 tff(1751,plain,
% 16.15/10.68 (~node21(c_e_h_1, c_r, s3, s4)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1750, 1732])).
% 16.15/10.68 tff(1752,plain,
% 16.15/10.68 (((~![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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1753,plain,
% 16.15/10.68 ((~![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))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1754,plain,
% 16.15/10.68 ((~![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)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 16.15/10.68 tff(1755,plain,
% 16.15/10.68 (node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1754, 112, 1013])).
% 16.15/10.68 tff(1756,plain,
% 16.15/10.68 (node22(c_e_h_1, c_r, s3, s4)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1755, 1751])).
% 16.15/10.68 tff(1757,plain,
% 16.15/10.68 (((~![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_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))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1758,plain,
% 16.15/10.68 ((~![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_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1759,plain,
% 16.15/10.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 16.15/10.68 tff(1760,plain,
% 16.15/10.68 ($false),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1759, 127, 1756, 1733, 1732])).
% 16.15/10.68 tff(1761,plain,((~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,[]))).
% 16.15/10.68 tff(1762,plain,
% 16.15/10.68 (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1761, 1731])).
% 16.15/10.68 tff(1763,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s5)), introduced(assumption)).
% 16.15/10.68 tff(1764,assumption,(node21(c_e_h_1, c_r, s4, s5)), introduced(assumption)).
% 16.15/10.68 tff(1765,plain,
% 16.15/10.68 (((~![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, 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_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, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1766,plain,
% 16.15/10.68 ((~![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, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1767,plain,
% 16.15/10.68 ((~![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, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 16.15/10.68 tff(1768,plain,
% 16.15/10.68 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s4)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1767, 1625, 1496])).
% 16.15/10.68 tff(1769,plain,
% 16.15/10.68 (((~![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_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, 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_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s4))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1770,plain,
% 16.15/10.68 ((~![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_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s4))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1771,plain,
% 16.15/10.68 ((~![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_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s4)),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 16.15/10.68 tff(1772,plain,
% 16.15/10.68 (~node20(c_e_h_1, c_r, s4)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1771, 68, 1768])).
% 16.15/10.68 tff(1773,plain,
% 16.15/10.68 (((~![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_r, s4) | (~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, 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) | (~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1774,plain,
% 16.15/10.68 ((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))) <=> (node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)))),
% 16.15/10.68 inference(rewrite,[status(thm)],[])).
% 16.15/10.68 tff(1775,plain,
% 16.15/10.68 (((~![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_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) | (~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5))))),
% 16.15/10.68 inference(monotonicity,[status(thm)],[1774])).
% 16.15/10.68 tff(1776,plain,
% 16.15/10.68 (((~![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_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) | (~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)))),
% 16.15/10.68 inference(transitivity,[status(thm)],[1775, 1773])).
% 16.15/10.68 tff(1777,plain,
% 16.15/10.68 ((~![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_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5)))),
% 16.15/10.68 inference(quant_inst,[status(thm)],[])).
% 16.15/10.68 tff(1778,plain,
% 16.15/10.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 16.15/10.68 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 16.15/10.68 tff(1779,plain,
% 16.15/10.68 ($false),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1778, 82, 1772, 1764, 1763])).
% 16.15/10.68 tff(1780,plain,((~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5))), inference(lemma,lemma(discharge,[]))).
% 16.15/10.68 tff(1781,plain,
% 16.15/10.68 (~node21(c_e_h_1, c_r, s4, s5)),
% 16.15/10.68 inference(unit_resolution,[status(thm)],[1780, 1763])).
% 16.15/10.68 tff(1782,plain,
% 16.15/10.68 (((~![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))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1783,plain,
% 16.15/10.69 ((~![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))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1784,plain,
% 16.15/10.69 ((~![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)),
% 16.15/10.69 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 16.15/10.69 tff(1785,plain,
% 16.15/10.69 (node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1784, 112, 1520])).
% 16.15/10.69 tff(1786,plain,
% 16.15/10.69 (node22(c_e_h_1, c_r, s4, s5)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1785, 1781])).
% 16.15/10.69 tff(1787,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 16.15/10.69 tff(1788,plain,
% 16.15/10.69 (((~![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_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))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1789,plain,
% 16.15/10.69 ((~![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_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))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1790,plain,
% 16.15/10.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 16.15/10.69 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 16.15/10.69 tff(1791,plain,
% 16.15/10.69 ($false),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1790, 127, 1787, 1786, 1763])).
% 16.15/10.69 tff(1792,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.69 tff(1793,plain,
% 16.15/10.69 (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1792, 1762])).
% 16.15/10.69 tff(1794,plain,
% 16.15/10.69 (((~![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, 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_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, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1795,plain,
% 16.15/10.69 ((~![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, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1796,plain,
% 16.15/10.69 ((~![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, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 16.15/10.69 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 16.15/10.69 tff(1797,plain,
% 16.15/10.69 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1796, 1625, 1584])).
% 16.15/10.69 tff(1798,plain,
% 16.15/10.69 (((~![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, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, 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_r, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s5))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1799,plain,
% 16.15/10.69 ((~![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, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s5))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1800,plain,
% 16.15/10.69 ((~![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, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s5)),
% 16.15/10.69 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 16.15/10.69 tff(1801,plain,
% 16.15/10.69 (~node20(c_e_h_1, c_r, s5)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1800, 68, 1797])).
% 16.15/10.69 tff(1802,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 16.15/10.69 tff(1803,assumption,(~node20(c_e_h_1, c_r, s5)), introduced(assumption)).
% 16.15/10.69 tff(1804,assumption,(node21(c_e_h_1, c_r, s5, s6)), introduced(assumption)).
% 16.15/10.69 tff(1805,plain,
% 16.15/10.69 (((~![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_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)))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1806,plain,
% 16.15/10.69 ((~![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_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1807,plain,
% 16.15/10.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6))),
% 16.15/10.69 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 16.15/10.69 tff(1808,plain,
% 16.15/10.69 ($false),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1807, 82, 1804, 1802, 1803])).
% 16.15/10.69 tff(1809,plain,((~node21(c_e_h_1, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | node20(c_e_h_1, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.69 tff(1810,plain,
% 16.15/10.69 (~node21(c_e_h_1, c_r, s5, s6)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1809, 1802, 1803])).
% 16.15/10.69 tff(1811,plain,
% 16.15/10.69 (((~![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))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1812,plain,
% 16.15/10.69 ((~![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))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1813,plain,
% 16.15/10.69 ((~![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)),
% 16.15/10.69 inference(modus_ponens,[status(thm)],[1812, 1811])).
% 16.15/10.69 tff(1814,plain,
% 16.15/10.69 (node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1813, 112, 1601])).
% 16.15/10.69 tff(1815,plain,
% 16.15/10.69 (node22(c_e_h_1, c_r, s5, s6)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1814, 1810])).
% 16.15/10.69 tff(1816,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s5)), introduced(assumption)).
% 16.15/10.69 tff(1817,plain,
% 16.15/10.69 (((~![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_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))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1818,plain,
% 16.15/10.69 ((~![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_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))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1819,plain,
% 16.15/10.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 16.15/10.69 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 16.15/10.69 tff(1820,plain,
% 16.15/10.69 ($false),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1819, 127, 1816, 1815, 1802])).
% 16.15/10.69 tff(1821,plain,((~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, s5) | node20(c_e_h_1, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 16.15/10.69 tff(1822,plain,
% 16.15/10.69 ((~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, s5)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1821, 1801])).
% 16.15/10.69 tff(1823,plain,
% 16.15/10.69 (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 16.15/10.69 inference(unit_resolution,[status(thm)],[1822, 1793])).
% 16.15/10.69 tff(1824,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 16.15/10.69 tff(1825,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 16.15/10.69 tff(1826,assumption,(~node20(c_e_h_1, c_r, s6)), introduced(assumption)).
% 16.15/10.69 tff(1827,assumption,(node21(c_e_h_1, c_r, s6, s7)), introduced(assumption)).
% 16.15/10.69 tff(1828,plain,
% 16.15/10.69 (((~![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_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)))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1829,plain,
% 16.15/10.69 ((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)))),
% 16.15/10.69 inference(rewrite,[status(thm)],[])).
% 16.15/10.69 tff(1830,plain,
% 16.15/10.69 (((~![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_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))))),
% 16.15/10.69 inference(monotonicity,[status(thm)],[1829])).
% 16.15/10.69 tff(1831,plain,
% 16.15/10.69 (((~![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_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)))),
% 16.15/10.69 inference(transitivity,[status(thm)],[1830, 1828])).
% 16.15/10.69 tff(1832,plain,
% 16.15/10.69 ((~![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_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 16.15/10.69 inference(quant_inst,[status(thm)],[])).
% 16.15/10.69 tff(1833,plain,
% 16.15/10.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7))),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 16.23/10.69 tff(1834,plain,
% 16.23/10.69 ($false),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1833, 82, 1827, 1826, 1824])).
% 16.23/10.69 tff(1835,plain,((~node21(c_e_h_1, c_r, s6, s7)) | node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 16.23/10.69 tff(1836,plain,
% 16.23/10.69 (~node21(c_e_h_1, c_r, s6, s7)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1835, 1824, 1826])).
% 16.23/10.69 tff(1837,plain,
% 16.23/10.69 (succ(s6, s7) <=> succ(s6, s7)),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1838,axiom,(succ(s6, s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 16.23/10.69 tff(1839,plain,
% 16.23/10.69 (succ(s6, s7)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 16.23/10.69 tff(1840,plain,
% 16.23/10.69 (((~![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))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1841,plain,
% 16.23/10.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1842,plain,
% 16.23/10.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 16.23/10.69 tff(1843,plain,
% 16.23/10.69 (trans(s6, s7)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1842, 1839, 95])).
% 16.23/10.69 tff(1844,plain,
% 16.23/10.69 (((~![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_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))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1845,plain,
% 16.23/10.69 ((~![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_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1846,plain,
% 16.23/10.69 ((~![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_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 16.23/10.69 tff(1847,plain,
% 16.23/10.69 (node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1846, 112, 1843])).
% 16.23/10.69 tff(1848,plain,
% 16.23/10.69 (node22(c_e_h_1, c_r, s6, s7)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1847, 1836])).
% 16.23/10.69 tff(1849,plain,
% 16.23/10.69 (((~![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_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))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1850,plain,
% 16.23/10.69 ((~![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_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))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1851,plain,
% 16.23/10.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 16.23/10.69 tff(1852,plain,
% 16.23/10.69 ($false),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1851, 127, 1848, 1825, 1824])).
% 16.23/10.69 tff(1853,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) | node20(c_e_h_1, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.69 tff(1854,plain,
% 16.23/10.69 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1853, 1823])).
% 16.23/10.69 tff(1855,plain,
% 16.23/10.69 (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1854, 1639])).
% 16.23/10.69 tff(1856,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 16.23/10.69 tff(1857,assumption,(m_user_v_ack(c_e_h_1, c_u, s7)), introduced(assumption)).
% 16.23/10.69 tff(1858,plain,
% 16.23/10.69 (^[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)))),
% 16.23/10.69 inference(bind,[status(th)],[])).
% 16.23/10.69 tff(1859,plain,
% 16.23/10.69 (![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))),
% 16.23/10.69 inference(quant_intro,[status(thm)],[1858])).
% 16.23/10.69 tff(1860,plain,
% 16.23/10.69 (![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))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1861,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')).
% 16.23/10.69 tff(1862,plain,
% 16.23/10.69 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 16.23/10.69 tff(1863,plain,(
% 16.23/10.69 ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 16.23/10.69 inference(skolemize,[status(sab)],[1862])).
% 16.23/10.69 tff(1864,plain,
% 16.23/10.69 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1863, 1859])).
% 16.23/10.69 tff(1865,plain,
% 16.23/10.69 (((~![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))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1866,plain,
% 16.23/10.69 ((~![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))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1867,plain,
% 16.23/10.69 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 16.23/10.69 tff(1868,plain,
% 16.23/10.69 ($false),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1867, 1864, 1857, 1856])).
% 16.23/10.69 tff(1869,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,[]))).
% 16.23/10.69 tff(1870,plain,
% 16.23/10.69 (~m_user_v_ack(c_e_h_1, c_u, s7)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1869, 1855])).
% 16.23/10.69 tff(1871,assumption,(node24(s7)), introduced(assumption)).
% 16.23/10.69 tff(1872,assumption,(~m_user_v_ack(c_e_h_1, c_u, s7)), introduced(assumption)).
% 16.23/10.69 tff(1873,plain,
% 16.23/10.69 (^[X: $i] : refl((m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))))),
% 16.23/10.69 inference(bind,[status(th)],[])).
% 16.23/10.69 tff(1874,plain,
% 16.23/10.69 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 16.23/10.69 inference(quant_intro,[status(thm)],[1873])).
% 16.23/10.69 tff(1875,plain,
% 16.23/10.69 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1876,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty3')).
% 16.23/10.69 tff(1877,plain,
% 16.23/10.69 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 16.23/10.69 tff(1878,plain,(
% 16.23/10.69 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 16.23/10.69 inference(skolemize,[status(sab)],[1877])).
% 16.23/10.69 tff(1879,plain,
% 16.23/10.69 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1878, 1874])).
% 16.23/10.69 tff(1880,plain,
% 16.23/10.69 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7)))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1881,plain,
% 16.23/10.69 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7)))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1882,plain,
% 16.23/10.69 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7))),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 16.23/10.69 tff(1883,plain,
% 16.23/10.69 ($false),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1882, 1879, 1872, 1871])).
% 16.23/10.69 tff(1884,plain,((~node24(s7)) | m_user_v_ack(c_e_h_1, c_u, s7)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.69 tff(1885,plain,
% 16.23/10.69 (~node24(s7)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1884, 1870])).
% 16.23/10.69 tff(1886,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s2)), introduced(assumption)).
% 16.23/10.69 tff(1887,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s1)), introduced(assumption)).
% 16.23/10.69 tff(1888,plain,
% 16.23/10.69 (((~![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_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))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1889,plain,
% 16.23/10.69 ((~![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_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1890,plain,
% 16.23/10.69 ((~![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_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 16.23/10.69 tff(1891,plain,
% 16.23/10.69 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1890, 420, 12])).
% 16.23/10.69 tff(1892,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s0)), introduced(assumption)).
% 16.23/10.69 tff(1893,plain,
% 16.23/10.69 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1894,plain,
% 16.23/10.69 ($false),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1893, 9, 1892])).
% 16.23/10.69 tff(1895,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.69 tff(1896,plain,
% 16.23/10.69 (m_cell_v_left(c_e_h_1, c_e_h_2) <=> m_cell_v_left(c_e_h_1, c_e_h_2)),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1897,axiom,(m_cell_v_left(c_e_h_1, c_e_h_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_1')).
% 16.23/10.69 tff(1898,plain,
% 16.23/10.69 (m_cell_v_left(c_e_h_1, c_e_h_2)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 16.23/10.69 tff(1899,plain,
% 16.23/10.69 (((~![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))),
% 16.23/10.69 inference(rewrite,[status(thm)],[])).
% 16.23/10.69 tff(1900,plain,
% 16.23/10.69 ((~![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))),
% 16.23/10.69 inference(quant_inst,[status(thm)],[])).
% 16.23/10.69 tff(1901,plain,
% 16.23/10.69 ((~![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)),
% 16.23/10.69 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 16.23/10.69 tff(1902,plain,
% 16.23/10.69 (node3(c_e_h_1, c_e_h_2, s0)),
% 16.23/10.69 inference(unit_resolution,[status(thm)],[1901, 1898, 376])).
% 16.23/10.70 tff(1903,plain,
% 16.23/10.70 (((~![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_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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1904,plain,
% 16.23/10.70 ((~![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_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))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1905,plain,
% 16.23/10.70 ((~![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_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)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1904, 1903])).
% 16.23/10.70 tff(1906,plain,
% 16.23/10.70 ((~m_cell_v_ack(c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1905, 393, 1902])).
% 16.23/10.70 tff(1907,plain,
% 16.23/10.70 (~m_cell_v_ack(c_e_h_2, s0)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1906, 1895])).
% 16.23/10.70 tff(1908,plain,
% 16.23/10.70 (((~![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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1909,plain,
% 16.23/10.70 ((~![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))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1910,plain,
% 16.23/10.70 ((~![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)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 16.23/10.70 tff(1911,plain,
% 16.23/10.70 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1910, 405, 1907])).
% 16.23/10.70 tff(1912,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s1)), introduced(assumption)).
% 16.23/10.70 tff(1913,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s0)), introduced(assumption)).
% 16.23/10.70 tff(1914,plain,
% 16.23/10.70 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1915,plain,
% 16.23/10.70 ($false),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1914, 141, 1913])).
% 16.23/10.70 tff(1916,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.70 tff(1917,assumption,(node6(c_e_h_2, c_j, s0, s1)), introduced(assumption)).
% 16.23/10.70 tff(1918,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s0)), introduced(assumption)).
% 16.23/10.70 tff(1919,plain,
% 16.23/10.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_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)))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1920,plain,
% 16.23/10.70 (((~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)))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1921,plain,
% 16.23/10.70 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 16.23/10.70 inference(monotonicity,[status(thm)],[1920])).
% 16.23/10.70 tff(1922,plain,
% 16.23/10.70 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.23/10.70 inference(transitivity,[status(thm)],[1921, 1919])).
% 16.23/10.70 tff(1923,plain,
% 16.23/10.70 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1924,plain,
% 16.23/10.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node6(c_e_h_2, c_j, s0, s1))),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 16.23/10.70 tff(1925,plain,
% 16.23/10.70 ($false),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1924, 436, 1918, 1912, 1917])).
% 16.23/10.70 tff(1926,plain,((~node6(c_e_h_2, c_j, s0, 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, s1))), inference(lemma,lemma(discharge,[]))).
% 16.23/10.70 tff(1927,plain,
% 16.23/10.70 ((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1))),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1926, 1916])).
% 16.23/10.70 tff(1928,plain,
% 16.23/10.70 (~node6(c_e_h_2, c_j, s0, s1)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1927, 1912])).
% 16.23/10.70 tff(1929,plain,
% 16.23/10.70 (((~![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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1930,plain,
% 16.23/10.70 ((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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1931,plain,
% 16.23/10.70 (((~![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)))),
% 16.23/10.70 inference(monotonicity,[status(thm)],[1930])).
% 16.23/10.70 tff(1932,plain,
% 16.23/10.70 (((~![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))),
% 16.23/10.70 inference(transitivity,[status(thm)],[1931, 1929])).
% 16.23/10.70 tff(1933,plain,
% 16.23/10.70 ((~![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)))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1934,plain,
% 16.23/10.70 ((~![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)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1933, 1932])).
% 16.23/10.70 tff(1935,plain,
% 16.23/10.70 (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1934, 455, 102])).
% 16.23/10.70 tff(1936,plain,
% 16.23/10.70 (node5(c_e_h_2, c_j, s0, s1)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1935, 1928])).
% 16.23/10.70 tff(1937,plain,
% 16.23/10.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, 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_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1938,plain,
% 16.23/10.70 ((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)) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1939,plain,
% 16.23/10.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0)))),
% 16.23/10.70 inference(monotonicity,[status(thm)],[1938])).
% 16.23/10.70 tff(1940,plain,
% 16.23/10.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0))),
% 16.23/10.70 inference(transitivity,[status(thm)],[1939, 1937])).
% 16.23/10.70 tff(1941,plain,
% 16.23/10.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1942,plain,
% 16.23/10.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1941, 1940])).
% 16.23/10.70 tff(1943,plain,
% 16.23/10.70 ($false),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1942, 473, 1912, 1936, 1911, 1891])).
% 16.23/10.70 tff(1944,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.70 tff(1945,plain,
% 16.23/10.70 (((~![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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1946,plain,
% 16.23/10.70 ((~![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))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1947,plain,
% 16.23/10.70 ((~![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)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 16.23/10.70 tff(1948,plain,
% 16.23/10.70 (~m_c_h_element_v_in2(c_e_h_2, c_h, s1)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1947, 195, 1944])).
% 16.23/10.70 tff(1949,plain,
% 16.23/10.70 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1950,plain,
% 16.23/10.70 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1951,plain,
% 16.23/10.70 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1950, 1949])).
% 16.23/10.70 tff(1952,plain,
% 16.23/10.70 ((~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1951, 209, 1948])).
% 16.23/10.70 tff(1953,plain,
% 16.23/10.70 (~node16(c_e_h_2, c_h, s1)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1952, 1887])).
% 16.23/10.70 tff(1954,plain,
% 16.23/10.70 (((~![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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1955,plain,
% 16.23/10.70 ((~![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))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1956,plain,
% 16.23/10.70 ((~![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)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1955, 1954])).
% 16.23/10.70 tff(1957,plain,
% 16.23/10.70 (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1956, 195, 1916])).
% 16.23/10.70 tff(1958,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s0)), introduced(assumption)).
% 16.23/10.70 tff(1959,plain,
% 16.23/10.70 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1960,plain,
% 16.23/10.70 ($false),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1959, 165, 1958])).
% 16.23/10.70 tff(1961,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.70 tff(1962,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s1)), introduced(assumption)).
% 16.23/10.70 tff(1963,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s0)), introduced(assumption)).
% 16.23/10.70 tff(1964,assumption,(node15(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 16.23/10.70 tff(1965,plain,
% 16.23/10.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1966,plain,
% 16.23/10.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1967,plain,
% 16.23/10.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 16.23/10.70 tff(1968,plain,
% 16.23/10.70 ($false),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1967, 178, 1962, 1963, 1964])).
% 16.23/10.70 tff(1969,plain,((~node15(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.70 tff(1970,plain,
% 16.23/10.70 (~node15(c_e_h_2, c_h, s0, s1)),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1969, 1963, 1962])).
% 16.23/10.70 tff(1971,assumption,(node18(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 16.23/10.70 tff(1972,plain,
% 16.23/10.70 (((~![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_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, 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_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1973,plain,
% 16.23/10.70 (((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, c_h, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)))),
% 16.23/10.70 inference(rewrite,[status(thm)],[])).
% 16.23/10.70 tff(1974,plain,
% 16.23/10.70 (((~![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_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, 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_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1))))),
% 16.23/10.70 inference(monotonicity,[status(thm)],[1973])).
% 16.23/10.70 tff(1975,plain,
% 16.23/10.70 (((~![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_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, 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_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)))),
% 16.23/10.70 inference(transitivity,[status(thm)],[1974, 1972])).
% 16.23/10.70 tff(1976,plain,
% 16.23/10.70 ((~![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_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, c_h, s0, s1)))),
% 16.23/10.70 inference(quant_inst,[status(thm)],[])).
% 16.23/10.70 tff(1977,plain,
% 16.23/10.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1))),
% 16.23/10.70 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 16.23/10.70 tff(1978,plain,
% 16.23/10.70 ($false),
% 16.23/10.70 inference(unit_resolution,[status(thm)],[1977, 560, 1962, 1963, 1971])).
% 16.23/10.71 tff(1979,plain,((~node18(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.71 tff(1980,plain,
% 16.23/10.71 (~node18(c_e_h_2, c_h, s0, s1)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[1979, 1963, 1962])).
% 16.23/10.71 tff(1981,plain,
% 16.23/10.71 (((~![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))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(1982,plain,
% 16.23/10.71 ((~![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))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(1983,plain,
% 16.23/10.71 ((~![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)),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 16.23/10.71 tff(1984,plain,
% 16.23/10.71 (node19(c_e_h_2, c_h, s0, s1)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[1983, 221, 102])).
% 16.23/10.71 tff(1985,plain,
% 16.23/10.71 (((~![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_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node18(c_e_h_2, 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)))) | node17(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node18(c_e_h_2, c_h, s0, s1))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(1986,plain,
% 16.23/10.71 ((node17(c_e_h_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1))) <=> (node17(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node18(c_e_h_2, c_h, s0, s1))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(1987,plain,
% 16.23/10.71 (((~![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_2, c_h, s0) | node18(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] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node18(c_e_h_2, c_h, s0, s1)))),
% 16.23/10.71 inference(monotonicity,[status(thm)],[1986])).
% 16.23/10.71 tff(1988,plain,
% 16.23/10.71 (((~![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_2, c_h, s0) | node18(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] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node18(c_e_h_2, c_h, s0, s1))),
% 16.23/10.71 inference(transitivity,[status(thm)],[1987, 1985])).
% 16.23/10.71 tff(1989,plain,
% 16.23/10.71 ((~![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_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(1990,plain,
% 16.23/10.71 ((~![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_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node18(c_e_h_2, c_h, s0, s1)),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 16.23/10.71 tff(1991,plain,
% 16.23/10.71 (node17(c_e_h_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[1990, 542, 1984])).
% 16.23/10.71 tff(1992,plain,
% 16.23/10.71 (node17(c_e_h_2, c_h, s0)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[1991, 1980])).
% 16.23/10.71 tff(1993,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s0)), introduced(assumption)).
% 16.23/10.71 tff(1994,plain,
% 16.23/10.71 (((~![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_2, c_h, s0)) | (~node17(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] : ((~m_c_h_element_v_in1(I0, 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, s0)) | (~node17(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(1995,plain,
% 16.23/10.71 (((~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) | (~node17(c_e_h_2, c_h, s0))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(1996,plain,
% 16.23/10.71 (((~![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_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, 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_in1(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0)))),
% 16.23/10.71 inference(monotonicity,[status(thm)],[1995])).
% 16.23/10.71 tff(1997,plain,
% 16.23/10.71 (((~![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_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, 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_in1(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 16.23/10.71 inference(transitivity,[status(thm)],[1996, 1994])).
% 16.23/10.71 tff(1998,plain,
% 16.23/10.71 ((~![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_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(1999,plain,
% 16.23/10.71 ((~![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_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 16.23/10.71 tff(2000,plain,
% 16.23/10.71 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0))),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[1999, 524, 1993])).
% 16.23/10.71 tff(2001,plain,
% 16.23/10.71 (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2000, 1992])).
% 16.23/10.71 tff(2002,plain,
% 16.23/10.71 (((~![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_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))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2003,plain,
% 16.23/10.71 ((~![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_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))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(2004,plain,
% 16.23/10.71 ((~![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_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)),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 16.23/10.71 tff(2005,plain,
% 16.23/10.71 ((~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2004, 209, 1993])).
% 16.23/10.71 tff(2006,plain,
% 16.23/10.71 (~node16(c_e_h_2, c_h, s0)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2005, 2001])).
% 16.23/10.71 tff(2007,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s0)), introduced(assumption)).
% 16.23/10.71 tff(2008,assumption,(node14(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 16.23/10.71 tff(2009,plain,
% 16.23/10.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, 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_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)))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2010,plain,
% 16.23/10.71 (((~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_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)))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2011,plain,
% 16.23/10.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_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))))),
% 16.23/10.71 inference(monotonicity,[status(thm)],[2010])).
% 16.23/10.71 tff(2012,plain,
% 16.23/10.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_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)))),
% 16.23/10.71 inference(transitivity,[status(thm)],[2011, 2009])).
% 16.23/10.71 tff(2013,plain,
% 16.23/10.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(2014,plain,
% 16.23/10.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, c_h, s0, s1))),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 16.23/10.71 tff(2015,plain,
% 16.23/10.71 ($false),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2014, 254, 1962, 2008, 2007])).
% 16.23/10.71 tff(2016,plain,((~node14(c_e_h_2, c_h, s0, s1)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.71 tff(2017,plain,
% 16.23/10.71 (~node14(c_e_h_2, c_h, s0, s1)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2016, 2001, 1962])).
% 16.23/10.71 tff(2018,plain,
% 16.23/10.71 (((~![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_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1) | node14(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) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1) | node14(c_e_h_2, c_h, s0, s1))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2019,plain,
% 16.23/10.71 ((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))) <=> (node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1) | node14(c_e_h_2, c_h, s0, s1))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2020,plain,
% 16.23/10.71 (((~![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_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) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1) | node14(c_e_h_2, c_h, s0, s1)))),
% 16.23/10.71 inference(monotonicity,[status(thm)],[2019])).
% 16.23/10.71 tff(2021,plain,
% 16.23/10.71 (((~![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_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) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1) | node14(c_e_h_2, c_h, s0, s1))),
% 16.23/10.71 inference(transitivity,[status(thm)],[2020, 2018])).
% 16.23/10.71 tff(2022,plain,
% 16.23/10.71 ((~![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_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)))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(2023,plain,
% 16.23/10.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1) | node14(c_e_h_2, c_h, s0, s1)),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 16.23/10.71 tff(2024,plain,
% 16.23/10.71 (node16(c_e_h_2, c_h, s0) | node15(c_e_h_2, c_h, s0, s1) | node14(c_e_h_2, c_h, s0, s1)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2023, 235, 1984])).
% 16.23/10.71 tff(2025,plain,
% 16.23/10.71 ($false),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2024, 2017, 2006, 1970])).
% 16.23/10.71 tff(2026,plain,(m_c_h_element_v_out(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_in2(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.71 tff(2027,plain,
% 16.23/10.71 ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2026, 1961])).
% 16.23/10.71 tff(2028,plain,
% 16.23/10.71 (~m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2027, 1957])).
% 16.23/10.71 tff(2029,assumption,(node15(c_e_h_2, c_h, s1, s2)), introduced(assumption)).
% 16.23/10.71 tff(2030,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s1)), introduced(assumption)).
% 16.23/10.71 tff(2031,plain,
% 16.23/10.71 (((~![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_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))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2032,plain,
% 16.23/10.71 ((~![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_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))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(2033,plain,
% 16.23/10.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 16.23/10.71 tff(2034,plain,
% 16.23/10.71 ($false),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2033, 178, 1886, 2030, 2029])).
% 16.23/10.71 tff(2035,plain,((~node15(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_out(c_e_h_2, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.71 tff(2036,plain,
% 16.23/10.71 ((~node15(c_e_h_2, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2035, 2028])).
% 16.23/10.71 tff(2037,plain,
% 16.23/10.71 (~node15(c_e_h_2, c_h, s1, s2)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2036, 1886])).
% 16.23/10.71 tff(2038,assumption,(node14(c_e_h_2, c_h, s1, s2)), introduced(assumption)).
% 16.23/10.71 tff(2039,plain,
% 16.23/10.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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)))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2040,plain,
% 16.23/10.71 (((~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)))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2041,plain,
% 16.23/10.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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))))),
% 16.23/10.71 inference(monotonicity,[status(thm)],[2040])).
% 16.23/10.71 tff(2042,plain,
% 16.23/10.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.23/10.71 inference(transitivity,[status(thm)],[2041, 2039])).
% 16.23/10.71 tff(2043,plain,
% 16.23/10.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(2044,plain,
% 16.23/10.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~node14(c_e_h_2, c_h, s1, s2))),
% 16.23/10.71 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 16.23/10.71 tff(2045,plain,
% 16.23/10.71 ($false),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2044, 254, 1886, 2038, 1887])).
% 16.23/10.71 tff(2046,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,[]))).
% 16.23/10.71 tff(2047,plain,
% 16.23/10.71 (~node14(c_e_h_2, c_h, s1, s2)),
% 16.23/10.71 inference(unit_resolution,[status(thm)],[2046, 1886, 1887])).
% 16.23/10.71 tff(2048,plain,
% 16.23/10.71 (((~![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))),
% 16.23/10.71 inference(rewrite,[status(thm)],[])).
% 16.23/10.71 tff(2049,plain,
% 16.23/10.71 ((~![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))),
% 16.23/10.71 inference(quant_inst,[status(thm)],[])).
% 16.23/10.71 tff(2050,plain,
% 16.23/10.71 ((~![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)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 16.23/10.72 tff(2051,plain,
% 16.23/10.72 (node19(c_e_h_2, c_h, s1, s2)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2050, 221, 348])).
% 16.23/10.72 tff(2052,plain,
% 16.23/10.72 (((~![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_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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2053,plain,
% 16.23/10.72 ((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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2054,plain,
% 16.23/10.72 (((~![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_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)))),
% 16.23/10.72 inference(monotonicity,[status(thm)],[2053])).
% 16.23/10.72 tff(2055,plain,
% 16.23/10.72 (((~![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_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))),
% 16.23/10.72 inference(transitivity,[status(thm)],[2054, 2052])).
% 16.23/10.72 tff(2056,plain,
% 16.23/10.72 ((~![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_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)))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2057,plain,
% 16.23/10.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 16.23/10.72 tff(2058,plain,
% 16.23/10.72 (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2057, 235, 2051])).
% 16.23/10.72 tff(2059,plain,
% 16.23/10.72 ($false),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2058, 2047, 2037, 1953])).
% 16.23/10.72 tff(2060,plain,((~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,[]))).
% 16.23/10.72 tff(2061,plain,
% 16.23/10.72 (m_c_h_element_v_in1(c_e_h_2, c_h, s1)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2060, 1886])).
% 16.23/10.72 tff(2062,assumption,(node18(c_e_h_2, c_h, s1, s2)), introduced(assumption)).
% 16.23/10.72 tff(2063,plain,
% 16.23/10.72 (((~![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_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, 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_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, c_h, s1, s2)))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2064,plain,
% 16.23/10.72 ((~![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_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, c_h, s1, s2)))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2065,plain,
% 16.23/10.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, c_h, s1, s2))),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 16.23/10.72 tff(2066,plain,
% 16.23/10.72 ($false),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2065, 560, 1886, 2030, 2062])).
% 16.23/10.72 tff(2067,plain,((~node18(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_out(c_e_h_2, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.72 tff(2068,plain,
% 16.23/10.72 ((~node18(c_e_h_2, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2067, 2028])).
% 16.23/10.72 tff(2069,plain,
% 16.23/10.72 (~node18(c_e_h_2, c_h, s1, s2)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2068, 1886])).
% 16.23/10.72 tff(2070,plain,
% 16.23/10.72 (((~![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_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, 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)))) | node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2071,plain,
% 16.23/10.72 ((node17(c_e_h_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2))) <=> (node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2072,plain,
% 16.23/10.72 (((~![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_2, c_h, s1) | node18(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] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2)))),
% 16.23/10.72 inference(monotonicity,[status(thm)],[2071])).
% 16.23/10.72 tff(2073,plain,
% 16.23/10.72 (((~![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_2, c_h, s1) | node18(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] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2))),
% 16.23/10.72 inference(transitivity,[status(thm)],[2072, 2070])).
% 16.23/10.72 tff(2074,plain,
% 16.23/10.72 ((~![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_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2075,plain,
% 16.23/10.72 ((~![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_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 16.23/10.72 tff(2076,plain,
% 16.23/10.72 (node17(c_e_h_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2075, 542, 2051])).
% 16.23/10.72 tff(2077,plain,
% 16.23/10.72 (node17(c_e_h_2, c_h, s1)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2076, 2069])).
% 16.23/10.72 tff(2078,plain,
% 16.23/10.72 (((~![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)))) | ((~node17(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] : ((~m_c_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, 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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2079,plain,
% 16.23/10.72 (((~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) | (~node17(c_e_h_2, c_h, s1))) <=> ((~node17(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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2080,plain,
% 16.23/10.72 (((~![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_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~node17(c_e_h_2, 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_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)))),
% 16.23/10.72 inference(monotonicity,[status(thm)],[2079])).
% 16.23/10.72 tff(2081,plain,
% 16.23/10.72 (((~![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_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~node17(c_e_h_2, 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_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))),
% 16.23/10.72 inference(transitivity,[status(thm)],[2080, 2078])).
% 16.23/10.72 tff(2082,plain,
% 16.23/10.72 ((~![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_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~node17(c_e_h_2, c_h, s1)))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2083,plain,
% 16.23/10.72 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 16.23/10.72 tff(2084,plain,
% 16.23/10.72 ((~node17(c_e_h_2, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1))),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2083, 524, 1948])).
% 16.23/10.72 tff(2085,plain,
% 16.23/10.72 ($false),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2084, 2077, 2061])).
% 16.23/10.72 tff(2086,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.72 tff(2087,plain,
% 16.23/10.72 (((~![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_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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2088,plain,
% 16.23/10.72 ((~![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_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2089,plain,
% 16.23/10.72 ((~![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_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 16.23/10.72 tff(2090,plain,
% 16.23/10.72 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2089, 269, 2086])).
% 16.23/10.72 tff(2091,plain,
% 16.23/10.72 (((~![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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2092,plain,
% 16.23/10.72 ((~![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))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2093,plain,
% 16.23/10.72 ((~![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)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 16.23/10.72 tff(2094,plain,
% 16.23/10.72 (~node20(c_e_h_2, c_i, s2)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2093, 283, 2090])).
% 16.23/10.72 tff(2095,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s3)), introduced(assumption)).
% 16.23/10.72 tff(2096,assumption,(~node20(c_e_h_2, c_i, s2)), introduced(assumption)).
% 16.23/10.72 tff(2097,assumption,(node21(c_e_h_2, c_i, s2, s3)), introduced(assumption)).
% 16.23/10.72 tff(2098,plain,
% 16.23/10.72 (((~![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_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)))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2099,plain,
% 16.23/10.72 ((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)))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2100,plain,
% 16.23/10.72 (((~![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_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))))),
% 16.23/10.72 inference(monotonicity,[status(thm)],[2099])).
% 16.23/10.72 tff(2101,plain,
% 16.23/10.72 (((~![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_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)))),
% 16.23/10.72 inference(transitivity,[status(thm)],[2100, 2098])).
% 16.23/10.72 tff(2102,plain,
% 16.23/10.72 ((~![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_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)))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2103,plain,
% 16.23/10.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | node20(c_e_h_2, c_i, s2) | (~node21(c_e_h_2, c_i, s2, s3))),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 16.23/10.72 tff(2104,plain,
% 16.23/10.72 ($false),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2103, 82, 2095, 2097, 2096])).
% 16.23/10.72 tff(2105,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.72 tff(2106,plain,
% 16.23/10.72 (~node21(c_e_h_2, c_i, s2, s3)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2105, 2095, 2094])).
% 16.23/10.72 tff(2107,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s1)), introduced(assumption)).
% 16.23/10.72 tff(2108,plain,
% 16.23/10.72 (((~![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_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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2109,plain,
% 16.23/10.72 ((~![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_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2110,plain,
% 16.23/10.72 ((~![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_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 16.23/10.72 tff(2111,plain,
% 16.23/10.72 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2110, 269, 1961])).
% 16.23/10.72 tff(2112,plain,
% 16.23/10.72 (((~![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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2113,plain,
% 16.23/10.72 ((~![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))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2114,plain,
% 16.23/10.72 ((~![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)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2113, 2112])).
% 16.23/10.72 tff(2115,plain,
% 16.23/10.72 (~node20(c_e_h_2, c_i, s0)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2114, 283, 2111])).
% 16.23/10.72 tff(2116,assumption,(node22(c_e_h_2, c_i, s0, s1)), introduced(assumption)).
% 16.23/10.72 tff(2117,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s0)), introduced(assumption)).
% 16.23/10.72 tff(2118,plain,
% 16.23/10.72 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2119,plain,
% 16.23/10.72 ($false),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2118, 9, 2117])).
% 16.23/10.72 tff(2120,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.72 tff(2121,plain,
% 16.23/10.72 (((~![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_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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2122,plain,
% 16.23/10.72 ((~![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_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))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2123,plain,
% 16.23/10.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 16.23/10.72 tff(2124,plain,
% 16.23/10.72 ($false),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2123, 127, 2120, 2116, 2107])).
% 16.23/10.72 tff(2125,plain,((~node22(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,[]))).
% 16.23/10.72 tff(2126,plain,
% 16.23/10.72 (~node22(c_e_h_2, c_i, s0, s1)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2125, 2107])).
% 16.23/10.72 tff(2127,plain,
% 16.23/10.72 (((~![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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2128,plain,
% 16.23/10.72 ((~![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))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2129,plain,
% 16.23/10.72 ((~![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)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 16.23/10.72 tff(2130,plain,
% 16.23/10.72 (node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2129, 112, 102])).
% 16.23/10.72 tff(2131,plain,
% 16.23/10.72 (node21(c_e_h_2, c_i, s0, s1)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2130, 2126])).
% 16.23/10.72 tff(2132,plain,
% 16.23/10.72 (((~![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_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)))) | 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)))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2133,plain,
% 16.23/10.72 ((~![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_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)))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2134,plain,
% 16.23/10.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1))),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 16.23/10.72 tff(2135,plain,
% 16.23/10.72 ($false),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2134, 82, 2131, 2115, 2107])).
% 16.23/10.72 tff(2136,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.72 tff(2137,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s2)), introduced(assumption)).
% 16.23/10.72 tff(2138,plain,
% 16.23/10.72 (((~![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_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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2139,plain,
% 16.23/10.72 ((~![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_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2140,plain,
% 16.23/10.72 ((~![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_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 16.23/10.72 tff(2141,plain,
% 16.23/10.72 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2140, 269, 2028])).
% 16.23/10.72 tff(2142,plain,
% 16.23/10.72 (((~![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))),
% 16.23/10.72 inference(rewrite,[status(thm)],[])).
% 16.23/10.72 tff(2143,plain,
% 16.23/10.72 ((~![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))),
% 16.23/10.72 inference(quant_inst,[status(thm)],[])).
% 16.23/10.72 tff(2144,plain,
% 16.23/10.72 ((~![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)),
% 16.23/10.72 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 16.23/10.72 tff(2145,plain,
% 16.23/10.72 (~node20(c_e_h_2, c_i, s1)),
% 16.23/10.72 inference(unit_resolution,[status(thm)],[2144, 283, 2141])).
% 16.23/10.73 tff(2146,assumption,(node21(c_e_h_2, c_i, s1, s2)), introduced(assumption)).
% 16.23/10.73 tff(2147,plain,
% 16.23/10.73 (((~![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_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)))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2148,plain,
% 16.23/10.73 ((~![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_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)))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2149,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2))),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 16.23/10.73 tff(2150,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2149, 82, 2146, 2137, 2145])).
% 16.23/10.73 tff(2151,plain,((~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2))), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2152,plain,
% 16.23/10.73 (~node21(c_e_h_2, c_i, s1, s2)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2151, 2137])).
% 16.23/10.73 tff(2153,plain,
% 16.23/10.73 (((~![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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2154,plain,
% 16.23/10.73 ((~![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))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2155,plain,
% 16.23/10.73 ((~![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)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 16.23/10.73 tff(2156,plain,
% 16.23/10.73 (node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2155, 112, 348])).
% 16.23/10.73 tff(2157,plain,
% 16.23/10.73 (node22(c_e_h_2, c_i, s1, s2)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2156, 2152])).
% 16.23/10.73 tff(2158,plain,
% 16.23/10.73 (((~![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_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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2159,plain,
% 16.23/10.73 ((~![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_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))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2160,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 16.23/10.73 tff(2161,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2160, 127, 2157, 2137, 2136])).
% 16.23/10.73 tff(2162,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2163,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s2)), introduced(assumption)).
% 16.23/10.73 tff(2164,assumption,(node22(c_e_h_2, c_i, s2, s3)), introduced(assumption)).
% 16.23/10.73 tff(2165,plain,
% 16.23/10.73 (((~![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_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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2166,plain,
% 16.23/10.73 ((~![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_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))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2167,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 16.23/10.73 tff(2168,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2167, 127, 2095, 2164, 2163])).
% 16.23/10.73 tff(2169,plain,((~node22(c_e_h_2, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2170,plain,
% 16.23/10.73 (~node22(c_e_h_2, c_i, s2, s3)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2169, 2095, 2162])).
% 16.23/10.73 tff(2171,plain,
% 16.23/10.73 (((~![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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2172,plain,
% 16.23/10.73 ((~![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))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2173,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 16.23/10.73 tff(2174,plain,
% 16.23/10.73 (node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2173, 112, 591])).
% 16.23/10.73 tff(2175,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2174, 2170, 2106])).
% 16.23/10.73 tff(2176,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2177,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s3)), introduced(assumption)).
% 16.23/10.73 tff(2178,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s3)), introduced(assumption)).
% 16.23/10.73 tff(2179,plain,
% 16.23/10.73 (((~![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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2180,plain,
% 16.23/10.73 ((~![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))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2181,plain,
% 16.23/10.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 16.23/10.73 tff(2182,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2181, 612, 2178, 2177])).
% 16.23/10.73 tff(2183,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,[]))).
% 16.23/10.73 tff(2184,plain,
% 16.23/10.73 (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2183, 2176])).
% 16.23/10.73 tff(2185,assumption,(m_user_v_req(c_e_h_2, c_u, s0)), introduced(assumption)).
% 16.23/10.73 tff(2186,plain,
% 16.23/10.73 ((~![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))) | (~m_user_v_req(c_e_h_2, c_u, s0))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2187,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2186, 836, 2185])).
% 16.23/10.73 tff(2188,plain,(~m_user_v_req(c_e_h_2, c_u, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2189,plain,
% 16.23/10.73 (((~![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_2, c_a, s0)) | m_user_v_req(c_e_h_2, 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_2, c_a, s0)) | m_user_v_req(c_e_h_2, c_u, s0))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2190,plain,
% 16.23/10.73 ((~![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_2, c_a, s0)) | m_user_v_req(c_e_h_2, c_u, s0))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2191,plain,
% 16.23/10.73 ((~![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_2, c_a, s0)) | m_user_v_req(c_e_h_2, c_u, s0)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 16.23/10.73 tff(2192,plain,
% 16.23/10.73 (~m_mutex_h_half_v_inp(c_e_h_2, c_a, s0)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2191, 846, 2188])).
% 16.23/10.73 tff(2193,assumption,(m_mutex_h_half_v_out(c_e_h_2, c_a, s1)), introduced(assumption)).
% 16.23/10.73 tff(2194,assumption,(~m_mutex_h_half_v_inp(c_e_h_2, c_a, s0)), introduced(assumption)).
% 16.23/10.73 tff(2195,assumption,(m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), introduced(assumption)).
% 16.23/10.73 tff(2196,plain,
% 16.23/10.73 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2197,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2196, 629, 2195])).
% 16.23/10.73 tff(2198,plain,(~m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2199,assumption,(node13(c_e_h_2, c_a, s0, s1)), introduced(assumption)).
% 16.23/10.73 tff(2200,plain,
% 16.23/10.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)) | (~node13(c_e_h_2, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_2, 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_2, c_a, s1)) | (~node13(c_e_h_2, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2201,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)) | (~node13(c_e_h_2, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2202,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)) | (~node13(c_e_h_2, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 16.23/10.73 tff(2203,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2202, 862, 2199, 2198, 2193])).
% 16.23/10.73 tff(2204,plain,((~node13(c_e_h_2, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s1))), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2205,plain,
% 16.23/10.73 (~node13(c_e_h_2, c_a, s0, s1)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2204, 2193])).
% 16.23/10.73 tff(2206,plain,
% 16.23/10.73 (((~![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_2, c_a, s0, s1) | node13(c_e_h_2, 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_2, c_a, s0, s1) | node13(c_e_h_2, c_a, s0, s1))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2207,plain,
% 16.23/10.73 ((~![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_2, c_a, s0, s1) | node13(c_e_h_2, c_a, s0, s1))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2208,plain,
% 16.23/10.73 ((~![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_2, c_a, s0, s1) | node13(c_e_h_2, c_a, s0, s1)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 16.23/10.73 tff(2209,plain,
% 16.23/10.73 (node12(c_e_h_2, c_a, s0, s1) | node13(c_e_h_2, c_a, s0, s1)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2208, 878, 102])).
% 16.23/10.73 tff(2210,plain,
% 16.23/10.73 (node12(c_e_h_2, c_a, s0, s1)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2209, 2205])).
% 16.23/10.73 tff(2211,plain,
% 16.23/10.73 (((~![Y: $i, I0: $i, X: $i, I1: $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_2, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~node12(c_e_h_2, c_a, 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_out(c_e_h_2, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~node12(c_e_h_2, c_a, s0, s1)))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2212,plain,
% 16.23/10.73 (((~node12(c_e_h_2, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s1))) <=> ((~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~node12(c_e_h_2, c_a, s0, s1)))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2213,plain,
% 16.23/10.73 (((~![Y: $i, I0: $i, X: $i, I1: $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_2, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_2, 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_out(c_e_h_2, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~node12(c_e_h_2, c_a, s0, s1))))),
% 16.23/10.73 inference(monotonicity,[status(thm)],[2212])).
% 16.23/10.73 tff(2214,plain,
% 16.23/10.73 (((~![Y: $i, I0: $i, X: $i, I1: $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_2, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_2, 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_out(c_e_h_2, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~node12(c_e_h_2, c_a, s0, s1)))),
% 16.23/10.73 inference(transitivity,[status(thm)],[2213, 2211])).
% 16.23/10.73 tff(2215,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $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_2, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2216,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0) | (~node12(c_e_h_2, c_a, s0, s1))),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 16.23/10.73 tff(2217,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2216, 893, 2210, 2194, 2193])).
% 16.23/10.73 tff(2218,plain,((~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_2, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2219,plain,
% 16.23/10.73 (~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2218, 2192])).
% 16.23/10.73 tff(2220,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_c, s1)), introduced(assumption)).
% 16.23/10.73 tff(2221,assumption,(~m_mutex_h_half_v_out(c_e_h_2, c_a, s1)), introduced(assumption)).
% 16.23/10.73 tff(2222,plain,
% 16.23/10.73 (((~![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, s1)) | m_mutex_h_half_v_out(c_e_h_2, 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_2, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s1))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2223,plain,
% 16.23/10.73 ((~![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, s1)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s1))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2224,plain,
% 16.23/10.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s1)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 16.23/10.73 tff(2225,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2224, 639, 2221, 2220])).
% 16.23/10.73 tff(2226,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2227,plain,
% 16.23/10.73 (~m_and_h_gate_v_in1(c_e_h_2, c_c, s1)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2226, 2219])).
% 16.23/10.73 tff(2228,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_c, s1)), introduced(assumption)).
% 16.23/10.73 tff(2229,assumption,(node20(c_e_h_2, c_c, s1)), introduced(assumption)).
% 16.23/10.73 tff(2230,plain,
% 16.23/10.73 (((~![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, s1)) | m_and_h_gate_v_in1(c_e_h_2, 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_2, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s1))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2231,plain,
% 16.23/10.73 ((~![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, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s1))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2232,plain,
% 16.23/10.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s1)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 16.23/10.73 tff(2233,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2232, 283, 2229, 2228])).
% 16.23/10.73 tff(2234,plain,((~node20(c_e_h_2, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2235,plain,
% 16.23/10.73 (~node20(c_e_h_2, c_c, s1)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2234, 2227])).
% 16.23/10.73 tff(2236,assumption,(m_and_h_gate_v_out(c_e_h_2, c_c, s2)), introduced(assumption)).
% 16.23/10.73 tff(2237,assumption,(m_and_h_gate_v_out(c_e_h_2, c_c, s1)), introduced(assumption)).
% 16.23/10.73 tff(2238,plain,
% 16.23/10.73 (((~![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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2239,plain,
% 16.23/10.73 ((~![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))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2240,plain,
% 16.23/10.73 ((~![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)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 16.23/10.73 tff(2241,plain,
% 16.23/10.73 (~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2240, 639, 2198])).
% 16.23/10.73 tff(2242,plain,
% 16.23/10.73 (((~![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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2243,plain,
% 16.23/10.73 ((~![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))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2244,plain,
% 16.23/10.73 ((~![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)),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2243, 2242])).
% 16.23/10.73 tff(2245,plain,
% 16.23/10.73 (~node20(c_e_h_2, c_c, s0)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2244, 283, 2241])).
% 16.23/10.73 tff(2246,assumption,(node21(c_e_h_2, c_c, s0, s1)), introduced(assumption)).
% 16.23/10.73 tff(2247,plain,
% 16.23/10.73 (((~![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_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)))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2248,plain,
% 16.23/10.73 ((~![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_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)))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2249,plain,
% 16.23/10.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1))),
% 16.23/10.73 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 16.23/10.73 tff(2250,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2249, 82, 2246, 2237, 2245])).
% 16.23/10.73 tff(2251,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,[]))).
% 16.23/10.73 tff(2252,plain,
% 16.23/10.73 (~node21(c_e_h_2, c_c, s0, s1)),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2251, 2237])).
% 16.23/10.73 tff(2253,assumption,(m_and_h_gate_v_out(c_e_h_2, c_c, s0)), introduced(assumption)).
% 16.23/10.73 tff(2254,plain,
% 16.23/10.73 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 16.23/10.73 inference(quant_inst,[status(thm)],[])).
% 16.23/10.73 tff(2255,plain,
% 16.23/10.73 ($false),
% 16.23/10.73 inference(unit_resolution,[status(thm)],[2254, 9, 2253])).
% 16.23/10.73 tff(2256,plain,(~m_and_h_gate_v_out(c_e_h_2, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.73 tff(2257,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_c, s0)), introduced(assumption)).
% 16.23/10.73 tff(2258,assumption,(node22(c_e_h_2, c_c, s0, s1)), introduced(assumption)).
% 16.23/10.73 tff(2259,plain,
% 16.23/10.73 (((~![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_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))),
% 16.23/10.73 inference(rewrite,[status(thm)],[])).
% 16.23/10.73 tff(2260,plain,
% 16.23/10.73 ((~![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_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))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2261,plain,
% 16.23/10.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 16.23/10.74 tff(2262,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2261, 127, 2258, 2257, 2237])).
% 16.23/10.74 tff(2263,plain,((~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 16.23/10.74 tff(2264,plain,
% 16.23/10.74 ((~node22(c_e_h_2, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2263, 2256])).
% 16.23/10.74 tff(2265,plain,
% 16.23/10.74 (~node22(c_e_h_2, c_c, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2264, 2237])).
% 16.23/10.74 tff(2266,plain,
% 16.23/10.74 (((~![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))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2267,plain,
% 16.23/10.74 ((~![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))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2268,plain,
% 16.23/10.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 16.23/10.74 tff(2269,plain,
% 16.23/10.74 (node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2268, 112, 102])).
% 16.23/10.74 tff(2270,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2269, 2265, 2252])).
% 16.23/10.74 tff(2271,plain,(~m_and_h_gate_v_out(c_e_h_2, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.74 tff(2272,assumption,(node22(c_e_h_2, c_c, s1, s2)), introduced(assumption)).
% 16.23/10.74 tff(2273,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_c, s1)), introduced(assumption)).
% 16.23/10.74 tff(2274,plain,
% 16.23/10.74 (((~![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_c, s2)) | (~node22(c_e_h_2, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_c, s2)) | (~node22(c_e_h_2, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2275,plain,
% 16.23/10.74 ((~![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_c, s2)) | (~node22(c_e_h_2, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2276,plain,
% 16.23/10.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2)) | (~node22(c_e_h_2, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 16.23/10.74 tff(2277,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2276, 127, 2273, 2236, 2272])).
% 16.23/10.74 tff(2278,plain,((~node22(c_e_h_2, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2))), inference(lemma,lemma(discharge,[]))).
% 16.23/10.74 tff(2279,plain,
% 16.23/10.74 ((~node22(c_e_h_2, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2))),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2278, 2271])).
% 16.23/10.74 tff(2280,plain,
% 16.23/10.74 (~node22(c_e_h_2, c_c, s1, s2)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2279, 2236])).
% 16.23/10.74 tff(2281,assumption,(~node20(c_e_h_2, c_c, s1)), introduced(assumption)).
% 16.23/10.74 tff(2282,assumption,(node21(c_e_h_2, c_c, s1, s2)), introduced(assumption)).
% 16.23/10.74 tff(2283,plain,
% 16.23/10.74 (((~![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_c, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2)) | (~node21(c_e_h_2, 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_2, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2)) | (~node21(c_e_h_2, c_c, s1, s2)))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2284,plain,
% 16.23/10.74 ((~![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_c, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2)) | (~node21(c_e_h_2, c_c, s1, s2)))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2285,plain,
% 16.23/10.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2)) | (~node21(c_e_h_2, c_c, s1, s2))),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 16.23/10.74 tff(2286,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2285, 82, 2236, 2282, 2281])).
% 16.23/10.74 tff(2287,plain,((~node21(c_e_h_2, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s2)) | node20(c_e_h_2, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.74 tff(2288,plain,
% 16.23/10.74 (~node21(c_e_h_2, c_c, s1, s2)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2287, 2236, 2281])).
% 16.23/10.74 tff(2289,plain,
% 16.23/10.74 (((~![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_c, s1, s2) | node22(c_e_h_2, 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_2, c_c, s1, s2) | node22(c_e_h_2, c_c, s1, s2))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2290,plain,
% 16.23/10.74 ((~![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_c, s1, s2) | node22(c_e_h_2, c_c, s1, s2))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2291,plain,
% 16.23/10.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_c, s1, s2) | node22(c_e_h_2, c_c, s1, s2)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2290, 2289])).
% 16.23/10.74 tff(2292,plain,
% 16.23/10.74 (node21(c_e_h_2, c_c, s1, s2) | node22(c_e_h_2, c_c, s1, s2)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2291, 112, 348])).
% 16.23/10.74 tff(2293,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2292, 2288, 2280])).
% 16.23/10.74 tff(2294,plain,((~m_and_h_gate_v_out(c_e_h_2, c_c, s2)) | node20(c_e_h_2, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.74 tff(2295,plain,
% 16.23/10.74 (~m_and_h_gate_v_out(c_e_h_2, c_c, s2)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2294, 2235])).
% 16.23/10.74 tff(2296,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_c, s2)), introduced(assumption)).
% 16.23/10.74 tff(2297,assumption,(m_c_h_element_v_in1(c_e_h_2, c_e, s2)), introduced(assumption)).
% 16.23/10.74 tff(2298,plain,
% 16.23/10.74 (((~![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, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s2))) <=> ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s2))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2299,plain,
% 16.23/10.74 ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s2))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2300,plain,
% 16.23/10.74 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s2)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 16.23/10.74 tff(2301,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2300, 678, 2297, 2296])).
% 16.23/10.74 tff(2302,plain,((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.74 tff(2303,plain,
% 16.23/10.74 (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2302, 2295])).
% 16.23/10.74 tff(2304,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s2)), introduced(assumption)).
% 16.23/10.74 tff(2305,assumption,(node18(c_e_h_2, c_e, s1, s2)), introduced(assumption)).
% 16.23/10.74 tff(2306,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s1)), introduced(assumption)).
% 16.23/10.74 tff(2307,assumption,(node18(c_e_h_2, c_e, s0, s1)), introduced(assumption)).
% 16.23/10.74 tff(2308,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s0)), introduced(assumption)).
% 16.23/10.74 tff(2309,plain,
% 16.23/10.74 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2310,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2309, 165, 2308])).
% 16.23/10.74 tff(2311,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.74 tff(2312,plain,
% 16.23/10.74 (((~![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_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)))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2313,plain,
% 16.23/10.74 (((~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)))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2314,plain,
% 16.23/10.74 (((~![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_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))))),
% 16.23/10.74 inference(monotonicity,[status(thm)],[2313])).
% 16.23/10.74 tff(2315,plain,
% 16.23/10.74 (((~![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_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)))),
% 16.23/10.74 inference(transitivity,[status(thm)],[2314, 2312])).
% 16.23/10.74 tff(2316,plain,
% 16.23/10.74 ((~![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_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)))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2317,plain,
% 16.23/10.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node18(c_e_h_2, c_e, s0, s1))),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 16.23/10.74 tff(2318,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2317, 560, 2311, 2306, 2307])).
% 16.23/10.74 tff(2319,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,[]))).
% 16.23/10.74 tff(2320,plain,
% 16.23/10.74 (~node18(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2319, 2306])).
% 16.23/10.74 tff(2321,plain,
% 16.23/10.74 (((~![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_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))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2322,plain,
% 16.23/10.74 ((~![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_e, s0, s1))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2323,plain,
% 16.23/10.74 ((~![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_e, s0, s1)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 16.23/10.74 tff(2324,plain,
% 16.23/10.74 (node19(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2323, 221, 102])).
% 16.23/10.74 tff(2325,plain,
% 16.23/10.74 (((~![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_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node18(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)))) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node18(c_e_h_2, c_e, s0, s1))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2326,plain,
% 16.23/10.74 ((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))) <=> (node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node18(c_e_h_2, c_e, s0, s1))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2327,plain,
% 16.23/10.74 (((~![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_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)))) | (node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node18(c_e_h_2, c_e, s0, s1)))),
% 16.23/10.74 inference(monotonicity,[status(thm)],[2326])).
% 16.23/10.74 tff(2328,plain,
% 16.23/10.74 (((~![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_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)))) | node17(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node18(c_e_h_2, c_e, s0, s1))),
% 16.23/10.74 inference(transitivity,[status(thm)],[2327, 2325])).
% 16.23/10.74 tff(2329,plain,
% 16.23/10.74 ((~![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_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2330,plain,
% 16.23/10.74 ((~![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_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node18(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2329, 2328])).
% 16.23/10.74 tff(2331,plain,
% 16.23/10.74 (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2330, 542, 2324])).
% 16.23/10.74 tff(2332,plain,
% 16.23/10.74 (node17(c_e_h_2, c_e, s0)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2331, 2320])).
% 16.23/10.74 tff(2333,plain,
% 16.23/10.74 (((~![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, 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_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2334,plain,
% 16.23/10.74 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2335,plain,
% 16.23/10.74 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 16.23/10.74 tff(2336,plain,
% 16.23/10.74 (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2335, 612, 2120])).
% 16.23/10.74 tff(2337,plain,
% 16.23/10.74 (((~![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_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)))) | (~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)))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2338,plain,
% 16.23/10.74 ((~![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_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)))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2339,plain,
% 16.23/10.74 ((~![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_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))),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 16.23/10.74 tff(2340,plain,
% 16.23/10.74 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0))),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2339, 524, 2336])).
% 16.23/10.74 tff(2341,plain,
% 16.23/10.74 (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2340, 2332])).
% 16.23/10.74 tff(2342,plain,
% 16.23/10.74 (((~![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_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))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2343,plain,
% 16.23/10.74 ((~![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_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))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2344,plain,
% 16.23/10.74 ((~![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_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)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 16.23/10.74 tff(2345,plain,
% 16.23/10.74 ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2344, 209, 2336])).
% 16.23/10.74 tff(2346,plain,
% 16.23/10.74 (~node16(c_e_h_2, c_e, s0)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2345, 2341])).
% 16.23/10.74 tff(2347,assumption,(node15(c_e_h_2, c_e, s0, s1)), introduced(assumption)).
% 16.23/10.74 tff(2348,plain,
% 16.23/10.74 (((~![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_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))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2349,plain,
% 16.23/10.74 ((~![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_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2350,plain,
% 16.23/10.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2349, 2348])).
% 16.23/10.74 tff(2351,plain,
% 16.23/10.74 ($false),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2350, 178, 2311, 2306, 2347])).
% 16.23/10.74 tff(2352,plain,((~node15(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,[]))).
% 16.23/10.74 tff(2353,plain,
% 16.23/10.74 (~node15(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2352, 2306])).
% 16.23/10.74 tff(2354,plain,
% 16.23/10.74 (((~![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_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node15(c_e_h_2, c_e, s0, s1) | node14(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) | (~node19(c_e_h_2, c_e, s0, s1)) | node15(c_e_h_2, c_e, s0, s1) | node14(c_e_h_2, c_e, s0, s1))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2355,plain,
% 16.23/10.74 ((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))) <=> (node16(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node15(c_e_h_2, c_e, s0, s1) | node14(c_e_h_2, c_e, s0, s1))),
% 16.23/10.74 inference(rewrite,[status(thm)],[])).
% 16.23/10.74 tff(2356,plain,
% 16.23/10.74 (((~![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_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) | (~node19(c_e_h_2, c_e, s0, s1)) | node15(c_e_h_2, c_e, s0, s1) | node14(c_e_h_2, c_e, s0, s1)))),
% 16.23/10.74 inference(monotonicity,[status(thm)],[2355])).
% 16.23/10.74 tff(2357,plain,
% 16.23/10.74 (((~![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_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) | (~node19(c_e_h_2, c_e, s0, s1)) | node15(c_e_h_2, c_e, s0, s1) | node14(c_e_h_2, c_e, s0, s1))),
% 16.23/10.74 inference(transitivity,[status(thm)],[2356, 2354])).
% 16.23/10.74 tff(2358,plain,
% 16.23/10.74 ((~![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_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)))),
% 16.23/10.74 inference(quant_inst,[status(thm)],[])).
% 16.23/10.74 tff(2359,plain,
% 16.23/10.74 ((~![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_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)) | node15(c_e_h_2, c_e, s0, s1) | node14(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 16.23/10.74 tff(2360,plain,
% 16.23/10.74 (node16(c_e_h_2, c_e, s0) | node15(c_e_h_2, c_e, s0, s1) | node14(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2359, 235, 2324])).
% 16.23/10.74 tff(2361,plain,
% 16.23/10.74 (node14(c_e_h_2, c_e, s0, s1)),
% 16.23/10.74 inference(unit_resolution,[status(thm)],[2360, 2353, 2346])).
% 16.23/10.74 tff(2362,plain,
% 16.23/10.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, 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, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~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_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2363,plain,
% 16.23/10.75 (((~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_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2364,plain,
% 16.23/10.75 (((~![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_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_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))))),
% 16.23/10.75 inference(monotonicity,[status(thm)],[2363])).
% 16.23/10.75 tff(2365,plain,
% 16.23/10.75 (((~![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_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_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 16.23/10.75 inference(transitivity,[status(thm)],[2364, 2362])).
% 16.23/10.75 tff(2366,plain,
% 16.23/10.75 ((~![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_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)))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2367,plain,
% 16.23/10.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 16.23/10.75 tff(2368,plain,
% 16.23/10.75 ($false),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2367, 254, 2306, 2341, 2361])).
% 16.23/10.75 tff(2369,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.75 tff(2370,plain,
% 16.23/10.75 (((~![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_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, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2371,plain,
% 16.23/10.75 ((~![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_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)))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2372,plain,
% 16.23/10.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2))),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 16.23/10.75 tff(2373,plain,
% 16.23/10.75 ($false),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2372, 560, 2304, 2369, 2305])).
% 16.23/10.75 tff(2374,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,[]))).
% 16.23/10.75 tff(2375,plain,
% 16.23/10.75 (~node18(c_e_h_2, c_e, s1, s2)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2374, 2304])).
% 16.23/10.75 tff(2376,plain,
% 16.23/10.75 (((~![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))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2377,plain,
% 16.23/10.75 ((~![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))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2378,plain,
% 16.23/10.75 ((~![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)),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 16.23/10.75 tff(2379,plain,
% 16.23/10.75 (node19(c_e_h_2, c_e, s1, s2)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2378, 221, 348])).
% 16.23/10.75 tff(2380,plain,
% 16.23/10.75 (((~![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_e, s1, s2)) | node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, 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_e, s1, s2)) | node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2381,plain,
% 16.23/10.75 ((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))) <=> ((~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))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2382,plain,
% 16.23/10.75 (((~![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_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)))) | ((~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)))),
% 16.23/10.75 inference(monotonicity,[status(thm)],[2381])).
% 16.23/10.75 tff(2383,plain,
% 16.23/10.75 (((~![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_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)))) | (~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))),
% 16.23/10.75 inference(transitivity,[status(thm)],[2382, 2380])).
% 16.23/10.75 tff(2384,plain,
% 16.23/10.75 ((~![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_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2385,plain,
% 16.23/10.75 ((~![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_e, s1, s2)) | node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 16.23/10.75 tff(2386,plain,
% 16.23/10.75 (node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2385, 542, 2379])).
% 16.23/10.75 tff(2387,plain,
% 16.23/10.75 (node17(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2386, 2375])).
% 16.23/10.75 tff(2388,assumption,(~node16(c_e_h_2, c_e, s1)), introduced(assumption)).
% 16.23/10.75 tff(2389,plain,
% 16.23/10.75 (((~![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))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2390,plain,
% 16.23/10.75 ((~![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))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2391,plain,
% 16.23/10.75 ((~![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)),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 16.23/10.75 tff(2392,plain,
% 16.23/10.75 (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2391, 678, 2271])).
% 16.23/10.75 tff(2393,assumption,(node14(c_e_h_2, c_e, s1, s2)), introduced(assumption)).
% 16.23/10.75 tff(2394,plain,
% 16.23/10.75 (((~![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_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)))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2395,plain,
% 16.23/10.75 (((~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)))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2396,plain,
% 16.23/10.75 (((~![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_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))))),
% 16.23/10.75 inference(monotonicity,[status(thm)],[2395])).
% 16.23/10.75 tff(2397,plain,
% 16.23/10.75 (((~![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_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)))),
% 16.23/10.75 inference(transitivity,[status(thm)],[2396, 2394])).
% 16.23/10.75 tff(2398,plain,
% 16.23/10.75 ((~![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_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)))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2399,plain,
% 16.23/10.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node14(c_e_h_2, c_e, s1, s2))),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 16.23/10.75 tff(2400,plain,
% 16.23/10.75 ($false),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2399, 254, 2304, 2393, 2392])).
% 16.23/10.75 tff(2401,plain,((~node14(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,[]))).
% 16.23/10.75 tff(2402,plain,
% 16.23/10.75 (~node14(c_e_h_2, c_e, s1, s2)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2401, 2304])).
% 16.23/10.75 tff(2403,plain,
% 16.23/10.75 (((~![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)))) | ((~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, 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)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2404,plain,
% 16.23/10.75 ((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))) <=> ((~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2405,plain,
% 16.23/10.75 (((~![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_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)))) | ((~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1)))),
% 16.23/10.75 inference(monotonicity,[status(thm)],[2404])).
% 16.23/10.75 tff(2406,plain,
% 16.23/10.75 (((~![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_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)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1))),
% 16.23/10.75 inference(transitivity,[status(thm)],[2405, 2403])).
% 16.23/10.75 tff(2407,plain,
% 16.23/10.75 ((~![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_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)))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2408,plain,
% 16.23/10.75 ((~![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)))) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2407, 2406])).
% 16.23/10.75 tff(2409,plain,
% 16.23/10.75 (node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | node16(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2408, 235, 2379])).
% 16.23/10.75 tff(2410,plain,
% 16.23/10.75 (node15(c_e_h_2, c_e, s1, s2)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2409, 2402, 2388])).
% 16.23/10.75 tff(2411,plain,
% 16.23/10.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2412,plain,
% 16.23/10.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2413,plain,
% 16.23/10.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2412, 2411])).
% 16.23/10.75 tff(2414,plain,
% 16.23/10.75 ($false),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2413, 178, 2304, 2369, 2410])).
% 16.23/10.75 tff(2415,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | node16(c_e_h_2, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.75 tff(2416,plain,
% 16.23/10.75 (node16(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2415, 2304])).
% 16.23/10.75 tff(2417,assumption,(m_c_h_element_v_in1(c_e_h_2, c_e, s1)), introduced(assumption)).
% 16.23/10.75 tff(2418,plain,
% 16.23/10.75 ($false),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2391, 678, 2271, 2417])).
% 16.23/10.75 tff(2419,plain,(~m_c_h_element_v_in1(c_e_h_2, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.75 tff(2420,plain,
% 16.23/10.75 (((~![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_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))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2421,plain,
% 16.23/10.75 ((~![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_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))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2422,plain,
% 16.23/10.75 ((~![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_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)),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2421, 2420])).
% 16.23/10.75 tff(2423,plain,
% 16.23/10.75 ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2422, 209, 2419])).
% 16.23/10.75 tff(2424,plain,
% 16.23/10.75 (m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2423, 2416])).
% 16.23/10.75 tff(2425,plain,
% 16.23/10.75 (((~![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_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)))),
% 16.23/10.75 inference(rewrite,[status(thm)],[])).
% 16.23/10.75 tff(2426,plain,
% 16.23/10.75 ((~![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_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)))),
% 16.23/10.75 inference(quant_inst,[status(thm)],[])).
% 16.23/10.75 tff(2427,plain,
% 16.23/10.75 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1))),
% 16.23/10.75 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 16.23/10.75 tff(2428,plain,
% 16.23/10.75 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1))),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2427, 767, 2419])).
% 16.23/10.75 tff(2429,plain,
% 16.23/10.75 ($false),
% 16.23/10.75 inference(unit_resolution,[status(thm)],[2428, 2424, 2387])).
% 16.23/10.75 tff(2430,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.75 tff(2431,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s2)), introduced(assumption)).
% 16.23/10.75 tff(2432,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s3)), introduced(assumption)).
% 16.23/10.75 tff(2433,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s2)), introduced(assumption)).
% 16.23/10.75 tff(2434,assumption,(~node14(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 16.23/10.75 tff(2435,assumption,(node15(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 16.23/10.75 tff(2436,plain,
% 16.23/10.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2437,plain,
% 16.23/10.76 ((~![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_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))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2438,plain,
% 16.23/10.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2437, 2436])).
% 16.23/10.76 tff(2439,plain,
% 16.23/10.76 ($false),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2438, 178, 2433, 2435, 2432])).
% 16.23/10.76 tff(2440,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,[]))).
% 16.23/10.76 tff(2441,plain,
% 16.23/10.76 (~node15(c_e_h_2, c_e, s2, s3)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2440, 2432, 2433])).
% 16.23/10.76 tff(2442,plain,
% 16.23/10.76 (((~![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))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2443,plain,
% 16.23/10.76 ((~![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))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2444,plain,
% 16.23/10.76 ((~![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)),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 16.23/10.76 tff(2445,plain,
% 16.23/10.76 (node19(c_e_h_2, c_e, s2, s3)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2444, 221, 591])).
% 16.23/10.76 tff(2446,plain,
% 16.23/10.76 (((~![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)))) | ((~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, 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_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2447,plain,
% 16.23/10.76 ((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))) <=> ((~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2448,plain,
% 16.23/10.76 (((~![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_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)))) | ((~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, s2)))),
% 16.23/10.76 inference(monotonicity,[status(thm)],[2447])).
% 16.23/10.76 tff(2449,plain,
% 16.23/10.76 (((~![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_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)))) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(transitivity,[status(thm)],[2448, 2446])).
% 16.23/10.76 tff(2450,plain,
% 16.23/10.76 ((~![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_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)))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2451,plain,
% 16.23/10.76 ((~![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)))) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 16.23/10.76 tff(2452,plain,
% 16.23/10.76 (node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2451, 235, 2445])).
% 16.23/10.76 tff(2453,plain,
% 16.23/10.76 (node16(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2452, 2441, 2434])).
% 16.23/10.76 tff(2454,plain,
% 16.23/10.76 (((~![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_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))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2455,plain,
% 16.23/10.76 ((~![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_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))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2456,plain,
% 16.23/10.76 ((~![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_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)),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 16.23/10.76 tff(2457,plain,
% 16.23/10.76 ((~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2456, 209, 2431])).
% 16.23/10.76 tff(2458,plain,
% 16.23/10.76 (m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2457, 2453])).
% 16.23/10.76 tff(2459,plain,
% 16.23/10.76 (((~![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_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))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2460,plain,
% 16.23/10.76 ((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))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2461,plain,
% 16.23/10.76 (((~![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_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)))),
% 16.23/10.76 inference(monotonicity,[status(thm)],[2460])).
% 16.23/10.76 tff(2462,plain,
% 16.23/10.76 (((~![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_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))),
% 16.23/10.76 inference(transitivity,[status(thm)],[2461, 2459])).
% 16.23/10.76 tff(2463,plain,
% 16.23/10.76 ((~![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_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)))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2464,plain,
% 16.23/10.76 ((~![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_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)),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 16.23/10.76 tff(2465,plain,
% 16.23/10.76 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2464, 767, 2431])).
% 16.23/10.76 tff(2466,plain,
% 16.23/10.76 (~node17(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2465, 2458])).
% 16.23/10.76 tff(2467,plain,
% 16.23/10.76 (((~![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_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3) | node17(c_e_h_2, c_e, 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_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3) | node17(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2468,plain,
% 16.23/10.76 ((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))) <=> ((~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3) | node17(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2469,plain,
% 16.23/10.76 (((~![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_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)))) | ((~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3) | node17(c_e_h_2, c_e, s2)))),
% 16.23/10.76 inference(monotonicity,[status(thm)],[2468])).
% 16.23/10.76 tff(2470,plain,
% 16.23/10.76 (((~![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_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)))) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3) | node17(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(transitivity,[status(thm)],[2469, 2467])).
% 16.23/10.76 tff(2471,plain,
% 16.23/10.76 ((~![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_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2472,plain,
% 16.23/10.76 ((~![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_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3) | node17(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2471, 2470])).
% 16.23/10.76 tff(2473,plain,
% 16.23/10.76 (node18(c_e_h_2, c_e, s2, s3) | node17(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2472, 542, 2445])).
% 16.23/10.76 tff(2474,plain,
% 16.23/10.76 (node18(c_e_h_2, c_e, s2, s3)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2473, 2466])).
% 16.23/10.76 tff(2475,plain,
% 16.23/10.76 (((~![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_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~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, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2476,plain,
% 16.23/10.76 (((~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))) <=> (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)) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2477,plain,
% 16.23/10.76 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3))))),
% 16.23/10.76 inference(monotonicity,[status(thm)],[2476])).
% 16.23/10.76 tff(2478,plain,
% 16.23/10.76 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 16.23/10.76 inference(transitivity,[status(thm)],[2477, 2475])).
% 16.23/10.76 tff(2479,plain,
% 16.23/10.76 ((~![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_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)))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2480,plain,
% 16.23/10.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3))),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 16.23/10.76 tff(2481,plain,
% 16.23/10.76 ($false),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2480, 560, 2433, 2474, 2432])).
% 16.23/10.76 tff(2482,plain,((~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) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.76 tff(2483,plain,
% 16.23/10.76 (m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2482, 2434, 2432, 2433])).
% 16.23/10.76 tff(2484,assumption,(node18(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 16.23/10.76 tff(2485,plain,
% 16.23/10.76 ($false),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2480, 560, 2433, 2484, 2432])).
% 16.23/10.76 tff(2486,plain,((~node18(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,[]))).
% 16.23/10.76 tff(2487,plain,
% 16.23/10.76 (~node18(c_e_h_2, c_e, s2, s3)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2486, 2433, 2432])).
% 16.23/10.76 tff(2488,plain,
% 16.23/10.76 (node17(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2473, 2487])).
% 16.23/10.76 tff(2489,plain,
% 16.23/10.76 (((~![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_2, c_e, s2) | (~m_c_h_element_v_in1(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) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2490,plain,
% 16.23/10.76 (((~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) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2491,plain,
% 16.23/10.76 (((~![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_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) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))))),
% 16.23/10.76 inference(monotonicity,[status(thm)],[2490])).
% 16.23/10.76 tff(2492,plain,
% 16.23/10.76 (((~![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_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) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))),
% 16.23/10.76 inference(transitivity,[status(thm)],[2491, 2489])).
% 16.23/10.76 tff(2493,plain,
% 16.23/10.76 ((~![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_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)))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2494,plain,
% 16.23/10.76 ((~![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_2, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 16.23/10.76 tff(2495,plain,
% 16.23/10.76 (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))),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2494, 524, 2488])).
% 16.23/10.76 tff(2496,plain,
% 16.23/10.76 (m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2495, 2483])).
% 16.23/10.76 tff(2497,plain,
% 16.23/10.76 (~node15(c_e_h_2, c_e, s2, s3)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2440, 2433, 2432])).
% 16.23/10.76 tff(2498,plain,
% 16.23/10.76 (node16(c_e_h_2, c_e, s2)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2452, 2434, 2497])).
% 16.23/10.76 tff(2499,plain,
% 16.23/10.76 (((~![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_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)))),
% 16.23/10.76 inference(rewrite,[status(thm)],[])).
% 16.23/10.76 tff(2500,plain,
% 16.23/10.76 ((~![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_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)))),
% 16.23/10.76 inference(quant_inst,[status(thm)],[])).
% 16.23/10.76 tff(2501,plain,
% 16.23/10.76 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 16.23/10.76 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 16.23/10.76 tff(2502,plain,
% 16.23/10.76 ($false),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2501, 983, 2498, 2483, 2496])).
% 16.23/10.76 tff(2503,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_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.76 tff(2504,plain,
% 16.23/10.76 (node14(c_e_h_2, c_e, s2, s3)),
% 16.23/10.76 inference(unit_resolution,[status(thm)],[2503, 2432, 2433])).
% 16.23/10.76 tff(2505,assumption,(node14(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 16.23/10.76 tff(2506,plain,
% 16.23/10.76 (((~![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_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~node14(c_e_h_2, 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_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~node14(c_e_h_2, c_e, s2, s3)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2507,plain,
% 16.23/10.77 (((~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)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~node14(c_e_h_2, c_e, s2, s3)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2508,plain,
% 16.23/10.77 (((~![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_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)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~node14(c_e_h_2, c_e, s2, s3))))),
% 16.23/10.77 inference(monotonicity,[status(thm)],[2507])).
% 16.23/10.77 tff(2509,plain,
% 16.23/10.77 (((~![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_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)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~node14(c_e_h_2, c_e, s2, s3)))),
% 16.23/10.77 inference(transitivity,[status(thm)],[2508, 2506])).
% 16.23/10.77 tff(2510,plain,
% 16.23/10.77 ((~![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_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)))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2511,plain,
% 16.23/10.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~node14(c_e_h_2, c_e, s2, s3))),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 16.23/10.77 tff(2512,plain,
% 16.23/10.77 ($false),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2511, 254, 2505, 2432, 2431])).
% 16.23/10.77 tff(2513,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,[]))).
% 16.23/10.77 tff(2514,plain,
% 16.23/10.77 ($false),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2513, 2504, 2432, 2431])).
% 16.23/10.77 tff(2515,plain,((~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) | m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.77 tff(2516,plain,
% 16.23/10.77 (~m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2515, 2430, 2303])).
% 16.23/10.77 tff(2517,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s4)), introduced(assumption)).
% 16.23/10.77 tff(2518,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s3)), introduced(assumption)).
% 16.23/10.77 tff(2519,assumption,(node18(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 16.23/10.77 tff(2520,plain,
% 16.23/10.77 (((~![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_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)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2521,plain,
% 16.23/10.77 (((~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)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2522,plain,
% 16.23/10.77 (((~![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_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))))),
% 16.23/10.77 inference(monotonicity,[status(thm)],[2521])).
% 16.23/10.77 tff(2523,plain,
% 16.23/10.77 (((~![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_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)))),
% 16.23/10.77 inference(transitivity,[status(thm)],[2522, 2520])).
% 16.23/10.77 tff(2524,plain,
% 16.23/10.77 ((~![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_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)))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2525,plain,
% 16.23/10.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4))),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 16.23/10.77 tff(2526,plain,
% 16.23/10.77 ($false),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2525, 560, 2517, 2519, 2518])).
% 16.23/10.77 tff(2527,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,[]))).
% 16.23/10.77 tff(2528,plain,
% 16.23/10.77 (~node18(c_e_h_2, c_e, s3, s4)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2527, 2518, 2517])).
% 16.23/10.77 tff(2529,plain,
% 16.23/10.77 (((~![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))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2530,plain,
% 16.23/10.77 ((~![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))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2531,plain,
% 16.23/10.77 ((~![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)),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 16.23/10.77 tff(2532,plain,
% 16.23/10.77 (node19(c_e_h_2, c_e, s3, s4)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2531, 221, 1013])).
% 16.23/10.77 tff(2533,plain,
% 16.23/10.77 (((~![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_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(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)))) | node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2534,plain,
% 16.23/10.77 ((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))) <=> (node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2535,plain,
% 16.23/10.77 (((~![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_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)))) | (node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4)))),
% 16.23/10.77 inference(monotonicity,[status(thm)],[2534])).
% 16.23/10.77 tff(2536,plain,
% 16.23/10.77 (((~![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_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)))) | node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4))),
% 16.23/10.77 inference(transitivity,[status(thm)],[2535, 2533])).
% 16.23/10.77 tff(2537,plain,
% 16.23/10.77 ((~![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_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2538,plain,
% 16.23/10.77 ((~![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_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4)),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 16.23/10.77 tff(2539,plain,
% 16.23/10.77 (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2538, 542, 2532])).
% 16.23/10.77 tff(2540,plain,
% 16.23/10.77 (node17(c_e_h_2, c_e, s3)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2539, 2528])).
% 16.23/10.77 tff(2541,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s3)), introduced(assumption)).
% 16.23/10.77 tff(2542,assumption,(node14(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 16.23/10.77 tff(2543,plain,
% 16.23/10.77 (((~![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_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)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2544,plain,
% 16.23/10.77 (((~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)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2545,plain,
% 16.23/10.77 (((~![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_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))))),
% 16.23/10.77 inference(monotonicity,[status(thm)],[2544])).
% 16.23/10.77 tff(2546,plain,
% 16.23/10.77 (((~![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_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)))),
% 16.23/10.77 inference(transitivity,[status(thm)],[2545, 2543])).
% 16.23/10.77 tff(2547,plain,
% 16.23/10.77 ((~![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_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)))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2548,plain,
% 16.23/10.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4))),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2547, 2546])).
% 16.23/10.77 tff(2549,plain,
% 16.23/10.77 ($false),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2548, 254, 2517, 2542, 2541])).
% 16.23/10.77 tff(2550,plain,((~node14(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_in1(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 16.23/10.77 tff(2551,plain,
% 16.23/10.77 (~node14(c_e_h_2, c_e, s3, s4)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2550, 2541, 2517])).
% 16.23/10.77 tff(2552,assumption,(node15(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 16.23/10.77 tff(2553,plain,
% 16.23/10.77 (((~![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_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))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2554,plain,
% 16.23/10.77 ((~![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_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))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2555,plain,
% 16.23/10.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2554, 2553])).
% 16.23/10.77 tff(2556,plain,
% 16.23/10.77 ($false),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2555, 178, 2517, 2552, 2518])).
% 16.23/10.77 tff(2557,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,[]))).
% 16.23/10.77 tff(2558,plain,
% 16.23/10.77 (~node15(c_e_h_2, c_e, s3, s4)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2557, 2518, 2517])).
% 16.23/10.77 tff(2559,plain,
% 16.23/10.77 (((~![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_2, c_e, s3) | node14(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))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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) | (~node19(c_e_h_2, c_e, s3, s4)) | node15(c_e_h_2, c_e, s3, s4))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2560,plain,
% 16.23/10.77 ((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))) <=> (node16(c_e_h_2, c_e, s3) | node14(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))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2561,plain,
% 16.23/10.77 (((~![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_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)))) | (node16(c_e_h_2, c_e, s3) | node14(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)))),
% 16.23/10.77 inference(monotonicity,[status(thm)],[2560])).
% 16.23/10.77 tff(2562,plain,
% 16.23/10.77 (((~![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_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)))) | node16(c_e_h_2, c_e, s3) | node14(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))),
% 16.23/10.77 inference(transitivity,[status(thm)],[2561, 2559])).
% 16.23/10.77 tff(2563,plain,
% 16.23/10.77 ((~![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_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)))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2564,plain,
% 16.23/10.77 ((~![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_2, c_e, s3) | node14(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)),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 16.23/10.77 tff(2565,plain,
% 16.23/10.77 (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)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2564, 235, 2532])).
% 16.23/10.77 tff(2566,plain,
% 16.23/10.77 (node16(c_e_h_2, c_e, s3)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2565, 2558, 2551])).
% 16.23/10.77 tff(2567,plain,
% 16.23/10.77 (((~![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_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))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2568,plain,
% 16.23/10.77 ((~![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_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))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2569,plain,
% 16.23/10.77 ((~![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_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)),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2568, 2567])).
% 16.23/10.77 tff(2570,plain,
% 16.23/10.77 ((~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2569, 209, 2541])).
% 16.23/10.77 tff(2571,plain,
% 16.23/10.77 (m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2570, 2566])).
% 16.23/10.77 tff(2572,plain,
% 16.23/10.77 (((~![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)))) | ((~node17(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] : (m_c_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_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2573,plain,
% 16.23/10.77 ((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_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2574,plain,
% 16.23/10.77 (((~![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_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_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3))))),
% 16.23/10.77 inference(monotonicity,[status(thm)],[2573])).
% 16.23/10.77 tff(2575,plain,
% 16.23/10.77 (((~![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_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_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)))),
% 16.23/10.77 inference(transitivity,[status(thm)],[2574, 2572])).
% 16.23/10.77 tff(2576,plain,
% 16.23/10.77 ((~![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_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)))),
% 16.23/10.77 inference(quant_inst,[status(thm)],[])).
% 16.23/10.77 tff(2577,plain,
% 16.23/10.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3))),
% 16.23/10.77 inference(modus_ponens,[status(thm)],[2576, 2575])).
% 16.23/10.77 tff(2578,plain,
% 16.23/10.77 ((~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3))),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2577, 767, 2541])).
% 16.23/10.77 tff(2579,plain,
% 16.23/10.77 ($false),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2578, 2571, 2540])).
% 16.23/10.77 tff(2580,plain,(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, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 16.23/10.77 tff(2581,plain,
% 16.23/10.77 (m_c_h_element_v_in1(c_e_h_2, c_e, s3)),
% 16.23/10.77 inference(unit_resolution,[status(thm)],[2580, 2518, 2517])).
% 16.23/10.77 tff(2582,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s3)), introduced(assumption)).
% 16.23/10.77 tff(2583,plain,
% 16.23/10.77 (((~![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_2, c_e, s3) | (~node17(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)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2584,plain,
% 16.23/10.77 (((~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))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 16.23/10.77 inference(rewrite,[status(thm)],[])).
% 16.23/10.77 tff(2585,plain,
% 16.23/10.77 (((~![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_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)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))))),
% 16.23/10.77 inference(monotonicity,[status(thm)],[2584])).
% 16.23/10.77 tff(2586,plain,
% 16.23/10.77 (((~![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_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)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 16.23/10.77 inference(transitivity,[status(thm)],[2585, 2583])).
% 16.32/10.78 tff(2587,plain,
% 16.32/10.78 ((~![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_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)))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2588,plain,
% 16.32/10.78 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 16.32/10.78 tff(2589,plain,
% 16.32/10.78 ((~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2588, 524, 2582])).
% 16.32/10.78 tff(2590,plain,
% 16.32/10.78 ($false),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2589, 2540, 2581])).
% 16.32/10.78 tff(2591,plain,(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, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 16.32/10.78 tff(2592,plain,
% 16.32/10.78 (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, s4))),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2591, 2516])).
% 16.32/10.78 tff(2593,plain,
% 16.32/10.78 (~m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2592, 2184])).
% 16.32/10.78 tff(2594,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2595,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2596,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 16.32/10.78 tff(2597,plain,
% 16.32/10.78 (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)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2596, 1099])).
% 16.32/10.78 tff(2598,plain,
% 16.32/10.78 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2597, 2593])).
% 16.32/10.78 tff(2599,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2600,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2601,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 16.32/10.78 tff(2602,plain,
% 16.32/10.78 (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)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2601, 1099])).
% 16.32/10.78 tff(2603,plain,
% 16.32/10.78 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2602, 2430])).
% 16.32/10.78 tff(2604,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)), introduced(assumption)).
% 16.32/10.78 tff(2605,assumption,(node11(c_e_h_2, c_n, s2, s3)), introduced(assumption)).
% 16.32/10.78 tff(2606,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), introduced(assumption)).
% 16.32/10.78 tff(2607,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), introduced(assumption)).
% 16.32/10.78 tff(2608,assumption,(node11(c_e_h_2, c_n, s0, s1)), introduced(assumption)).
% 16.32/10.78 tff(2609,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2610,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2611,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 16.32/10.78 tff(2612,plain,
% 16.32/10.78 (m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2611, 1194, 24])).
% 16.32/10.78 tff(2613,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2614,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2615,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 16.32/10.78 tff(2616,plain,
% 16.32/10.78 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2615, 1209, 2612])).
% 16.32/10.78 tff(2617,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2618,plain,
% 16.32/10.78 ((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)))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2619,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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))))),
% 16.32/10.78 inference(monotonicity,[status(thm)],[2618])).
% 16.32/10.78 tff(2620,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.78 inference(transitivity,[status(thm)],[2619, 2617])).
% 16.32/10.78 tff(2621,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2622,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1))),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2621, 2620])).
% 16.32/10.78 tff(2623,plain,
% 16.32/10.78 ($false),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2622, 1223, 2616, 2607, 2608])).
% 16.32/10.78 tff(2624,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,[]))).
% 16.32/10.78 tff(2625,plain,
% 16.32/10.78 (~node11(c_e_h_2, c_n, s0, s1)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2624, 2607])).
% 16.32/10.78 tff(2626,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2627,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2628,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2627, 2626])).
% 16.32/10.78 tff(2629,plain,
% 16.32/10.78 (node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2628, 1179, 102])).
% 16.32/10.78 tff(2630,plain,
% 16.32/10.78 (node10(c_e_h_2, c_n, s0, s1)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2629, 2625])).
% 16.32/10.78 tff(2631,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2632,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2633,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2632, 2631])).
% 16.32/10.78 tff(2634,plain,
% 16.32/10.78 (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)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2633, 1099])).
% 16.32/10.78 tff(2635,plain,
% 16.32/10.78 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2634, 2311])).
% 16.32/10.78 tff(2636,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2637,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2638,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 16.32/10.78 tff(2639,plain,
% 16.32/10.78 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2638, 1145, 46])).
% 16.32/10.78 tff(2640,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2641,plain,
% 16.32/10.78 (((~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)))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2642,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))))),
% 16.32/10.78 inference(monotonicity,[status(thm)],[2641])).
% 16.32/10.78 tff(2643,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 16.32/10.78 inference(transitivity,[status(thm)],[2642, 2640])).
% 16.32/10.78 tff(2644,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2645,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0))),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 16.32/10.78 tff(2646,plain,
% 16.32/10.78 ($false),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2645, 1160, 2639, 2635, 2607, 2630])).
% 16.32/10.78 tff(2647,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 16.32/10.78 tff(2648,assumption,(node11(c_e_h_2, c_n, s1, s2)), introduced(assumption)).
% 16.32/10.78 tff(2649,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), introduced(assumption)).
% 16.32/10.78 tff(2650,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2651,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2652,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 16.32/10.78 tff(2653,plain,
% 16.32/10.78 ($false),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2652, 1223, 2606, 2649, 2648])).
% 16.32/10.78 tff(2654,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,[]))).
% 16.32/10.78 tff(2655,plain,
% 16.32/10.78 ((~node11(c_e_h_2, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2654, 2647])).
% 16.32/10.78 tff(2656,plain,
% 16.32/10.78 (~node11(c_e_h_2, c_n, s1, s2)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2655, 2606])).
% 16.32/10.78 tff(2657,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2658,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2659,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 16.32/10.78 tff(2660,plain,
% 16.32/10.78 (node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2659, 1179, 348])).
% 16.32/10.78 tff(2661,plain,
% 16.32/10.78 (node10(c_e_h_2, c_n, s1, s2)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2660, 2656])).
% 16.32/10.78 tff(2662,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2663,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2664,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2663, 2662])).
% 16.32/10.78 tff(2665,plain,
% 16.32/10.78 (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)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2664, 1099])).
% 16.32/10.78 tff(2666,plain,
% 16.32/10.78 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2665, 2369])).
% 16.32/10.78 tff(2667,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), introduced(assumption)).
% 16.32/10.78 tff(2668,assumption,(node11(c_e_h_2, c_m, s0, s1)), introduced(assumption)).
% 16.32/10.78 tff(2669,plain,
% 16.32/10.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2670,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2671,plain,
% 16.32/10.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 16.32/10.78 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 16.32/10.78 tff(2672,plain,
% 16.32/10.78 ($false),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2671, 1258, 46, 2667, 2668])).
% 16.32/10.78 tff(2673,plain,((~node11(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,[]))).
% 16.32/10.78 tff(2674,plain,
% 16.32/10.78 (~node11(c_e_h_2, c_m, s0, s1)),
% 16.32/10.78 inference(unit_resolution,[status(thm)],[2673, 2667])).
% 16.32/10.78 tff(2675,plain,
% 16.32/10.78 (((~![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))),
% 16.32/10.78 inference(rewrite,[status(thm)],[])).
% 16.32/10.78 tff(2676,plain,
% 16.32/10.78 ((~![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))),
% 16.32/10.78 inference(quant_inst,[status(thm)],[])).
% 16.32/10.78 tff(2677,plain,
% 16.32/10.78 ((~![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)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 16.32/10.79 tff(2678,plain,
% 16.32/10.79 (node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2677, 1179, 102])).
% 16.32/10.79 tff(2679,plain,
% 16.32/10.79 (node10(c_e_h_2, c_m, s0, s1)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2678, 2674])).
% 16.32/10.79 tff(2680,plain,
% 16.32/10.79 (((~![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)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2681,plain,
% 16.32/10.79 ((~![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)))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2682,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 16.32/10.79 tff(2683,plain,
% 16.32/10.79 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2682, 1276, 2616])).
% 16.32/10.79 tff(2684,plain,
% 16.32/10.79 (((~![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))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2685,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2686,plain,
% 16.32/10.79 ((~![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)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 16.32/10.79 tff(2687,plain,
% 16.32/10.79 (~node9(c_e_h_2, c_m, s0)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2686, 1290, 2683])).
% 16.32/10.79 tff(2688,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, 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) | (~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, 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) | (~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2689,plain,
% 16.32/10.79 ((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))) <=> (node9(c_e_h_2, c_m, s0) | (~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2690,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, 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) | (~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))))),
% 16.32/10.79 inference(monotonicity,[status(thm)],[2689])).
% 16.32/10.79 tff(2691,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, 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) | (~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)))),
% 16.32/10.79 inference(transitivity,[status(thm)],[2690, 2688])).
% 16.32/10.79 tff(2692,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, 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)))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2693,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s0) | (~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 16.32/10.79 tff(2694,plain,
% 16.32/10.79 ($false),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2693, 1304, 2687, 2667, 2679])).
% 16.32/10.79 tff(2695,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 16.32/10.79 tff(2696,plain,
% 16.32/10.79 (((~![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))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2697,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2698,plain,
% 16.32/10.79 ((~![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)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2697, 2696])).
% 16.32/10.79 tff(2699,plain,
% 16.32/10.79 (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)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2698, 1145])).
% 16.32/10.79 tff(2700,plain,
% 16.32/10.79 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2699, 2695])).
% 16.32/10.79 tff(2701,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(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, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2702,plain,
% 16.32/10.79 (((~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)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2703,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1))))),
% 16.32/10.79 inference(monotonicity,[status(thm)],[2702])).
% 16.32/10.79 tff(2704,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)))),
% 16.32/10.79 inference(transitivity,[status(thm)],[2703, 2701])).
% 16.32/10.79 tff(2705,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2706,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1))),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 16.32/10.79 tff(2707,plain,
% 16.32/10.79 ($false),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2706, 1160, 2606, 2700, 2666, 2661])).
% 16.32/10.79 tff(2708,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 16.32/10.79 tff(2709,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2710,plain,
% 16.32/10.79 ((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)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2711,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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))))),
% 16.32/10.79 inference(monotonicity,[status(thm)],[2710])).
% 16.32/10.79 tff(2712,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.79 inference(transitivity,[status(thm)],[2711, 2709])).
% 16.32/10.79 tff(2713,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2714,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) | (~node11(c_e_h_2, c_n, s2, s3))),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2713, 2712])).
% 16.32/10.79 tff(2715,plain,
% 16.32/10.79 ($false),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2714, 1223, 2708, 2604, 2605])).
% 16.32/10.79 tff(2716,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)), inference(lemma,lemma(discharge,[]))).
% 16.32/10.79 tff(2717,plain,
% 16.32/10.79 (~node11(c_e_h_2, c_n, s2, s3)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2716, 2604])).
% 16.32/10.79 tff(2718,plain,
% 16.32/10.79 (((~![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))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2719,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2720,plain,
% 16.32/10.79 ((~![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)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 16.32/10.79 tff(2721,plain,
% 16.32/10.79 (node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2720, 1179, 591])).
% 16.32/10.79 tff(2722,plain,
% 16.32/10.79 (node10(c_e_h_2, c_n, s2, s3)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2721, 2717])).
% 16.32/10.79 tff(2723,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)), introduced(assumption)).
% 16.32/10.79 tff(2724,plain,
% 16.32/10.79 (((~![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)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2725,plain,
% 16.32/10.79 ((~![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)))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2726,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 16.32/10.79 tff(2727,plain,
% 16.32/10.79 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2726, 1276, 2647])).
% 16.32/10.79 tff(2728,plain,
% 16.32/10.79 (((~![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))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2729,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2730,plain,
% 16.32/10.79 ((~![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)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2729, 2728])).
% 16.32/10.79 tff(2731,plain,
% 16.32/10.79 (~node9(c_e_h_2, c_m, s1)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2730, 1290, 2727])).
% 16.32/10.79 tff(2732,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), introduced(assumption)).
% 16.32/10.79 tff(2733,assumption,(node11(c_e_h_2, c_m, s1, s2)), introduced(assumption)).
% 16.32/10.79 tff(2734,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), introduced(assumption)).
% 16.32/10.79 tff(2735,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2736,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2737,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2736, 2735])).
% 16.32/10.79 tff(2738,plain,
% 16.32/10.79 ($false),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2737, 1258, 2732, 2734, 2733])).
% 16.32/10.79 tff(2739,plain,((~node11(c_e_h_2, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 16.32/10.79 tff(2740,plain,
% 16.32/10.79 ((~node11(c_e_h_2, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2739, 2695])).
% 16.32/10.79 tff(2741,plain,
% 16.32/10.79 (~node11(c_e_h_2, c_m, s1, s2)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2740, 2732])).
% 16.32/10.79 tff(2742,plain,
% 16.32/10.79 (((~![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))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2743,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2744,plain,
% 16.32/10.79 ((~![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)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 16.32/10.79 tff(2745,plain,
% 16.32/10.79 (node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2744, 1179, 348])).
% 16.32/10.79 tff(2746,plain,
% 16.32/10.79 (node10(c_e_h_2, c_m, s1, s2)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2745, 2741])).
% 16.32/10.79 tff(2747,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, 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)))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2748,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, 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)))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2749,plain,
% 16.32/10.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2))),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2748, 2747])).
% 16.32/10.79 tff(2750,plain,
% 16.32/10.79 ($false),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2749, 1304, 2732, 2746, 2731])).
% 16.32/10.79 tff(2751,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 16.32/10.79 tff(2752,plain,
% 16.32/10.79 (((~![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))),
% 16.32/10.79 inference(rewrite,[status(thm)],[])).
% 16.32/10.79 tff(2753,plain,
% 16.32/10.79 ((~![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))),
% 16.32/10.79 inference(quant_inst,[status(thm)],[])).
% 16.32/10.79 tff(2754,plain,
% 16.32/10.79 ((~![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)),
% 16.32/10.79 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 16.32/10.79 tff(2755,plain,
% 16.32/10.79 (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)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2754, 1145])).
% 16.32/10.79 tff(2756,plain,
% 16.32/10.79 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)),
% 16.32/10.79 inference(unit_resolution,[status(thm)],[2755, 2751])).
% 16.32/10.79 tff(2757,plain,
% 16.32/10.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_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_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, 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_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_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3)))),
% 16.32/10.80 inference(rewrite,[status(thm)],[])).
% 16.32/10.80 tff(2758,plain,
% 16.32/10.80 (((~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_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_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3)))),
% 16.32/10.80 inference(rewrite,[status(thm)],[])).
% 16.32/10.80 tff(2759,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_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_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3))))),
% 16.34/10.80 inference(monotonicity,[status(thm)],[2758])).
% 16.34/10.80 tff(2760,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_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_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3)))),
% 16.34/10.80 inference(transitivity,[status(thm)],[2759, 2757])).
% 16.34/10.80 tff(2761,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2762,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3))),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 16.34/10.80 tff(2763,plain,
% 16.34/10.80 ($false),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2762, 1160, 2756, 2723, 2604, 2722])).
% 16.34/10.80 tff(2764,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,[]))).
% 16.34/10.80 tff(2765,plain,
% 16.34/10.80 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2764, 2603])).
% 16.34/10.80 tff(2766,plain,
% 16.34/10.80 (((~![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)))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2767,plain,
% 16.34/10.80 ((~![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)))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2768,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2767, 2766])).
% 16.34/10.80 tff(2769,plain,
% 16.34/10.80 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2768, 1276, 2765])).
% 16.34/10.80 tff(2770,plain,
% 16.34/10.80 (((~![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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2771,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2772,plain,
% 16.34/10.80 ((~![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)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2771, 2770])).
% 16.34/10.80 tff(2773,plain,
% 16.34/10.80 (~node9(c_e_h_2, c_m, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2772, 1290, 2769])).
% 16.34/10.80 tff(2774,assumption,(~node9(c_e_h_2, c_m, s3)), introduced(assumption)).
% 16.34/10.80 tff(2775,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)), introduced(assumption)).
% 16.34/10.80 tff(2776,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), introduced(assumption)).
% 16.34/10.80 tff(2777,assumption,(node11(c_e_h_2, c_m, s2, s3)), introduced(assumption)).
% 16.34/10.80 tff(2778,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2779,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2780,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 16.34/10.80 tff(2781,plain,
% 16.34/10.80 ($false),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2780, 1258, 2751, 2776, 2777])).
% 16.34/10.80 tff(2782,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,[]))).
% 16.34/10.80 tff(2783,plain,
% 16.34/10.80 (~node11(c_e_h_2, c_m, s2, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2782, 2776])).
% 16.34/10.80 tff(2784,plain,
% 16.34/10.80 (((~![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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2785,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2786,plain,
% 16.34/10.80 ((~![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)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 16.34/10.80 tff(2787,plain,
% 16.34/10.80 (node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2786, 1179, 591])).
% 16.34/10.80 tff(2788,plain,
% 16.34/10.80 (node10(c_e_h_2, c_m, s2, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2787, 2783])).
% 16.34/10.80 tff(2789,plain,
% 16.34/10.80 (((~![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)))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2790,plain,
% 16.34/10.80 ((~![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)))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2791,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 16.34/10.80 tff(2792,plain,
% 16.34/10.80 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2791, 1276, 2708])).
% 16.34/10.80 tff(2793,plain,
% 16.34/10.80 (((~![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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2794,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2795,plain,
% 16.34/10.80 ((~![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)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 16.34/10.80 tff(2796,plain,
% 16.34/10.80 (~node9(c_e_h_2, c_m, s2)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2795, 1290, 2792])).
% 16.34/10.80 tff(2797,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, 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)))) | 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)))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2798,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, 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)))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2799,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3))),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 16.34/10.80 tff(2800,plain,
% 16.34/10.80 ($false),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2799, 1304, 2776, 2796, 2788])).
% 16.34/10.80 tff(2801,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 16.34/10.80 tff(2802,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), introduced(assumption)).
% 16.34/10.80 tff(2803,assumption,(node11(c_e_h_2, c_m, s3, s4)), introduced(assumption)).
% 16.34/10.80 tff(2804,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2805,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2806,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 16.34/10.80 tff(2807,plain,
% 16.34/10.80 ($false),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2806, 1258, 2775, 2803, 2802])).
% 16.34/10.80 tff(2808,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)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 16.34/10.80 tff(2809,plain,
% 16.34/10.80 ((~node11(c_e_h_2, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2808, 2801])).
% 16.34/10.80 tff(2810,plain,
% 16.34/10.80 (~node11(c_e_h_2, c_m, s3, s4)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2809, 2775])).
% 16.34/10.80 tff(2811,plain,
% 16.34/10.80 (((~![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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2812,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2813,plain,
% 16.34/10.80 ((~![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)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 16.34/10.80 tff(2814,plain,
% 16.34/10.80 (node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2813, 1179, 1013])).
% 16.34/10.80 tff(2815,plain,
% 16.34/10.80 (node10(c_e_h_2, c_m, s3, s4)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2814, 2810])).
% 16.34/10.80 tff(2816,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, 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, s4)) | node9(c_e_h_2, c_m, s3) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2817,plain,
% 16.34/10.80 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2818,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, 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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4))))),
% 16.34/10.80 inference(monotonicity,[status(thm)],[2817])).
% 16.34/10.80 tff(2819,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 16.34/10.80 inference(transitivity,[status(thm)],[2818, 2816])).
% 16.34/10.80 tff(2820,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, 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)))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2821,plain,
% 16.34/10.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4))),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2820, 2819])).
% 16.34/10.80 tff(2822,plain,
% 16.34/10.80 ($false),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2821, 1304, 2775, 2815, 2774])).
% 16.34/10.80 tff(2823,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,[]))).
% 16.34/10.80 tff(2824,plain,
% 16.34/10.80 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2823, 2773])).
% 16.34/10.80 tff(2825,plain,
% 16.34/10.80 (((~![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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2826,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2827,plain,
% 16.34/10.80 ((~![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)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 16.34/10.80 tff(2828,plain,
% 16.34/10.80 (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)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2827, 1145])).
% 16.34/10.80 tff(2829,plain,
% 16.34/10.80 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2828, 2824])).
% 16.34/10.80 tff(2830,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)), introduced(assumption)).
% 16.34/10.80 tff(2831,plain,
% 16.34/10.80 (((~![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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2832,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2833,plain,
% 16.34/10.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2832, 2831])).
% 16.34/10.80 tff(2834,plain,
% 16.34/10.80 ($false),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2833, 1099, 2518, 2830])).
% 16.34/10.80 tff(2835,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,[]))).
% 16.34/10.80 tff(2836,plain,
% 16.34/10.80 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2835, 2516])).
% 16.34/10.80 tff(2837,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)), introduced(assumption)).
% 16.34/10.80 tff(2838,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), introduced(assumption)).
% 16.34/10.80 tff(2839,assumption,(node10(c_e_h_2, c_n, s3, s4)), introduced(assumption)).
% 16.34/10.80 tff(2840,plain,
% 16.34/10.80 (((~![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))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2841,plain,
% 16.34/10.80 ((~![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))),
% 16.34/10.80 inference(quant_inst,[status(thm)],[])).
% 16.34/10.80 tff(2842,plain,
% 16.34/10.80 ((~![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)),
% 16.34/10.80 inference(modus_ponens,[status(thm)],[2841, 2840])).
% 16.34/10.80 tff(2843,plain,
% 16.34/10.80 (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)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2842, 1145])).
% 16.34/10.80 tff(2844,plain,
% 16.34/10.80 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)),
% 16.34/10.80 inference(unit_resolution,[status(thm)],[2843, 2801])).
% 16.34/10.80 tff(2845,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2846,plain,
% 16.34/10.80 (((~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)))),
% 16.34/10.80 inference(rewrite,[status(thm)],[])).
% 16.34/10.80 tff(2847,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))))),
% 16.34/10.80 inference(monotonicity,[status(thm)],[2846])).
% 16.34/10.80 tff(2848,plain,
% 16.34/10.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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)))),
% 16.34/10.81 inference(transitivity,[status(thm)],[2847, 2845])).
% 16.34/10.81 tff(2849,plain,
% 16.34/10.81 ((~![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_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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2850,plain,
% 16.34/10.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4))),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2849, 2848])).
% 16.34/10.81 tff(2851,plain,
% 16.34/10.81 ($false),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2850, 1160, 2838, 2844, 2839, 2837])).
% 16.34/10.81 tff(2852,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,[]))).
% 16.34/10.81 tff(2853,plain,
% 16.34/10.81 (~node10(c_e_h_2, c_n, s3, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2852, 2838, 2837])).
% 16.34/10.81 tff(2854,plain,
% 16.34/10.81 (((~![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))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2855,plain,
% 16.34/10.81 ((~![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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2856,plain,
% 16.34/10.81 ((~![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)),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2855, 2854])).
% 16.34/10.81 tff(2857,plain,
% 16.34/10.81 (node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2856, 1179, 1013])).
% 16.34/10.81 tff(2858,plain,
% 16.34/10.81 (node11(c_e_h_2, c_n, s3, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2857, 2853])).
% 16.34/10.81 tff(2859,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)), introduced(assumption)).
% 16.34/10.81 tff(2860,plain,
% 16.34/10.81 (((~![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_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~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, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2861,plain,
% 16.34/10.81 ((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, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2862,plain,
% 16.34/10.81 (((~![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_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, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4))))),
% 16.34/10.81 inference(monotonicity,[status(thm)],[2861])).
% 16.34/10.81 tff(2863,plain,
% 16.34/10.81 (((~![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_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, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 16.34/10.81 inference(transitivity,[status(thm)],[2862, 2860])).
% 16.34/10.81 tff(2864,plain,
% 16.34/10.81 ((~![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_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)))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2865,plain,
% 16.34/10.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4))),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2864, 2863])).
% 16.34/10.81 tff(2866,plain,
% 16.34/10.81 ($false),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2865, 1223, 2859, 2838, 2858])).
% 16.34/10.81 tff(2867,plain,(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, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 16.34/10.81 tff(2868,plain,
% 16.34/10.81 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2867, 2836, 2765])).
% 16.34/10.81 tff(2869,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)), introduced(assumption)).
% 16.34/10.81 tff(2870,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)), introduced(assumption)).
% 16.34/10.81 tff(2871,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)), introduced(assumption)).
% 16.34/10.81 tff(2872,assumption,(node10(c_e_h_2, c_n, s4, s5)), introduced(assumption)).
% 16.34/10.81 tff(2873,plain,
% 16.34/10.81 (((~![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_2, c_n, s5) | (~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)) | (~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_out(c_e_h_2, c_n, s5) | (~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)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2874,plain,
% 16.34/10.81 (((~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_out(c_e_h_2, c_n, s5) | (~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)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2875,plain,
% 16.34/10.81 (((~![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_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_out(c_e_h_2, c_n, s5) | (~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)) | (~node10(c_e_h_2, c_n, s4, s5))))),
% 16.34/10.81 inference(monotonicity,[status(thm)],[2874])).
% 16.34/10.81 tff(2876,plain,
% 16.34/10.81 (((~![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_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_out(c_e_h_2, c_n, s5) | (~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)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 16.34/10.81 inference(transitivity,[status(thm)],[2875, 2873])).
% 16.34/10.81 tff(2877,plain,
% 16.34/10.81 ((~![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_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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2878,plain,
% 16.34/10.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5))),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 16.34/10.81 tff(2879,plain,
% 16.34/10.81 ($false),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2878, 1160, 2871, 2869, 2870, 2872])).
% 16.34/10.81 tff(2880,plain,((~node10(c_e_h_2, c_n, s4, s5)) | 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)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 16.34/10.81 tff(2881,plain,
% 16.34/10.81 (~node10(c_e_h_2, c_n, s4, s5)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2880, 2871, 2870, 2869])).
% 16.34/10.81 tff(2882,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), introduced(assumption)).
% 16.34/10.81 tff(2883,assumption,(node11(c_e_h_2, c_n, s4, s5)), introduced(assumption)).
% 16.34/10.81 tff(2884,plain,
% 16.34/10.81 (((~![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_2, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2885,plain,
% 16.34/10.81 ((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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2886,plain,
% 16.34/10.81 (((~![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_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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5))))),
% 16.34/10.81 inference(monotonicity,[status(thm)],[2885])).
% 16.34/10.81 tff(2887,plain,
% 16.34/10.81 (((~![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_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, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)))),
% 16.34/10.81 inference(transitivity,[status(thm)],[2886, 2884])).
% 16.34/10.81 tff(2888,plain,
% 16.34/10.81 ((~![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_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)))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2889,plain,
% 16.34/10.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5))),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2888, 2887])).
% 16.34/10.81 tff(2890,plain,
% 16.34/10.81 ($false),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2889, 1223, 2871, 2882, 2883])).
% 16.34/10.81 tff(2891,plain,((~node11(c_e_h_2, c_n, s4, 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, s4))), inference(lemma,lemma(discharge,[]))).
% 16.34/10.81 tff(2892,plain,
% 16.34/10.81 (~node11(c_e_h_2, c_n, s4, s5)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2891, 2871, 2882])).
% 16.34/10.81 tff(2893,plain,
% 16.34/10.81 (((~![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))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2894,plain,
% 16.34/10.81 ((~![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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2895,plain,
% 16.34/10.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5)),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 16.34/10.81 tff(2896,plain,
% 16.34/10.81 (node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2895, 1179, 1520])).
% 16.34/10.81 tff(2897,plain,
% 16.34/10.81 ($false),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2896, 2892, 2881])).
% 16.34/10.81 tff(2898,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_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 16.34/10.81 tff(2899,plain,
% 16.34/10.81 (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))),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2898, 2868, 2829])).
% 16.34/10.81 tff(2900,plain,
% 16.34/10.81 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2899, 2598])).
% 16.34/10.81 tff(2901,plain,
% 16.34/10.81 (((~![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_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)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2902,plain,
% 16.34/10.81 ((~![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_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2903,plain,
% 16.34/10.81 ((~![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_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 16.34/10.81 tff(2904,plain,
% 16.34/10.81 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2903, 1276, 2900])).
% 16.34/10.81 tff(2905,plain,
% 16.34/10.81 (((~![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))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2906,plain,
% 16.34/10.81 ((~![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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2907,plain,
% 16.34/10.81 ((~![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)),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 16.34/10.81 tff(2908,plain,
% 16.34/10.81 (~node9(c_e_h_2, c_m, s5)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2907, 1290, 2904])).
% 16.34/10.81 tff(2909,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), introduced(assumption)).
% 16.34/10.81 tff(2910,plain,
% 16.34/10.81 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2602, 2433])).
% 16.34/10.81 tff(2911,plain,
% 16.34/10.81 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2764, 2910])).
% 16.34/10.81 tff(2912,plain,
% 16.34/10.81 (~m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2515, 2433, 2303])).
% 16.34/10.81 tff(2913,plain,
% 16.34/10.81 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2835, 2912])).
% 16.34/10.81 tff(2914,plain,
% 16.34/10.81 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2867, 2913, 2911])).
% 16.34/10.81 tff(2915,plain,
% 16.34/10.81 (((~![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_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)))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2916,plain,
% 16.34/10.81 ((~![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_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2917,plain,
% 16.34/10.81 ((~![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_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2916, 2915])).
% 16.34/10.81 tff(2918,plain,
% 16.34/10.81 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2917, 1276, 2914])).
% 16.34/10.81 tff(2919,plain,
% 16.34/10.81 (((~![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))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2920,plain,
% 16.34/10.81 ((~![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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2921,plain,
% 16.34/10.81 ((~![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)),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2920, 2919])).
% 16.34/10.81 tff(2922,plain,
% 16.34/10.81 (~node9(c_e_h_2, c_m, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2921, 1290, 2918])).
% 16.34/10.81 tff(2923,plain,
% 16.34/10.81 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2768, 1276, 2911])).
% 16.34/10.81 tff(2924,plain,
% 16.34/10.81 (~node9(c_e_h_2, c_m, s3)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2772, 1290, 2923])).
% 16.34/10.81 tff(2925,plain,
% 16.34/10.81 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2823, 2924])).
% 16.34/10.81 tff(2926,assumption,(~node9(c_e_h_2, c_m, s4)), introduced(assumption)).
% 16.34/10.81 tff(2927,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)), introduced(assumption)).
% 16.34/10.81 tff(2928,assumption,(node11(c_e_h_2, c_m, s4, s5)), introduced(assumption)).
% 16.34/10.81 tff(2929,plain,
% 16.34/10.81 (((~![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_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))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2930,plain,
% 16.34/10.81 ((~![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_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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2931,plain,
% 16.34/10.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 16.34/10.81 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 16.34/10.81 tff(2932,plain,
% 16.34/10.81 ($false),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2931, 1258, 2909, 2927, 2928])).
% 16.34/10.81 tff(2933,plain,((~node11(c_e_h_2, c_m, s4, s5)) | (~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, s4)), inference(lemma,lemma(discharge,[]))).
% 16.34/10.81 tff(2934,plain,
% 16.34/10.81 (~node11(c_e_h_2, c_m, s4, s5)),
% 16.34/10.81 inference(unit_resolution,[status(thm)],[2933, 2909, 2927])).
% 16.34/10.81 tff(2935,plain,
% 16.34/10.81 (((~![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))),
% 16.34/10.81 inference(rewrite,[status(thm)],[])).
% 16.34/10.81 tff(2936,plain,
% 16.34/10.81 ((~![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))),
% 16.34/10.81 inference(quant_inst,[status(thm)],[])).
% 16.34/10.81 tff(2937,plain,
% 16.34/10.81 ((~![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)),
% 16.34/10.82 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 16.34/10.82 tff(2938,plain,
% 16.34/10.82 (node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5)),
% 16.34/10.82 inference(unit_resolution,[status(thm)],[2937, 1179, 1520])).
% 16.34/10.82 tff(2939,plain,
% 16.34/10.82 (node10(c_e_h_2, c_m, s4, s5)),
% 16.34/10.82 inference(unit_resolution,[status(thm)],[2938, 2934])).
% 16.34/10.82 tff(2940,plain,
% 16.34/10.82 (((~![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_2, c_m, s5)) | node9(c_e_h_2, c_m, s4) | (~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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4) | (~node10(c_e_h_2, c_m, s4, s5)))),
% 16.34/10.82 inference(rewrite,[status(thm)],[])).
% 16.34/10.82 tff(2941,plain,
% 16.34/10.82 ((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))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4) | (~node10(c_e_h_2, c_m, s4, s5)))),
% 16.34/10.82 inference(rewrite,[status(thm)],[])).
% 16.34/10.82 tff(2942,plain,
% 16.34/10.82 (((~![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_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)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4) | (~node10(c_e_h_2, c_m, s4, s5))))),
% 16.34/10.82 inference(monotonicity,[status(thm)],[2941])).
% 16.34/10.82 tff(2943,plain,
% 16.34/10.82 (((~![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_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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4) | (~node10(c_e_h_2, c_m, s4, s5)))),
% 16.34/10.82 inference(transitivity,[status(thm)],[2942, 2940])).
% 16.34/10.82 tff(2944,plain,
% 16.34/10.82 ((~![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_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)))),
% 16.34/10.82 inference(quant_inst,[status(thm)],[])).
% 16.34/10.82 tff(2945,plain,
% 16.34/10.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4) | (~node10(c_e_h_2, c_m, s4, s5))),
% 16.34/10.82 inference(modus_ponens,[status(thm)],[2944, 2943])).
% 16.34/10.82 tff(2946,plain,
% 16.34/10.82 ($false),
% 16.34/10.82 inference(unit_resolution,[status(thm)],[2945, 1304, 2909, 2939, 2926])).
% 16.36/10.82 tff(2947,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,[]))).
% 16.36/10.82 tff(2948,plain,
% 16.36/10.82 ($false),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2947, 2925, 2922, 2909])).
% 16.36/10.82 tff(2949,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_m, s5))), inference(lemma,lemma(discharge,[]))).
% 16.36/10.82 tff(2950,plain,
% 16.36/10.82 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2949, 2430])).
% 16.36/10.82 tff(2951,assumption,(~node9(c_e_h_2, c_m, s5)), introduced(assumption)).
% 16.36/10.82 tff(2952,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), introduced(assumption)).
% 16.36/10.82 tff(2953,assumption,(node10(c_e_h_2, c_m, s5, s6)), introduced(assumption)).
% 16.36/10.82 tff(2954,plain,
% 16.36/10.82 (((~![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_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)))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2955,plain,
% 16.36/10.82 ((~![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_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)))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2956,plain,
% 16.36/10.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6))),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2955, 2954])).
% 16.36/10.82 tff(2957,plain,
% 16.36/10.82 ($false),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2956, 1304, 2952, 2953, 2951])).
% 16.36/10.82 tff(2958,plain,((~node10(c_e_h_2, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | node9(c_e_h_2, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 16.36/10.82 tff(2959,plain,
% 16.36/10.82 (~node10(c_e_h_2, c_m, s5, s6)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2958, 2952, 2951])).
% 16.36/10.82 tff(2960,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), introduced(assumption)).
% 16.36/10.82 tff(2961,assumption,(node11(c_e_h_2, c_m, s5, s6)), introduced(assumption)).
% 16.36/10.82 tff(2962,plain,
% 16.36/10.82 (((~![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_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))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2963,plain,
% 16.36/10.82 ((~![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_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))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2964,plain,
% 16.36/10.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 16.36/10.82 tff(2965,plain,
% 16.36/10.82 ($false),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2964, 1258, 2960, 2952, 2961])).
% 16.36/10.82 tff(2966,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,[]))).
% 16.36/10.82 tff(2967,plain,
% 16.36/10.82 (~node11(c_e_h_2, c_m, s5, s6)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2966, 2952, 2960])).
% 16.36/10.82 tff(2968,plain,
% 16.36/10.82 (((~![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))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2969,plain,
% 16.36/10.82 ((~![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))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2970,plain,
% 16.36/10.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 16.36/10.82 tff(2971,plain,
% 16.36/10.82 (node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2970, 1179, 1601])).
% 16.36/10.82 tff(2972,plain,
% 16.36/10.82 ($false),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2971, 2967, 2959])).
% 16.36/10.82 tff(2973,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5) | node9(c_e_h_2, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 16.36/10.82 tff(2974,plain,
% 16.36/10.82 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | node9(c_e_h_2, c_m, s5)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2973, 2950])).
% 16.36/10.82 tff(2975,plain,
% 16.36/10.82 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2974, 2908])).
% 16.36/10.82 tff(2976,plain,
% 16.36/10.82 (((~![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_2, c_r, 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_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2977,plain,
% 16.36/10.82 ((~![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_2, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2978,plain,
% 16.36/10.82 ((~![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_2, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 16.36/10.82 tff(2979,plain,
% 16.36/10.82 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s6)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2978, 1625, 2975])).
% 16.36/10.82 tff(2980,plain,
% 16.36/10.82 (((~![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_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, 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_2, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s6))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2981,plain,
% 16.36/10.82 ((~![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_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s6))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2982,plain,
% 16.36/10.82 ((~![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_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s6)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2981, 2980])).
% 16.36/10.82 tff(2983,plain,
% 16.36/10.82 (~node20(c_e_h_2, c_r, s6)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2982, 68, 2979])).
% 16.36/10.82 tff(2984,plain,
% 16.36/10.82 (((~![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_2, c_r, 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_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2985,plain,
% 16.36/10.82 ((~![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_2, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2986,plain,
% 16.36/10.82 ((~![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_2, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 16.36/10.82 tff(2987,plain,
% 16.36/10.82 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s5)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2986, 1625, 2950])).
% 16.36/10.82 tff(2988,plain,
% 16.36/10.82 (((~![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_r, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_r, 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_r, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s5))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2989,plain,
% 16.36/10.82 ((~![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_r, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s5))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2990,plain,
% 16.36/10.82 ((~![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_r, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s5)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2989, 2988])).
% 16.36/10.82 tff(2991,plain,
% 16.36/10.82 (~node20(c_e_h_2, c_r, s5)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2990, 68, 2987])).
% 16.36/10.82 tff(2992,plain,
% 16.36/10.82 (((~![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_2, c_r, 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_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2993,plain,
% 16.36/10.82 ((~![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_2, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2994,plain,
% 16.36/10.82 ((~![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_2, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2993, 2992])).
% 16.36/10.82 tff(2995,plain,
% 16.36/10.82 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s4)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2994, 1625, 2824])).
% 16.36/10.82 tff(2996,plain,
% 16.36/10.82 (((~![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_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, 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_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s4))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(2997,plain,
% 16.36/10.82 ((~![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_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s4))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(2998,plain,
% 16.36/10.82 ((~![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_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s4)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[2997, 2996])).
% 16.36/10.82 tff(2999,plain,
% 16.36/10.82 (~node20(c_e_h_2, c_r, s4)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[2998, 68, 2995])).
% 16.36/10.82 tff(3000,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s5)), introduced(assumption)).
% 16.36/10.82 tff(3001,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s2)), introduced(assumption)).
% 16.36/10.82 tff(3002,assumption,(node22(c_e_h_2, c_r, s1, s2)), introduced(assumption)).
% 16.36/10.82 tff(3003,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s1)), introduced(assumption)).
% 16.36/10.82 tff(3004,assumption,(node21(c_e_h_2, c_r, s0, s1)), introduced(assumption)).
% 16.36/10.82 tff(3005,plain,
% 16.36/10.82 (((~![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_2, c_r, 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_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(3006,plain,
% 16.36/10.82 ((~![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_2, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(3007,plain,
% 16.36/10.82 ((~![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_2, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 16.36/10.82 tff(3008,plain,
% 16.36/10.82 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3007, 1625, 46])).
% 16.36/10.82 tff(3009,plain,
% 16.36/10.82 (((~![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_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, 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_2, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s0))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(3010,plain,
% 16.36/10.82 ((~![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_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s0))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(3011,plain,
% 16.36/10.82 ((~![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_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s0)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[3010, 3009])).
% 16.36/10.82 tff(3012,plain,
% 16.36/10.82 (~node20(c_e_h_2, c_r, s0)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3011, 68, 3008])).
% 16.36/10.82 tff(3013,plain,
% 16.36/10.82 (((~![Y: $i, I0: $i, X: $i, 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_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, 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_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(3014,plain,
% 16.36/10.82 ((node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1))) <=> (node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(3015,plain,
% 16.36/10.82 (((~![Y: $i, I0: $i, X: $i, 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_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, 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_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1))))),
% 16.36/10.82 inference(monotonicity,[status(thm)],[3014])).
% 16.36/10.82 tff(3016,plain,
% 16.36/10.82 (((~![Y: $i, I0: $i, X: $i, 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_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, 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_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)))),
% 16.36/10.82 inference(transitivity,[status(thm)],[3015, 3013])).
% 16.36/10.82 tff(3017,plain,
% 16.36/10.82 ((~![Y: $i, I0: $i, X: $i, 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_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(3018,plain,
% 16.36/10.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[3017, 3016])).
% 16.36/10.82 tff(3019,plain,
% 16.36/10.82 ($false),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3018, 82, 3012, 3004, 3003])).
% 16.36/10.82 tff(3020,plain,((~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1))), inference(lemma,lemma(discharge,[]))).
% 16.36/10.82 tff(3021,plain,
% 16.36/10.82 (~node21(c_e_h_2, c_r, s0, s1)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3020, 3003])).
% 16.36/10.82 tff(3022,plain,
% 16.36/10.82 (((~![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_r, s0, s1) | node22(c_e_h_2, 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_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(3023,plain,
% 16.36/10.82 ((~![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_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(3024,plain,
% 16.36/10.82 ((~![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_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 16.36/10.82 tff(3025,plain,
% 16.36/10.82 (node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3024, 112, 102])).
% 16.36/10.82 tff(3026,plain,
% 16.36/10.82 (node22(c_e_h_2, c_r, s0, s1)),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3025, 3021])).
% 16.36/10.82 tff(3027,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s0)), introduced(assumption)).
% 16.36/10.82 tff(3028,plain,
% 16.36/10.82 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(3029,plain,
% 16.36/10.82 ($false),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3028, 9, 3027])).
% 16.36/10.82 tff(3030,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 16.36/10.82 tff(3031,plain,
% 16.36/10.82 (((~![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_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(3032,plain,
% 16.36/10.82 ((~![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_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(3033,plain,
% 16.36/10.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0)),
% 16.36/10.82 inference(modus_ponens,[status(thm)],[3032, 3031])).
% 16.36/10.82 tff(3034,plain,
% 16.36/10.82 ($false),
% 16.36/10.82 inference(unit_resolution,[status(thm)],[3033, 127, 3030, 3026, 3003])).
% 16.36/10.82 tff(3035,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 16.36/10.82 tff(3036,plain,
% 16.36/10.82 (((~![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_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 16.36/10.82 inference(rewrite,[status(thm)],[])).
% 16.36/10.82 tff(3037,plain,
% 16.36/10.82 ((~![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_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 16.36/10.82 inference(quant_inst,[status(thm)],[])).
% 16.36/10.82 tff(3038,plain,
% 16.36/10.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1)),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 16.36/10.83 tff(3039,plain,
% 16.36/10.83 ($false),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3038, 127, 3035, 3002, 3001])).
% 16.36/10.83 tff(3040,plain,((~node22(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2))), inference(lemma,lemma(discharge,[]))).
% 16.36/10.83 tff(3041,plain,
% 16.36/10.83 (~node22(c_e_h_2, c_r, s1, s2)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3040, 3001])).
% 16.36/10.83 tff(3042,plain,
% 16.36/10.83 (((~![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_r, s1, s2) | node22(c_e_h_2, 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_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3043,plain,
% 16.36/10.83 ((~![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_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3044,plain,
% 16.36/10.83 ((~![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_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2)),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3043, 3042])).
% 16.36/10.83 tff(3045,plain,
% 16.36/10.83 (node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3044, 112, 348])).
% 16.36/10.83 tff(3046,plain,
% 16.36/10.83 (node21(c_e_h_2, c_r, s1, s2)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3045, 3041])).
% 16.36/10.83 tff(3047,plain,
% 16.36/10.83 (((~![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_2, c_r, s1)) | m_c_h_element_v_out(c_e_h_2, 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_2, c_r, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3048,plain,
% 16.36/10.83 ((~![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_2, c_r, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3049,plain,
% 16.36/10.83 ((~![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_2, c_r, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 16.36/10.83 tff(3050,plain,
% 16.36/10.83 (~m_and_h_gate_v_in1(c_e_h_2, c_r, s1)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3049, 1707, 2369])).
% 16.36/10.83 tff(3051,plain,
% 16.36/10.83 (((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_2, 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_2, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s1))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3052,plain,
% 16.36/10.83 ((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s1))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3053,plain,
% 16.36/10.83 ((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s1)),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 16.36/10.83 tff(3054,plain,
% 16.36/10.83 (~node20(c_e_h_2, c_r, s1)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3053, 283, 3050])).
% 16.36/10.83 tff(3055,plain,
% 16.36/10.83 (((~![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_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, 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_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3056,plain,
% 16.36/10.83 ((node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2))) <=> (node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3057,plain,
% 16.36/10.83 (((~![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_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, 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_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2))))),
% 16.36/10.83 inference(monotonicity,[status(thm)],[3056])).
% 16.36/10.83 tff(3058,plain,
% 16.36/10.83 (((~![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_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, 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_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)))),
% 16.36/10.83 inference(transitivity,[status(thm)],[3057, 3055])).
% 16.36/10.83 tff(3059,plain,
% 16.36/10.83 ((~![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_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2)))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3060,plain,
% 16.36/10.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s1) | (~node21(c_e_h_2, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3059, 3058])).
% 16.36/10.83 tff(3061,plain,
% 16.36/10.83 ($false),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3060, 82, 3054, 3046, 3001])).
% 16.36/10.83 tff(3062,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 16.36/10.83 tff(3063,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s3)), introduced(assumption)).
% 16.36/10.83 tff(3064,plain,
% 16.36/10.83 (((~![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_2, c_r, 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_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3065,plain,
% 16.36/10.83 ((~![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_2, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3066,plain,
% 16.36/10.83 ((~![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_2, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3065, 3064])).
% 16.36/10.83 tff(3067,plain,
% 16.36/10.83 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s2)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3066, 1625, 2751])).
% 16.36/10.83 tff(3068,plain,
% 16.36/10.83 (((~![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_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, 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_2, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s2))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3069,plain,
% 16.36/10.83 ((~![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_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s2))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3070,plain,
% 16.36/10.83 ((~![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_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s2)),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3069, 3068])).
% 16.36/10.83 tff(3071,plain,
% 16.36/10.83 (~node20(c_e_h_2, c_r, s2)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3070, 68, 3067])).
% 16.36/10.83 tff(3072,assumption,(~node20(c_e_h_2, c_r, s2)), introduced(assumption)).
% 16.36/10.83 tff(3073,assumption,(node21(c_e_h_2, c_r, s2, s3)), introduced(assumption)).
% 16.36/10.83 tff(3074,plain,
% 16.36/10.83 (((~![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_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, 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)))) | node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3075,plain,
% 16.36/10.83 ((~![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_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3076,plain,
% 16.36/10.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3))),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3075, 3074])).
% 16.36/10.83 tff(3077,plain,
% 16.36/10.83 ($false),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3076, 82, 3073, 3072, 3063])).
% 16.36/10.83 tff(3078,plain,((~node21(c_e_h_2, c_r, s2, s3)) | node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3))), inference(lemma,lemma(discharge,[]))).
% 16.36/10.83 tff(3079,plain,
% 16.36/10.83 ((~node21(c_e_h_2, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3078, 3071])).
% 16.36/10.83 tff(3080,plain,
% 16.36/10.83 (~node21(c_e_h_2, c_r, s2, s3)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3079, 3063])).
% 16.36/10.83 tff(3081,plain,
% 16.36/10.83 (((~![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_r, s2, s3) | node22(c_e_h_2, 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_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3082,plain,
% 16.36/10.83 ((~![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_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.36/10.83 tff(3083,plain,
% 16.36/10.83 ((~![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_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3)),
% 16.36/10.83 inference(modus_ponens,[status(thm)],[3082, 3081])).
% 16.36/10.83 tff(3084,plain,
% 16.36/10.83 (node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3083, 112, 591])).
% 16.36/10.83 tff(3085,plain,
% 16.36/10.83 (node22(c_e_h_2, c_r, s2, s3)),
% 16.36/10.83 inference(unit_resolution,[status(thm)],[3084, 3080])).
% 16.36/10.83 tff(3086,plain,
% 16.36/10.83 (((~![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_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 16.36/10.83 inference(rewrite,[status(thm)],[])).
% 16.36/10.83 tff(3087,plain,
% 16.36/10.83 ((~![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_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 16.36/10.83 inference(quant_inst,[status(thm)],[])).
% 16.37/10.83 tff(3088,plain,
% 16.37/10.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2)),
% 16.37/10.83 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 16.37/10.83 tff(3089,plain,
% 16.37/10.83 ($false),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3088, 127, 3085, 3063, 3062])).
% 16.37/10.83 tff(3090,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.83 tff(3091,plain,
% 16.37/10.83 (((~![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_2, c_r, 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_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 16.37/10.83 inference(rewrite,[status(thm)],[])).
% 16.37/10.83 tff(3092,plain,
% 16.37/10.83 ((~![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_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 16.37/10.83 inference(quant_inst,[status(thm)],[])).
% 16.37/10.83 tff(3093,plain,
% 16.37/10.83 ((~![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_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 16.37/10.83 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 16.37/10.83 tff(3094,plain,
% 16.37/10.83 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3093, 1625, 2801])).
% 16.37/10.83 tff(3095,plain,
% 16.37/10.83 (((~![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_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, 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_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))),
% 16.37/10.83 inference(rewrite,[status(thm)],[])).
% 16.37/10.83 tff(3096,plain,
% 16.37/10.83 ((~![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_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))),
% 16.37/10.83 inference(quant_inst,[status(thm)],[])).
% 16.37/10.83 tff(3097,plain,
% 16.37/10.83 ((~![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_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3)),
% 16.37/10.83 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 16.37/10.83 tff(3098,plain,
% 16.37/10.83 (~node20(c_e_h_2, c_r, s3)),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3097, 68, 3094])).
% 16.37/10.83 tff(3099,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s4)), introduced(assumption)).
% 16.37/10.83 tff(3100,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s3)), introduced(assumption)).
% 16.37/10.83 tff(3101,assumption,(~node20(c_e_h_2, c_r, s3)), introduced(assumption)).
% 16.37/10.83 tff(3102,assumption,(node21(c_e_h_2, c_r, s3, s4)), introduced(assumption)).
% 16.37/10.83 tff(3103,plain,
% 16.37/10.83 (((~![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)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, 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_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 16.37/10.83 inference(rewrite,[status(thm)],[])).
% 16.37/10.83 tff(3104,plain,
% 16.37/10.83 ((node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 16.37/10.83 inference(rewrite,[status(thm)],[])).
% 16.37/10.83 tff(3105,plain,
% 16.37/10.83 (((~![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_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, 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_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4))))),
% 16.37/10.83 inference(monotonicity,[status(thm)],[3104])).
% 16.37/10.83 tff(3106,plain,
% 16.37/10.83 (((~![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_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, 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_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 16.37/10.83 inference(transitivity,[status(thm)],[3105, 3103])).
% 16.37/10.83 tff(3107,plain,
% 16.37/10.83 ((~![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_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 16.37/10.83 inference(quant_inst,[status(thm)],[])).
% 16.37/10.83 tff(3108,plain,
% 16.37/10.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4))),
% 16.37/10.83 inference(modus_ponens,[status(thm)],[3107, 3106])).
% 16.37/10.83 tff(3109,plain,
% 16.37/10.83 ($false),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3108, 82, 3102, 3101, 3099])).
% 16.37/10.83 tff(3110,plain,((~node21(c_e_h_2, c_r, s3, s4)) | node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4))), inference(lemma,lemma(discharge,[]))).
% 16.37/10.83 tff(3111,plain,
% 16.37/10.83 (~node21(c_e_h_2, c_r, s3, s4)),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3110, 3099, 3101])).
% 16.37/10.83 tff(3112,plain,
% 16.37/10.83 (((~![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_r, s3, s4) | node22(c_e_h_2, 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_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))),
% 16.37/10.83 inference(rewrite,[status(thm)],[])).
% 16.37/10.83 tff(3113,plain,
% 16.37/10.83 ((~![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_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))),
% 16.37/10.83 inference(quant_inst,[status(thm)],[])).
% 16.37/10.83 tff(3114,plain,
% 16.37/10.83 ((~![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_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4)),
% 16.37/10.83 inference(modus_ponens,[status(thm)],[3113, 3112])).
% 16.37/10.83 tff(3115,plain,
% 16.37/10.83 (node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4)),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3114, 112, 1013])).
% 16.37/10.83 tff(3116,plain,
% 16.37/10.83 (node22(c_e_h_2, c_r, s3, s4)),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3115, 3111])).
% 16.37/10.83 tff(3117,plain,
% 16.37/10.83 (((~![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_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 16.37/10.83 inference(rewrite,[status(thm)],[])).
% 16.37/10.83 tff(3118,plain,
% 16.37/10.83 ((~![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_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 16.37/10.83 inference(quant_inst,[status(thm)],[])).
% 16.37/10.83 tff(3119,plain,
% 16.37/10.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 16.37/10.83 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 16.37/10.83 tff(3120,plain,
% 16.37/10.83 ($false),
% 16.37/10.83 inference(unit_resolution,[status(thm)],[3119, 127, 3116, 3100, 3099])).
% 16.37/10.84 tff(3121,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3) | node20(c_e_h_2, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3122,plain,
% 16.37/10.84 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3121, 3098])).
% 16.37/10.84 tff(3123,plain,
% 16.37/10.84 (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3122, 3090])).
% 16.37/10.84 tff(3124,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s4)), introduced(assumption)).
% 16.37/10.84 tff(3125,assumption,(node22(c_e_h_2, c_r, s4, s5)), introduced(assumption)).
% 16.37/10.84 tff(3126,plain,
% 16.37/10.84 (((~![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_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3127,plain,
% 16.37/10.84 ((~![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_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3128,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3127, 3126])).
% 16.37/10.84 tff(3129,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3128, 127, 3125, 3124, 3000])).
% 16.37/10.84 tff(3130,plain,((~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5))), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3131,plain,
% 16.37/10.84 ((~node22(c_e_h_2, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3130, 3123])).
% 16.37/10.84 tff(3132,plain,
% 16.37/10.84 (~node22(c_e_h_2, c_r, s4, s5)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3131, 3000])).
% 16.37/10.84 tff(3133,assumption,(~node20(c_e_h_2, c_r, s4)), introduced(assumption)).
% 16.37/10.84 tff(3134,assumption,(node21(c_e_h_2, c_r, s4, s5)), introduced(assumption)).
% 16.37/10.84 tff(3135,plain,
% 16.37/10.84 (((~![Y: $i, I0: $i, X: $i, 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_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, 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_2, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3136,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, 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_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5)))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3137,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3136, 3135])).
% 16.37/10.84 tff(3138,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3137, 82, 3134, 3000, 3133])).
% 16.37/10.84 tff(3139,plain,((~node21(c_e_h_2, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | node20(c_e_h_2, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3140,plain,
% 16.37/10.84 (~node21(c_e_h_2, c_r, s4, s5)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3139, 3000, 3133])).
% 16.37/10.84 tff(3141,plain,
% 16.37/10.84 (((~![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_r, s4, s5) | node22(c_e_h_2, 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_2, c_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3142,plain,
% 16.37/10.84 ((~![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_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3143,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 16.37/10.84 tff(3144,plain,
% 16.37/10.84 (node21(c_e_h_2, c_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3143, 112, 1520])).
% 16.37/10.84 tff(3145,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3144, 3140, 3132])).
% 16.37/10.84 tff(3146,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | node20(c_e_h_2, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3147,plain,
% 16.37/10.84 (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3146, 2999])).
% 16.37/10.84 tff(3148,assumption,(~node20(c_e_h_2, c_r, s5)), introduced(assumption)).
% 16.37/10.84 tff(3149,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s6)), introduced(assumption)).
% 16.37/10.84 tff(3150,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s5)), introduced(assumption)).
% 16.37/10.84 tff(3151,assumption,(node22(c_e_h_2, c_r, s5, s6)), introduced(assumption)).
% 16.37/10.84 tff(3152,plain,
% 16.37/10.84 (((~![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_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3153,plain,
% 16.37/10.84 ((~![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_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3154,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 16.37/10.84 tff(3155,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3154, 127, 3151, 3150, 3149])).
% 16.37/10.84 tff(3156,plain,((~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6))), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3157,plain,
% 16.37/10.84 (~node22(c_e_h_2, c_r, s5, s6)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3156, 3149, 3150])).
% 16.37/10.84 tff(3158,plain,
% 16.37/10.84 (((~![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_r, s5, s6) | node22(c_e_h_2, 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_2, c_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3159,plain,
% 16.37/10.84 ((~![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_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3160,plain,
% 16.37/10.84 ((~![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_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3159, 3158])).
% 16.37/10.84 tff(3161,plain,
% 16.37/10.84 (node21(c_e_h_2, c_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3160, 112, 1601])).
% 16.37/10.84 tff(3162,plain,
% 16.37/10.84 (node21(c_e_h_2, c_r, s5, s6)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3161, 3157])).
% 16.37/10.84 tff(3163,plain,
% 16.37/10.84 (((~![Y: $i, I0: $i, X: $i, 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_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, 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_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3164,plain,
% 16.37/10.84 ((node20(c_e_h_2, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, c_r, s5, s6))) <=> (node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3165,plain,
% 16.37/10.84 (((~![Y: $i, I0: $i, X: $i, 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_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, 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_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6))))),
% 16.37/10.84 inference(monotonicity,[status(thm)],[3164])).
% 16.37/10.84 tff(3166,plain,
% 16.37/10.84 (((~![Y: $i, I0: $i, X: $i, 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_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, 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_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)))),
% 16.37/10.84 inference(transitivity,[status(thm)],[3165, 3163])).
% 16.37/10.84 tff(3167,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, 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_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, c_r, s5, s6)))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3168,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3167, 3166])).
% 16.37/10.84 tff(3169,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3168, 82, 3162, 3149, 3148])).
% 16.37/10.84 tff(3170,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | node20(c_e_h_2, c_r, s5) | m_and_h_gate_v_out(c_e_h_2, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3171,plain,
% 16.37/10.84 (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3170, 3147, 2991])).
% 16.37/10.84 tff(3172,assumption,(~node20(c_e_h_2, c_r, s6)), introduced(assumption)).
% 16.37/10.84 tff(3173,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s7)), introduced(assumption)).
% 16.37/10.84 tff(3174,assumption,(node21(c_e_h_2, c_r, s6, s7)), introduced(assumption)).
% 16.37/10.84 tff(3175,plain,
% 16.37/10.84 (((~![Y: $i, I0: $i, X: $i, 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_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, 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)))) | node20(c_e_h_2, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, c_r, s6, s7)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3176,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, 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_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, c_r, s6, s7)))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3177,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, c_r, s6, s7))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 16.37/10.84 tff(3178,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3177, 82, 3174, 3173, 3172])).
% 16.37/10.84 tff(3179,plain,((~node21(c_e_h_2, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | node20(c_e_h_2, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3180,plain,
% 16.37/10.84 (~node21(c_e_h_2, c_r, s6, s7)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3179, 3173, 3172])).
% 16.37/10.84 tff(3181,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s6)), introduced(assumption)).
% 16.37/10.84 tff(3182,assumption,(node22(c_e_h_2, c_r, s6, s7)), introduced(assumption)).
% 16.37/10.84 tff(3183,plain,
% 16.37/10.84 (((~![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_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3184,plain,
% 16.37/10.84 ((~![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_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3185,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 16.37/10.84 tff(3186,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3185, 127, 3182, 3173, 3181])).
% 16.37/10.84 tff(3187,plain,((~node22(c_e_h_2, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3188,plain,
% 16.37/10.84 (~node22(c_e_h_2, c_r, s6, s7)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3187, 3173, 3181])).
% 16.37/10.84 tff(3189,plain,
% 16.37/10.84 (((~![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_r, s6, s7) | node22(c_e_h_2, 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_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3190,plain,
% 16.37/10.84 ((~![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_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3191,plain,
% 16.37/10.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3190, 3189])).
% 16.37/10.84 tff(3192,plain,
% 16.37/10.84 (node21(c_e_h_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3191, 112, 1843])).
% 16.37/10.84 tff(3193,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3192, 3188, 3180])).
% 16.37/10.84 tff(3194,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6) | node20(c_e_h_2, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3195,plain,
% 16.37/10.84 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | node20(c_e_h_2, c_r, s6)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3194, 3171])).
% 16.37/10.84 tff(3196,plain,
% 16.37/10.84 (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3195, 2983])).
% 16.37/10.84 tff(3197,assumption,(m_user_v_ack(c_e_h_2, c_u, s7)), introduced(assumption)).
% 16.37/10.84 tff(3198,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s7)), introduced(assumption)).
% 16.37/10.84 tff(3199,plain,
% 16.37/10.84 (((~![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_2, c_u, s7)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3200,plain,
% 16.37/10.84 ((~![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_2, c_u, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3201,plain,
% 16.37/10.84 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 16.37/10.84 tff(3202,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3201, 1864, 3198, 3197])).
% 16.37/10.84 tff(3203,plain,((~m_user_v_ack(c_e_h_2, c_u, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3204,plain,
% 16.37/10.84 (~m_user_v_ack(c_e_h_2, c_u, s7)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3203, 3196])).
% 16.37/10.84 tff(3205,assumption,(~m_user_v_ack(c_e_h_2, c_u, s7)), introduced(assumption)).
% 16.37/10.84 tff(3206,assumption,(node25(s7)), introduced(assumption)).
% 16.37/10.84 tff(3207,plain,
% 16.37/10.84 (^[X: $i] : refl((m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))) <=> (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))))),
% 16.37/10.84 inference(bind,[status(th)],[])).
% 16.37/10.84 tff(3208,plain,
% 16.37/10.84 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 16.37/10.84 inference(quant_intro,[status(thm)],[3207])).
% 16.37/10.84 tff(3209,plain,
% 16.37/10.84 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3210,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty5')).
% 16.37/10.84 tff(3211,plain,
% 16.37/10.84 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 16.37/10.84 tff(3212,plain,(
% 16.37/10.84 ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 16.37/10.84 inference(skolemize,[status(sab)],[3211])).
% 16.37/10.84 tff(3213,plain,
% 16.37/10.84 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3212, 3208])).
% 16.37/10.84 tff(3214,plain,
% 16.37/10.84 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s7) | (~node25(s7)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s7) | (~node25(s7)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3215,plain,
% 16.37/10.84 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s7) | (~node25(s7)))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3216,plain,
% 16.37/10.84 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s7) | (~node25(s7))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 16.37/10.84 tff(3217,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3216, 3213, 3206, 3205])).
% 16.37/10.84 tff(3218,plain,((~node25(s7)) | m_user_v_ack(c_e_h_2, c_u, s7)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3219,plain,
% 16.37/10.84 (~node25(s7)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3218, 3204])).
% 16.37/10.84 tff(3220,assumption,(m_user_v_ack(c_e_h_2, c_u, s5)), introduced(assumption)).
% 16.37/10.84 tff(3221,plain,
% 16.37/10.84 (((~![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_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3222,plain,
% 16.37/10.84 ((~![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_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3223,plain,
% 16.37/10.84 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3222, 3221])).
% 16.37/10.84 tff(3224,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3223, 1864, 3150, 3220])).
% 16.37/10.84 tff(3225,plain,((~m_user_v_ack(c_e_h_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3226,plain,
% 16.37/10.84 (~m_user_v_ack(c_e_h_2, c_u, s5)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3225, 3147])).
% 16.37/10.84 tff(3227,assumption,(~m_user_v_ack(c_e_h_2, c_u, s5)), introduced(assumption)).
% 16.37/10.84 tff(3228,assumption,(node25(s5)), introduced(assumption)).
% 16.37/10.84 tff(3229,plain,
% 16.37/10.84 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3230,plain,
% 16.37/10.84 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5)))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3231,plain,
% 16.37/10.84 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 16.37/10.84 tff(3232,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3231, 3213, 3228, 3227])).
% 16.37/10.84 tff(3233,plain,((~node25(s5)) | m_user_v_ack(c_e_h_2, c_u, s5)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3234,plain,
% 16.37/10.84 (~node25(s5)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3233, 3226])).
% 16.37/10.84 tff(3235,assumption,(m_user_v_ack(c_e_h_1, c_u, s5)), introduced(assumption)).
% 16.37/10.84 tff(3236,plain,
% 16.37/10.84 (((~![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))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3237,plain,
% 16.37/10.84 ((~![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))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3238,plain,
% 16.37/10.84 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 16.37/10.84 tff(3239,plain,
% 16.37/10.84 ($false),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3238, 1864, 3235, 1816])).
% 16.37/10.84 tff(3240,plain,((~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.84 tff(3241,plain,
% 16.37/10.84 (~m_user_v_ack(c_e_h_1, c_u, s5)),
% 16.37/10.84 inference(unit_resolution,[status(thm)],[3240, 1793])).
% 16.37/10.84 tff(3242,plain,
% 16.37/10.84 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5)))),
% 16.37/10.84 inference(rewrite,[status(thm)],[])).
% 16.37/10.84 tff(3243,plain,
% 16.37/10.84 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5)))),
% 16.37/10.84 inference(quant_inst,[status(thm)],[])).
% 16.37/10.84 tff(3244,plain,
% 16.37/10.84 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5))),
% 16.37/10.84 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 16.37/10.84 tff(3245,plain,
% 16.37/10.84 (~node24(s5)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3244, 1879, 3241])).
% 16.37/10.85 tff(3246,plain,
% 16.37/10.85 (^[X: $i] : refl((m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))) <=> (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))))),
% 16.37/10.85 inference(bind,[status(th)],[])).
% 16.37/10.85 tff(3247,plain,
% 16.37/10.85 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 16.37/10.85 inference(quant_intro,[status(thm)],[3246])).
% 16.37/10.85 tff(3248,plain,
% 16.37/10.85 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3249,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty1')).
% 16.37/10.85 tff(3250,plain,
% 16.37/10.85 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 16.37/10.85 tff(3251,plain,(
% 16.37/10.85 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 16.37/10.85 inference(skolemize,[status(sab)],[3250])).
% 16.37/10.85 tff(3252,plain,
% 16.37/10.85 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3251, 3247])).
% 16.37/10.85 tff(3253,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3254,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3255,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3254, 3253])).
% 16.37/10.85 tff(3256,plain,
% 16.37/10.85 (~node23(s5)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3255, 3252, 3241])).
% 16.37/10.85 tff(3257,plain,
% 16.37/10.85 (^[X: $i] : refl((node23(X) | node24(X) | node25(X) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X))))),
% 16.37/10.85 inference(bind,[status(th)],[])).
% 16.37/10.85 tff(3258,plain,
% 16.37/10.85 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 16.37/10.85 inference(quant_intro,[status(thm)],[3257])).
% 16.37/10.85 tff(3259,plain,
% 16.37/10.85 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3260,plain,
% 16.37/10.85 (^[X: $i] : trans(monotonicity(rewrite(((node23(X) | node24(X)) | node25(X)) <=> (node23(X) | node24(X) | node25(X))), ((((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> ((node23(X) | node24(X) | node25(X)) | (~node26(X))))), rewrite(((node23(X) | node24(X) | node25(X)) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X)))), ((((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X)))))),
% 16.37/10.85 inference(bind,[status(th)],[])).
% 16.37/10.85 tff(3261,plain,
% 16.37/10.85 (![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 16.37/10.85 inference(quant_intro,[status(thm)],[3260])).
% 16.37/10.85 tff(3262,axiom,(![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty7')).
% 16.37/10.85 tff(3263,plain,
% 16.37/10.85 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 16.37/10.85 tff(3264,plain,
% 16.37/10.85 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3263, 3259])).
% 16.37/10.85 tff(3265,plain,(
% 16.37/10.85 ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 16.37/10.85 inference(skolemize,[status(sab)],[3264])).
% 16.37/10.85 tff(3266,plain,
% 16.37/10.85 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3265, 3258])).
% 16.37/10.85 tff(3267,plain,
% 16.37/10.85 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s5) | node24(s5) | node25(s5) | (~node26(s5)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s5) | node24(s5) | node25(s5) | (~node26(s5)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3268,plain,
% 16.37/10.85 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s5) | node24(s5) | node25(s5) | (~node26(s5)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3269,plain,
% 16.37/10.85 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s5) | node24(s5) | node25(s5) | (~node26(s5))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3268, 3267])).
% 16.37/10.85 tff(3270,plain,
% 16.37/10.85 (node25(s5) | (~node26(s5))),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3269, 3266, 3256, 3245])).
% 16.37/10.85 tff(3271,plain,
% 16.37/10.85 (~node26(s5)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3270, 3234])).
% 16.37/10.85 tff(3272,assumption,(m_user_v_ack(c_e_h_2, c_u, s4)), introduced(assumption)).
% 16.37/10.85 tff(3273,plain,
% 16.37/10.85 (((~![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_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3274,plain,
% 16.37/10.85 ((~![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_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3275,plain,
% 16.37/10.85 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 16.37/10.85 tff(3276,plain,
% 16.37/10.85 ($false),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3275, 1864, 3272, 3124])).
% 16.37/10.85 tff(3277,plain,((~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.85 tff(3278,plain,
% 16.37/10.85 (~m_user_v_ack(c_e_h_2, c_u, s4)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3277, 3123])).
% 16.37/10.85 tff(3279,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3280,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3281,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3280, 3279])).
% 16.37/10.85 tff(3282,plain,
% 16.37/10.85 (~node25(s4)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3281, 3213, 3278])).
% 16.37/10.85 tff(3283,assumption,(m_user_v_ack(c_e_h_1, c_u, s4)), introduced(assumption)).
% 16.37/10.85 tff(3284,plain,
% 16.37/10.85 (((~![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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3285,plain,
% 16.37/10.85 ((~![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))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3286,plain,
% 16.37/10.85 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3285, 3284])).
% 16.37/10.85 tff(3287,plain,
% 16.37/10.85 ($false),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3286, 1864, 3283, 1787])).
% 16.37/10.85 tff(3288,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,[]))).
% 16.37/10.85 tff(3289,plain,
% 16.37/10.85 (~m_user_v_ack(c_e_h_1, c_u, s4)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3288, 1762])).
% 16.37/10.85 tff(3290,assumption,(node26(s4)), introduced(assumption)).
% 16.37/10.85 tff(3291,assumption,(~m_user_v_ack(c_e_h_1, c_u, s4)), introduced(assumption)).
% 16.37/10.85 tff(3292,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3293,plain,
% 16.37/10.85 ((m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4))) <=> ((~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3294,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4)))),
% 16.37/10.85 inference(monotonicity,[status(thm)],[3293])).
% 16.37/10.85 tff(3295,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 16.37/10.85 inference(transitivity,[status(thm)],[3294, 3292])).
% 16.37/10.85 tff(3296,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3297,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 16.37/10.85 tff(3298,plain,
% 16.37/10.85 (~node23(s4)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3297, 3252, 3291])).
% 16.37/10.85 tff(3299,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3300,plain,
% 16.37/10.85 ((m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4))) <=> ((~node24(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3301,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s4)) | m_user_v_ack(c_e_h_1, c_u, s4)))),
% 16.37/10.85 inference(monotonicity,[status(thm)],[3300])).
% 16.37/10.85 tff(3302,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 16.37/10.85 inference(transitivity,[status(thm)],[3301, 3299])).
% 16.37/10.85 tff(3303,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3304,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s4)) | m_user_v_ack(c_e_h_1, c_u, s4)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 16.37/10.85 tff(3305,plain,
% 16.37/10.85 (~node24(s4)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3304, 1879, 3291])).
% 16.37/10.85 tff(3306,assumption,(~node25(s4)), introduced(assumption)).
% 16.37/10.85 tff(3307,plain,
% 16.37/10.85 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3308,plain,
% 16.37/10.85 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3309,plain,
% 16.37/10.85 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s4) | node24(s4) | node25(s4) | (~node26(s4))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 16.37/10.85 tff(3310,plain,
% 16.37/10.85 (node23(s4) | node24(s4) | (~node26(s4))),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3309, 3266, 3306])).
% 16.37/10.85 tff(3311,plain,
% 16.37/10.85 ($false),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3310, 3305, 3298, 3290])).
% 16.37/10.85 tff(3312,plain,(m_user_v_ack(c_e_h_1, c_u, s4) | (~node26(s4)) | node25(s4)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.85 tff(3313,plain,
% 16.37/10.85 ((~node26(s4)) | node25(s4)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3312, 3289])).
% 16.37/10.85 tff(3314,plain,
% 16.37/10.85 (~node26(s4)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3313, 3282])).
% 16.37/10.85 tff(3315,assumption,(m_user_v_ack(c_e_h_1, c_u, s3)), introduced(assumption)).
% 16.37/10.85 tff(3316,plain,
% 16.37/10.85 (((~![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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3317,plain,
% 16.37/10.85 ((~![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))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3318,plain,
% 16.37/10.85 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3317, 3316])).
% 16.37/10.85 tff(3319,plain,
% 16.37/10.85 ($false),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3318, 1864, 3315, 1733])).
% 16.37/10.85 tff(3320,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,[]))).
% 16.37/10.85 tff(3321,plain,
% 16.37/10.85 (~m_user_v_ack(c_e_h_1, c_u, s3)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3320, 1731])).
% 16.37/10.85 tff(3322,plain,
% 16.37/10.85 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3323,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3324,plain,
% 16.37/10.85 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 16.37/10.85 tff(3325,plain,
% 16.37/10.85 (~node23(s3)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3324, 3252, 3321])).
% 16.37/10.85 tff(3326,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 16.37/10.85 tff(3327,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s0)), introduced(assumption)).
% 16.37/10.85 tff(3328,plain,
% 16.37/10.85 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3329,plain,
% 16.37/10.85 ($false),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3328, 9, 3327])).
% 16.37/10.85 tff(3330,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.85 tff(3331,plain,
% 16.37/10.85 (((~![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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3332,plain,
% 16.37/10.85 ((~![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))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3333,plain,
% 16.37/10.85 ((~![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)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3332, 3331])).
% 16.37/10.85 tff(3334,plain,
% 16.37/10.85 (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3333, 678, 3330])).
% 16.37/10.85 tff(3335,assumption,(node14(c_e_h_3, c_e, s0, s1)), introduced(assumption)).
% 16.37/10.85 tff(3336,plain,
% 16.37/10.85 (((~![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_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~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_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3337,plain,
% 16.37/10.85 (((~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_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3338,plain,
% 16.37/10.85 (((~![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_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_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node14(c_e_h_3, c_e, s0, s1))))),
% 16.37/10.85 inference(monotonicity,[status(thm)],[3337])).
% 16.37/10.85 tff(3339,plain,
% 16.37/10.85 (((~![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_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_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 16.37/10.85 inference(transitivity,[status(thm)],[3338, 3336])).
% 16.37/10.85 tff(3340,plain,
% 16.37/10.85 ((~![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_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)))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3341,plain,
% 16.37/10.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node14(c_e_h_3, c_e, s0, s1))),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 16.37/10.85 tff(3342,plain,
% 16.37/10.85 ($false),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3341, 254, 3326, 3335, 3334])).
% 16.37/10.85 tff(3343,plain,((~node14(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,[]))).
% 16.37/10.85 tff(3344,plain,
% 16.37/10.85 (~node14(c_e_h_3, c_e, s0, s1)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3343, 3326])).
% 16.37/10.85 tff(3345,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 16.37/10.85 tff(3346,plain,
% 16.37/10.85 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3347,plain,
% 16.37/10.85 ($false),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3346, 9, 3345])).
% 16.37/10.85 tff(3348,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.85 tff(3349,plain,
% 16.37/10.85 (((~![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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3350,plain,
% 16.37/10.85 ((~![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))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3351,plain,
% 16.37/10.85 ((~![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)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3350, 3349])).
% 16.37/10.85 tff(3352,plain,
% 16.37/10.85 (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3351, 612, 3348])).
% 16.37/10.85 tff(3353,plain,
% 16.37/10.85 (((~![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_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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3354,plain,
% 16.37/10.85 ((~![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_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))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3355,plain,
% 16.37/10.85 ((~![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_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)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3354, 3353])).
% 16.37/10.85 tff(3356,plain,
% 16.37/10.85 ((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3355, 209, 3334])).
% 16.37/10.85 tff(3357,plain,
% 16.37/10.85 (~node16(c_e_h_3, c_e, s0)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3356, 3352])).
% 16.37/10.85 tff(3358,plain,
% 16.37/10.85 (((~![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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3359,plain,
% 16.37/10.85 ((~![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))),
% 16.37/10.85 inference(quant_inst,[status(thm)],[])).
% 16.37/10.85 tff(3360,plain,
% 16.37/10.85 ((~![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)),
% 16.37/10.85 inference(modus_ponens,[status(thm)],[3359, 3358])).
% 16.37/10.85 tff(3361,plain,
% 16.37/10.85 (node19(c_e_h_3, c_e, s0, s1)),
% 16.37/10.85 inference(unit_resolution,[status(thm)],[3360, 221, 102])).
% 16.37/10.85 tff(3362,plain,
% 16.37/10.85 (((~![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_e, s0) | 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))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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) | 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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3363,plain,
% 16.37/10.85 ((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))) <=> (node16(c_e_h_3, c_e, s0) | 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))),
% 16.37/10.85 inference(rewrite,[status(thm)],[])).
% 16.37/10.85 tff(3364,plain,
% 16.37/10.85 (((~![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_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)))) | (node16(c_e_h_3, c_e, s0) | 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)))),
% 16.37/10.86 inference(monotonicity,[status(thm)],[3363])).
% 16.37/10.86 tff(3365,plain,
% 16.37/10.86 (((~![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_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)))) | node16(c_e_h_3, c_e, s0) | 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))),
% 16.37/10.86 inference(transitivity,[status(thm)],[3364, 3362])).
% 16.37/10.86 tff(3366,plain,
% 16.37/10.86 ((~![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_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)))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3367,plain,
% 16.37/10.86 ((~![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_e, s0) | 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)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3366, 3365])).
% 16.37/10.86 tff(3368,plain,
% 16.37/10.86 (node16(c_e_h_3, c_e, s0) | node15(c_e_h_3, c_e, s0, s1) | node14(c_e_h_3, c_e, s0, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3367, 235, 3361])).
% 16.37/10.86 tff(3369,plain,
% 16.37/10.86 (node15(c_e_h_3, c_e, s0, s1) | node14(c_e_h_3, c_e, s0, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3368, 3357])).
% 16.37/10.86 tff(3370,plain,
% 16.37/10.86 (node15(c_e_h_3, c_e, s0, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3369, 3344])).
% 16.37/10.86 tff(3371,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s0)), introduced(assumption)).
% 16.37/10.86 tff(3372,plain,
% 16.37/10.86 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3373,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3372, 165, 3371])).
% 16.37/10.86 tff(3374,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3375,plain,
% 16.37/10.86 (((~![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_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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3376,plain,
% 16.37/10.86 ((~![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_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3377,plain,
% 16.37/10.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3376, 3375])).
% 16.37/10.86 tff(3378,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3377, 178, 3374, 3326, 3370])).
% 16.37/10.86 tff(3379,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3380,plain,
% 16.37/10.86 (((~![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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3381,plain,
% 16.37/10.86 ((~![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))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3382,plain,
% 16.37/10.86 ((~![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)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 16.37/10.86 tff(3383,plain,
% 16.37/10.86 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3382, 1707, 3379])).
% 16.37/10.86 tff(3384,plain,
% 16.37/10.86 (((~![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_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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3385,plain,
% 16.37/10.86 ((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3386,plain,
% 16.37/10.86 ((~![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_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3385, 3384])).
% 16.37/10.86 tff(3387,plain,
% 16.37/10.86 (~node20(c_e_h_3, c_r, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3386, 283, 3383])).
% 16.37/10.86 tff(3388,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 16.37/10.86 tff(3389,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 16.37/10.86 tff(3390,plain,
% 16.37/10.86 (((~![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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3391,plain,
% 16.37/10.86 ((~![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))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3392,plain,
% 16.37/10.86 ((~![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)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3391, 3390])).
% 16.37/10.86 tff(3393,plain,
% 16.37/10.86 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3392, 1707, 3374])).
% 16.37/10.86 tff(3394,plain,
% 16.37/10.86 (((~![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_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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3395,plain,
% 16.37/10.86 ((~![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_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3396,plain,
% 16.37/10.86 ((~![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_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3395, 3394])).
% 16.37/10.86 tff(3397,plain,
% 16.37/10.86 (~node20(c_e_h_3, c_r, s0)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3396, 283, 3393])).
% 16.37/10.86 tff(3398,assumption,(node21(c_e_h_3, c_r, s0, s1)), introduced(assumption)).
% 16.37/10.86 tff(3399,plain,
% 16.37/10.86 (((~![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)))) | ((~node21(c_e_h_3, c_r, s0, s1)) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, 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_r, s0, s1)) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3400,plain,
% 16.37/10.86 ((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))) <=> ((~node21(c_e_h_3, c_r, s0, s1)) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3401,plain,
% 16.37/10.86 (((~![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_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)))) | ((~node21(c_e_h_3, c_r, s0, s1)) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1))))),
% 16.37/10.86 inference(monotonicity,[status(thm)],[3400])).
% 16.37/10.86 tff(3402,plain,
% 16.37/10.86 (((~![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_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)))) | (~node21(c_e_h_3, c_r, s0, s1)) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)))),
% 16.37/10.86 inference(transitivity,[status(thm)],[3401, 3399])).
% 16.37/10.86 tff(3403,plain,
% 16.37/10.86 ((~![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_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3404,plain,
% 16.37/10.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_r, s0, s1)) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3403, 3402])).
% 16.37/10.86 tff(3405,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3404, 82, 3398, 3397, 3389])).
% 16.37/10.86 tff(3406,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,[]))).
% 16.37/10.86 tff(3407,plain,
% 16.37/10.86 (~node21(c_e_h_3, c_r, s0, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3406, 3389])).
% 16.37/10.86 tff(3408,plain,
% 16.37/10.86 (((~![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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3409,plain,
% 16.37/10.86 ((~![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))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3410,plain,
% 16.37/10.86 ((~![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)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3409, 3408])).
% 16.37/10.86 tff(3411,plain,
% 16.37/10.86 (node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3410, 112, 102])).
% 16.37/10.86 tff(3412,plain,
% 16.37/10.86 (node22(c_e_h_3, c_r, s0, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3411, 3407])).
% 16.37/10.86 tff(3413,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s0)), introduced(assumption)).
% 16.37/10.86 tff(3414,plain,
% 16.37/10.86 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3415,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3414, 9, 3413])).
% 16.37/10.86 tff(3416,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3417,plain,
% 16.37/10.86 (((~![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_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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3418,plain,
% 16.37/10.86 ((~![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_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3419,plain,
% 16.37/10.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 16.37/10.86 tff(3420,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3419, 127, 3416, 3412, 3389])).
% 16.37/10.86 tff(3421,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3422,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 16.37/10.86 tff(3423,assumption,(node22(c_e_h_3, c_r, s1, s2)), introduced(assumption)).
% 16.37/10.86 tff(3424,plain,
% 16.37/10.86 (((~![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_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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3425,plain,
% 16.37/10.86 ((~![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_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3426,plain,
% 16.37/10.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3425, 3424])).
% 16.37/10.86 tff(3427,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3426, 127, 3423, 3388, 3422])).
% 16.37/10.86 tff(3428,plain,((~node22(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3429,plain,
% 16.37/10.86 ((~node22(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3428, 3421])).
% 16.37/10.86 tff(3430,plain,
% 16.37/10.86 (~node22(c_e_h_3, c_r, s1, s2)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3429, 3388])).
% 16.37/10.86 tff(3431,assumption,(~node20(c_e_h_3, c_r, s1)), introduced(assumption)).
% 16.37/10.86 tff(3432,assumption,(node21(c_e_h_3, c_r, s1, s2)), introduced(assumption)).
% 16.37/10.86 tff(3433,plain,
% 16.37/10.86 (((~![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_r, s1) | (~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, 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) | (~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3434,plain,
% 16.37/10.86 ((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))) <=> (node20(c_e_h_3, c_r, s1) | (~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3435,plain,
% 16.37/10.86 (((~![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_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) | (~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2))))),
% 16.37/10.86 inference(monotonicity,[status(thm)],[3434])).
% 16.37/10.86 tff(3436,plain,
% 16.37/10.86 (((~![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_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) | (~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)))),
% 16.37/10.86 inference(transitivity,[status(thm)],[3435, 3433])).
% 16.37/10.86 tff(3437,plain,
% 16.37/10.86 ((~![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_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3438,plain,
% 16.37/10.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s1) | (~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3437, 3436])).
% 16.37/10.86 tff(3439,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3438, 82, 3432, 3431, 3388])).
% 16.37/10.86 tff(3440,plain,((~node21(c_e_h_3, c_r, s1, s2)) | node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2))), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3441,plain,
% 16.37/10.86 (~node21(c_e_h_3, c_r, s1, s2)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3440, 3388, 3431])).
% 16.37/10.86 tff(3442,plain,
% 16.37/10.86 (((~![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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3443,plain,
% 16.37/10.86 ((~![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))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3444,plain,
% 16.37/10.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3443, 3442])).
% 16.37/10.86 tff(3445,plain,
% 16.37/10.86 (node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3444, 112, 348])).
% 16.37/10.86 tff(3446,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3445, 3441, 3430])).
% 16.37/10.86 tff(3447,plain,((~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,[]))).
% 16.37/10.86 tff(3448,plain,
% 16.37/10.86 (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3447, 3387])).
% 16.37/10.86 tff(3449,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s1)), introduced(assumption)).
% 16.37/10.86 tff(3450,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s0)), introduced(assumption)).
% 16.37/10.86 tff(3451,plain,
% 16.37/10.86 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3452,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3451, 165, 3450])).
% 16.37/10.86 tff(3453,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3454,plain,
% 16.37/10.86 (((~![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_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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3455,plain,
% 16.37/10.86 ((~![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_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3456,plain,
% 16.37/10.86 ((~![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_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3455, 3454])).
% 16.37/10.86 tff(3457,plain,
% 16.37/10.86 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3456, 269, 3453])).
% 16.37/10.86 tff(3458,plain,
% 16.37/10.86 (((~![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_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))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3459,plain,
% 16.37/10.86 ((~![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_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3460,plain,
% 16.37/10.86 ((~![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_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0)),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3459, 3458])).
% 16.37/10.86 tff(3461,plain,
% 16.37/10.86 (~node20(c_e_h_3, c_i, s0)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3460, 283, 3457])).
% 16.37/10.86 tff(3462,assumption,(~node20(c_e_h_3, c_i, s0)), introduced(assumption)).
% 16.37/10.86 tff(3463,assumption,(node21(c_e_h_3, c_i, s0, s1)), introduced(assumption)).
% 16.37/10.86 tff(3464,plain,
% 16.37/10.86 (((~![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_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)))) | 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)))),
% 16.37/10.86 inference(rewrite,[status(thm)],[])).
% 16.37/10.86 tff(3465,plain,
% 16.37/10.86 ((~![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_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))),
% 16.37/10.86 inference(quant_inst,[status(thm)],[])).
% 16.37/10.86 tff(3466,plain,
% 16.37/10.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1))),
% 16.37/10.86 inference(modus_ponens,[status(thm)],[3465, 3464])).
% 16.37/10.86 tff(3467,plain,
% 16.37/10.86 ($false),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3466, 82, 3463, 3449, 3462])).
% 16.37/10.86 tff(3468,plain,((~node21(c_e_h_3, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | node20(c_e_h_3, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.86 tff(3469,plain,
% 16.37/10.86 ((~node21(c_e_h_3, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3468, 3461])).
% 16.37/10.86 tff(3470,plain,
% 16.37/10.86 (~node21(c_e_h_3, c_i, s0, s1)),
% 16.37/10.86 inference(unit_resolution,[status(thm)],[3469, 3449])).
% 16.37/10.86 tff(3471,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 16.37/10.87 tff(3472,assumption,(node22(c_e_h_3, c_i, s0, s1)), introduced(assumption)).
% 16.37/10.87 tff(3473,plain,
% 16.37/10.87 (((~![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_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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3474,plain,
% 16.37/10.87 ((~![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_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3475,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3474, 3473])).
% 16.37/10.87 tff(3476,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3475, 127, 3472, 3449, 3471])).
% 16.37/10.87 tff(3477,plain,((~node22(c_e_h_3, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3478,plain,
% 16.37/10.87 ((~node22(c_e_h_3, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3477, 3348])).
% 16.37/10.87 tff(3479,plain,
% 16.37/10.87 (~node22(c_e_h_3, c_i, s0, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3478, 3449])).
% 16.37/10.87 tff(3480,plain,
% 16.37/10.87 (((~![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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3481,plain,
% 16.37/10.87 ((~![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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3482,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 16.37/10.87 tff(3483,plain,
% 16.37/10.87 (node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3482, 112, 102])).
% 16.37/10.87 tff(3484,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3483, 3479, 3470])).
% 16.37/10.87 tff(3485,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3486,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s1)), introduced(assumption)).
% 16.37/10.87 tff(3487,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s1)), introduced(assumption)).
% 16.37/10.87 tff(3488,plain,
% 16.37/10.87 (((~![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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3489,plain,
% 16.37/10.87 ((~![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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3490,plain,
% 16.37/10.87 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3489, 3488])).
% 16.37/10.87 tff(3491,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3490, 612, 3487, 3486])).
% 16.37/10.87 tff(3492,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3493,plain,
% 16.37/10.87 (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3492, 3485])).
% 16.37/10.87 tff(3494,assumption,(m_c_h_element_v_in1(c_e_h_3, c_e, s1)), introduced(assumption)).
% 16.37/10.87 tff(3495,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), introduced(assumption)).
% 16.37/10.87 tff(3496,plain,
% 16.37/10.87 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3497,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3496, 629, 3495])).
% 16.37/10.87 tff(3498,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3499,plain,
% 16.37/10.87 (((~![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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3500,plain,
% 16.37/10.87 ((~![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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3501,plain,
% 16.37/10.87 ((~![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)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3500, 3499])).
% 16.37/10.87 tff(3502,plain,
% 16.37/10.87 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3501, 639, 3498])).
% 16.37/10.87 tff(3503,plain,
% 16.37/10.87 (((~![I0: $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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3504,plain,
% 16.37/10.87 ((~![I0: $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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3505,plain,
% 16.37/10.87 ((~![I0: $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)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3504, 3503])).
% 16.37/10.87 tff(3506,plain,
% 16.37/10.87 (~node20(c_e_h_3, c_c, s0)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3505, 283, 3502])).
% 16.37/10.87 tff(3507,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 16.37/10.87 tff(3508,assumption,(node22(c_e_h_3, c_c, s0, s1)), introduced(assumption)).
% 16.37/10.87 tff(3509,plain,
% 16.37/10.87 (((~![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_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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3510,plain,
% 16.37/10.87 ((~![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_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3511,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 16.37/10.87 tff(3512,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3511, 127, 3508, 3330, 3507])).
% 16.37/10.87 tff(3513,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,[]))).
% 16.37/10.87 tff(3514,plain,
% 16.37/10.87 (~node22(c_e_h_3, c_c, s0, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3513, 3507])).
% 16.37/10.87 tff(3515,plain,
% 16.37/10.87 (((~![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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3516,plain,
% 16.37/10.87 ((~![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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3517,plain,
% 16.37/10.87 ((~![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)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3516, 3515])).
% 16.37/10.87 tff(3518,plain,
% 16.37/10.87 (node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3517, 112, 102])).
% 16.37/10.87 tff(3519,plain,
% 16.37/10.87 (node21(c_e_h_3, c_c, s0, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3518, 3514])).
% 16.37/10.87 tff(3520,plain,
% 16.37/10.87 (((~![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_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)))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3521,plain,
% 16.37/10.87 ((~![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_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3522,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1))),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 16.37/10.87 tff(3523,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3522, 82, 3519, 3507, 3506])).
% 16.37/10.87 tff(3524,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3525,plain,
% 16.37/10.87 (((~![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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3526,plain,
% 16.37/10.87 ((~![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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3527,plain,
% 16.37/10.87 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 16.37/10.87 tff(3528,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3527, 678, 3524, 3494])).
% 16.37/10.87 tff(3529,plain,(~m_c_h_element_v_in1(c_e_h_3, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3530,plain,
% 16.37/10.87 (((~![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_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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3531,plain,
% 16.37/10.87 ((~![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_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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3532,plain,
% 16.37/10.87 ((~![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_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)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3531, 3530])).
% 16.37/10.87 tff(3533,plain,
% 16.37/10.87 ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3532, 209, 3529])).
% 16.37/10.87 tff(3534,plain,
% 16.37/10.87 (~node16(c_e_h_3, c_e, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3533, 3493])).
% 16.37/10.87 tff(3535,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 16.37/10.87 tff(3536,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 16.37/10.87 tff(3537,assumption,(node15(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 16.37/10.87 tff(3538,plain,
% 16.37/10.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3539,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3540,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3539, 3538])).
% 16.37/10.87 tff(3541,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3540, 178, 3536, 3535, 3537])).
% 16.37/10.87 tff(3542,plain,((~node15(c_e_h_3, c_e, s1, s2)) | (~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, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3543,plain,
% 16.37/10.87 (~node15(c_e_h_3, c_e, s1, s2)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3542, 3536, 3535])).
% 16.37/10.87 tff(3544,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s1)), introduced(assumption)).
% 16.37/10.87 tff(3545,assumption,(node14(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 16.37/10.87 tff(3546,plain,
% 16.37/10.87 (((~![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_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(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, s2)) | (~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3547,plain,
% 16.37/10.87 (((~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)) | (~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3548,plain,
% 16.37/10.87 (((~![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_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)) | (~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1)))),
% 16.37/10.87 inference(monotonicity,[status(thm)],[3547])).
% 16.37/10.87 tff(3549,plain,
% 16.37/10.87 (((~![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_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)) | (~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1))),
% 16.37/10.87 inference(transitivity,[status(thm)],[3548, 3546])).
% 16.37/10.87 tff(3550,plain,
% 16.37/10.87 ((~![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_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)))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3551,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3550, 3549])).
% 16.37/10.87 tff(3552,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3551, 254, 3536, 3545, 3544])).
% 16.37/10.87 tff(3553,plain,((~node14(c_e_h_3, c_e, s1, 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)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3554,plain,
% 16.37/10.87 ((~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3553, 3529])).
% 16.37/10.87 tff(3555,plain,
% 16.37/10.87 (~node14(c_e_h_3, c_e, s1, s2)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3554, 3536])).
% 16.37/10.87 tff(3556,plain,
% 16.37/10.87 (((~![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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3557,plain,
% 16.37/10.87 ((~![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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3558,plain,
% 16.37/10.87 ((~![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)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 16.37/10.87 tff(3559,plain,
% 16.37/10.87 (node19(c_e_h_3, c_e, s1, s2)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3558, 221, 348])).
% 16.37/10.87 tff(3560,plain,
% 16.37/10.87 (((~![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)))) | ((~node19(c_e_h_3, c_e, s1, s2)) | 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))) <=> ((~![Y: $i, I0: $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, s1, s2)) | 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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3561,plain,
% 16.37/10.87 ((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))) <=> ((~node19(c_e_h_3, c_e, s1, s2)) | 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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3562,plain,
% 16.37/10.87 (((~![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_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)))) | ((~node19(c_e_h_3, c_e, s1, s2)) | 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)))),
% 16.37/10.87 inference(monotonicity,[status(thm)],[3561])).
% 16.37/10.87 tff(3563,plain,
% 16.37/10.87 (((~![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_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)))) | (~node19(c_e_h_3, c_e, s1, s2)) | 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))),
% 16.37/10.87 inference(transitivity,[status(thm)],[3562, 3560])).
% 16.37/10.87 tff(3564,plain,
% 16.37/10.87 ((~![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_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)))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3565,plain,
% 16.37/10.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s1, s2)) | node15(c_e_h_3, c_e, s1, s2) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3564, 3563])).
% 16.37/10.87 tff(3566,plain,
% 16.37/10.87 (node15(c_e_h_3, c_e, s1, s2) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3565, 235, 3559])).
% 16.37/10.87 tff(3567,plain,
% 16.37/10.87 ($false),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3566, 3555, 3543, 3534])).
% 16.37/10.87 tff(3568,plain,((~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, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.87 tff(3569,plain,
% 16.37/10.87 (~m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3568, 3379])).
% 16.37/10.87 tff(3570,plain,
% 16.37/10.87 (((~![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))),
% 16.37/10.87 inference(rewrite,[status(thm)],[])).
% 16.37/10.87 tff(3571,plain,
% 16.37/10.87 ((~![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))),
% 16.37/10.87 inference(quant_inst,[status(thm)],[])).
% 16.37/10.87 tff(3572,plain,
% 16.37/10.87 ((~![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)),
% 16.37/10.87 inference(modus_ponens,[status(thm)],[3571, 3570])).
% 16.37/10.87 tff(3573,plain,
% 16.37/10.87 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 16.37/10.87 inference(unit_resolution,[status(thm)],[3572, 1707, 3569])).
% 16.37/10.87 tff(3574,plain,
% 16.37/10.87 (((~![I0: $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))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3575,plain,
% 16.37/10.88 ((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3576,plain,
% 16.37/10.88 ((~![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_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3575, 3574])).
% 16.37/10.88 tff(3577,plain,
% 16.37/10.88 (~node20(c_e_h_3, c_r, s2)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3576, 283, 3573])).
% 16.37/10.88 tff(3578,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 16.37/10.88 tff(3579,assumption,(~node20(c_e_h_3, c_r, s2)), introduced(assumption)).
% 16.37/10.88 tff(3580,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 16.37/10.88 tff(3581,assumption,(node22(c_e_h_3, c_r, s2, s3)), introduced(assumption)).
% 16.37/10.88 tff(3582,plain,
% 16.37/10.88 (((~![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_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))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3583,plain,
% 16.37/10.88 ((~![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_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3584,plain,
% 16.37/10.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3583, 3582])).
% 16.37/10.88 tff(3585,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3584, 127, 3581, 3580, 3578])).
% 16.37/10.88 tff(3586,plain,((~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3))), inference(lemma,lemma(discharge,[]))).
% 16.37/10.88 tff(3587,plain,
% 16.37/10.88 (~node22(c_e_h_3, c_r, s2, s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3586, 3578, 3580])).
% 16.37/10.88 tff(3588,plain,
% 16.37/10.88 (((~![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))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3589,plain,
% 16.37/10.88 ((~![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))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3590,plain,
% 16.37/10.88 ((~![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)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 16.37/10.88 tff(3591,plain,
% 16.37/10.88 (node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3590, 112, 591])).
% 16.37/10.88 tff(3592,plain,
% 16.37/10.88 (node21(c_e_h_3, c_r, s2, s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3591, 3587])).
% 16.37/10.88 tff(3593,plain,
% 16.37/10.88 (((~![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_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)))) | 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)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3594,plain,
% 16.37/10.88 ((~![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_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3595,plain,
% 16.37/10.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3594, 3593])).
% 16.37/10.88 tff(3596,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3595, 82, 3592, 3579, 3578])).
% 16.37/10.88 tff(3597,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.88 tff(3598,plain,
% 16.37/10.88 (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3597, 3577, 3448])).
% 16.37/10.88 tff(3599,assumption,(m_user_v_ack(c_e_h_3, c_u, s3)), introduced(assumption)).
% 16.37/10.88 tff(3600,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 16.37/10.88 tff(3601,plain,
% 16.37/10.88 (((~![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))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3602,plain,
% 16.37/10.88 ((~![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))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3603,plain,
% 16.37/10.88 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3602, 3601])).
% 16.37/10.88 tff(3604,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3603, 1864, 3600, 3599])).
% 16.37/10.88 tff(3605,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,[]))).
% 16.37/10.88 tff(3606,plain,
% 16.37/10.88 (~m_user_v_ack(c_e_h_3, c_u, s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3605, 3598])).
% 16.37/10.88 tff(3607,assumption,(node25(s3)), introduced(assumption)).
% 16.37/10.88 tff(3608,assumption,(~m_user_v_ack(c_e_h_3, c_u, s3)), introduced(assumption)).
% 16.37/10.88 tff(3609,plain,
% 16.37/10.88 (^[X: $i] : refl((m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))) <=> (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))))),
% 16.37/10.88 inference(bind,[status(th)],[])).
% 16.37/10.88 tff(3610,plain,
% 16.37/10.88 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 16.37/10.88 inference(quant_intro,[status(thm)],[3609])).
% 16.37/10.88 tff(3611,plain,
% 16.37/10.88 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3612,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty6')).
% 16.37/10.88 tff(3613,plain,
% 16.37/10.88 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 16.37/10.88 tff(3614,plain,(
% 16.37/10.88 ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 16.37/10.88 inference(skolemize,[status(sab)],[3613])).
% 16.37/10.88 tff(3615,plain,
% 16.37/10.88 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3614, 3610])).
% 16.37/10.88 tff(3616,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s3) | (~node25(s3)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s3) | (~node25(s3)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3617,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s3) | (~node25(s3)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3618,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s3) | (~node25(s3))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 16.37/10.88 tff(3619,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3618, 3615, 3608, 3607])).
% 16.37/10.88 tff(3620,plain,((~node25(s3)) | m_user_v_ack(c_e_h_3, c_u, s3)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.88 tff(3621,plain,
% 16.37/10.88 (~node25(s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3620, 3606])).
% 16.37/10.88 tff(3622,assumption,(node24(s3)), introduced(assumption)).
% 16.37/10.88 tff(3623,plain,
% 16.37/10.88 (^[X: $i] : refl(((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)) <=> ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)))),
% 16.37/10.88 inference(bind,[status(th)],[])).
% 16.37/10.88 tff(3624,plain,
% 16.37/10.88 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)) <=> ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 16.37/10.88 inference(quant_intro,[status(thm)],[3623])).
% 16.37/10.88 tff(3625,plain,
% 16.37/10.88 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)) <=> ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3626,plain,
% 16.37/10.88 (^[X: $i] : rewrite((m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X))) <=> ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X)))),
% 16.37/10.88 inference(bind,[status(th)],[])).
% 16.37/10.88 tff(3627,plain,
% 16.37/10.88 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X))) <=> ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 16.37/10.88 inference(quant_intro,[status(thm)],[3626])).
% 16.37/10.88 tff(3628,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty4')).
% 16.37/10.88 tff(3629,plain,
% 16.37/10.88 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3628, 3627])).
% 16.37/10.88 tff(3630,plain,
% 16.37/10.88 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3629, 3625])).
% 16.37/10.88 tff(3631,plain,(
% 16.37/10.88 ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 16.37/10.88 inference(skolemize,[status(sab)],[3630])).
% 16.37/10.88 tff(3632,plain,
% 16.37/10.88 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3631, 3624])).
% 16.37/10.88 tff(3633,plain,
% 16.37/10.88 (((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s3)) | m_user_v_ack(c_e_h_3, c_u, s3))) <=> ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s3)) | m_user_v_ack(c_e_h_3, c_u, s3))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3634,plain,
% 16.37/10.88 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | ((~node24(s3)) | m_user_v_ack(c_e_h_3, c_u, s3))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3635,plain,
% 16.37/10.88 ((~![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))) | (~node24(s3)) | m_user_v_ack(c_e_h_3, c_u, s3)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3634, 3633])).
% 16.37/10.88 tff(3636,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3635, 3632, 3608, 3622])).
% 16.37/10.88 tff(3637,plain,((~node24(s3)) | m_user_v_ack(c_e_h_3, c_u, s3)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.88 tff(3638,plain,
% 16.37/10.88 (~node24(s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3637, 3606])).
% 16.37/10.88 tff(3639,plain,
% 16.37/10.88 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3640,plain,
% 16.37/10.88 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3641,plain,
% 16.37/10.88 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s3) | node24(s3) | node25(s3) | (~node26(s3))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 16.37/10.88 tff(3642,plain,
% 16.37/10.88 (~node26(s3)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3641, 3266, 3638, 3621, 3325])).
% 16.37/10.88 tff(3643,assumption,(m_user_v_ack(c_e_h_3, c_u, s2)), introduced(assumption)).
% 16.37/10.88 tff(3644,plain,
% 16.37/10.88 (((~![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))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3645,plain,
% 16.37/10.88 ((~![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))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3646,plain,
% 16.37/10.88 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3645, 3644])).
% 16.37/10.88 tff(3647,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3646, 1864, 3643, 3580])).
% 16.37/10.88 tff(3648,plain,((~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.88 tff(3649,plain,
% 16.37/10.88 (~m_user_v_ack(c_e_h_3, c_u, s2)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3648, 3448])).
% 16.37/10.88 tff(3650,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s2) | (~node25(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s2) | (~node25(s2)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3651,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s2) | (~node25(s2)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3652,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s2) | (~node25(s2))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 16.37/10.88 tff(3653,plain,
% 16.37/10.88 (~node25(s2)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3652, 3615, 3649])).
% 16.37/10.88 tff(3654,plain,
% 16.37/10.88 (((~![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))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3655,plain,
% 16.37/10.88 ((~![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))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3656,plain,
% 16.37/10.88 ((~![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)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3655, 3654])).
% 16.37/10.88 tff(3657,plain,
% 16.37/10.88 (~m_user_v_ack(c_e_h_1, c_u, s2)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3656, 1864, 1698])).
% 16.37/10.88 tff(3658,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3659,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3660,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3659, 3658])).
% 16.37/10.88 tff(3661,plain,
% 16.37/10.88 (~node24(s2)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3660, 1879, 3657])).
% 16.37/10.88 tff(3662,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3663,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3664,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3663, 3662])).
% 16.37/10.88 tff(3665,plain,
% 16.37/10.88 (~node23(s2)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3664, 3252, 3657])).
% 16.37/10.88 tff(3666,plain,
% 16.37/10.88 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3667,plain,
% 16.37/10.88 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3668,plain,
% 16.37/10.88 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s2) | node24(s2) | node25(s2) | (~node26(s2))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3667, 3666])).
% 16.37/10.88 tff(3669,plain,
% 16.37/10.88 (node25(s2) | (~node26(s2))),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3668, 3266, 3665, 3661])).
% 16.37/10.88 tff(3670,plain,
% 16.37/10.88 (~node26(s2)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3669, 3653])).
% 16.37/10.88 tff(3671,plain,
% 16.37/10.88 (((~![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_2, c_u, s1)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3672,plain,
% 16.37/10.88 ((~![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_2, c_u, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3673,plain,
% 16.37/10.88 ((~![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_2, c_u, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3672, 3671])).
% 16.37/10.88 tff(3674,plain,
% 16.37/10.88 (~m_user_v_ack(c_e_h_2, c_u, s1)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3673, 1864, 3035])).
% 16.37/10.88 tff(3675,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s1) | (~node25(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s1) | (~node25(s1)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3676,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s1) | (~node25(s1)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3677,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s1) | (~node25(s1))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3676, 3675])).
% 16.37/10.88 tff(3678,plain,
% 16.37/10.88 (~node25(s1)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3677, 3213, 3674])).
% 16.37/10.88 tff(3679,plain,
% 16.37/10.88 (((~![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))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3680,plain,
% 16.37/10.88 ((~![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))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3681,plain,
% 16.37/10.88 ((~![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)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3680, 3679])).
% 16.37/10.88 tff(3682,plain,
% 16.37/10.88 (~m_user_v_ack(c_e_h_1, c_u, s1)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3681, 1864, 1671])).
% 16.37/10.88 tff(3683,assumption,(~node25(s1)), introduced(assumption)).
% 16.37/10.88 tff(3684,assumption,(~m_user_v_ack(c_e_h_1, c_u, s1)), introduced(assumption)).
% 16.37/10.88 tff(3685,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3686,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3687,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 16.37/10.88 tff(3688,plain,
% 16.37/10.88 (~node23(s1)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3687, 3252, 3684])).
% 16.37/10.88 tff(3689,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3690,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3691,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3690, 3689])).
% 16.37/10.88 tff(3692,plain,
% 16.37/10.88 (~node24(s1)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3691, 1879, 3684])).
% 16.37/10.88 tff(3693,assumption,(node26(s1)), introduced(assumption)).
% 16.37/10.88 tff(3694,plain,
% 16.37/10.88 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3695,plain,
% 16.37/10.88 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3696,plain,
% 16.37/10.88 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s1) | node24(s1) | node25(s1) | (~node26(s1))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3695, 3694])).
% 16.37/10.88 tff(3697,plain,
% 16.37/10.88 (node23(s1) | node24(s1) | node25(s1)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3696, 3266, 3693])).
% 16.37/10.88 tff(3698,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3697, 3692, 3688, 3683])).
% 16.37/10.88 tff(3699,plain,(m_user_v_ack(c_e_h_1, c_u, s1) | node25(s1) | (~node26(s1))), inference(lemma,lemma(discharge,[]))).
% 16.37/10.88 tff(3700,plain,
% 16.37/10.88 (node25(s1) | (~node26(s1))),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3699, 3682])).
% 16.37/10.88 tff(3701,plain,
% 16.37/10.88 (~node26(s1)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3700, 3678])).
% 16.37/10.88 tff(3702,plain,
% 16.37/10.88 (((~![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, s0)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_u, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3703,plain,
% 16.37/10.88 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3704,plain,
% 16.37/10.88 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 16.37/10.88 tff(3705,plain,
% 16.37/10.88 (~m_user_v_ack(c_e_h_1, c_u, s0)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3704, 1864, 1666])).
% 16.37/10.88 tff(3706,assumption,(node24(s0)), introduced(assumption)).
% 16.37/10.88 tff(3707,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3708,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3709,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3708, 3707])).
% 16.37/10.88 tff(3710,plain,
% 16.37/10.88 ($false),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3709, 1879, 3706, 3705])).
% 16.37/10.88 tff(3711,plain,(~node24(s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.88 tff(3712,plain,
% 16.37/10.88 (((~![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_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3713,plain,
% 16.37/10.88 ((~![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_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3714,plain,
% 16.37/10.88 ((~![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_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0)),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 16.37/10.88 tff(3715,plain,
% 16.37/10.88 (~m_user_v_ack(c_e_h_2, c_u, s0)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3714, 1864, 3030])).
% 16.37/10.88 tff(3716,plain,
% 16.37/10.88 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0)))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3717,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0)))),
% 16.37/10.88 inference(quant_inst,[status(thm)],[])).
% 16.37/10.88 tff(3718,plain,
% 16.37/10.88 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3717, 3716])).
% 16.37/10.88 tff(3719,plain,
% 16.37/10.88 (~node25(s0)),
% 16.37/10.88 inference(unit_resolution,[status(thm)],[3718, 3213, 3715])).
% 16.37/10.88 tff(3720,plain,
% 16.37/10.88 (^[X: $i] : refl(((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)) <=> ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)))),
% 16.37/10.88 inference(bind,[status(th)],[])).
% 16.37/10.88 tff(3721,plain,
% 16.37/10.88 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)) <=> ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 16.37/10.88 inference(quant_intro,[status(thm)],[3720])).
% 16.37/10.88 tff(3722,plain,
% 16.37/10.88 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)) <=> ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 16.37/10.88 inference(rewrite,[status(thm)],[])).
% 16.37/10.88 tff(3723,plain,
% 16.37/10.88 (^[X: $i] : rewrite((m_user_v_ack(c_e_h_2, c_u, X) | (~node23(X))) <=> ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X)))),
% 16.37/10.88 inference(bind,[status(th)],[])).
% 16.37/10.88 tff(3724,plain,
% 16.37/10.88 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node23(X))) <=> ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 16.37/10.88 inference(quant_intro,[status(thm)],[3723])).
% 16.37/10.88 tff(3725,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty2')).
% 16.37/10.88 tff(3726,plain,
% 16.37/10.88 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3725, 3724])).
% 16.37/10.88 tff(3727,plain,
% 16.37/10.88 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 16.37/10.88 inference(modus_ponens,[status(thm)],[3726, 3722])).
% 16.37/10.88 tff(3728,plain,(
% 16.37/10.88 ![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 16.37/10.89 inference(skolemize,[status(sab)],[3727])).
% 16.37/10.89 tff(3729,plain,
% 16.37/10.89 (![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3728, 3721])).
% 16.37/10.89 tff(3730,plain,
% 16.37/10.89 (((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))) <=> ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3731,plain,
% 16.37/10.89 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3732,plain,
% 16.37/10.89 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s0)) | m_user_v_ack(c_e_h_2, c_u, s0)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3731, 3730])).
% 16.37/10.89 tff(3733,plain,
% 16.37/10.89 (~node23(s0)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3732, 3729, 3715])).
% 16.37/10.89 tff(3734,plain,
% 16.37/10.89 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3735,plain,
% 16.37/10.89 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3736,plain,
% 16.37/10.89 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s0) | node24(s0) | node25(s0) | (~node26(s0))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 16.37/10.89 tff(3737,plain,
% 16.37/10.89 (node24(s0) | (~node26(s0))),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3736, 3266, 3733, 3719])).
% 16.37/10.89 tff(3738,plain,
% 16.37/10.89 (~node26(s0)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3737, 3711])).
% 16.37/10.89 tff(3739,plain,
% 16.37/10.89 (until27(s0) <=> until27(s0)),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3740,axiom,(until27(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty15')).
% 16.37/10.89 tff(3741,plain,
% 16.37/10.89 (until27(s0)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 16.37/10.89 tff(3742,plain,
% 16.37/10.89 (^[X: $i] : refl(((~until27(X)) | node26(X) | xuntil28(X)) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 16.37/10.89 inference(bind,[status(th)],[])).
% 16.37/10.89 tff(3743,plain,
% 16.37/10.89 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 16.37/10.89 inference(quant_intro,[status(thm)],[3742])).
% 16.37/10.89 tff(3744,plain,
% 16.37/10.89 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3745,plain,
% 16.37/10.89 (^[X: $i] : rewrite(((node26(X) | xuntil28(X)) | (~until27(X))) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 16.37/10.89 inference(bind,[status(th)],[])).
% 16.37/10.89 tff(3746,plain,
% 16.37/10.89 (![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X))) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 16.37/10.89 inference(quant_intro,[status(thm)],[3745])).
% 16.37/10.89 tff(3747,axiom,(![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty8')).
% 16.37/10.89 tff(3748,plain,
% 16.37/10.89 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3747, 3746])).
% 16.37/10.89 tff(3749,plain,
% 16.37/10.89 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3748, 3744])).
% 16.37/10.89 tff(3750,plain,(
% 16.37/10.89 ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 16.37/10.89 inference(skolemize,[status(sab)],[3749])).
% 16.37/10.89 tff(3751,plain,
% 16.37/10.89 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3750, 3743])).
% 16.37/10.89 tff(3752,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s0) | (~until27(s0)) | node26(s0))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3753,plain,
% 16.37/10.89 (((~until27(s0)) | node26(s0) | xuntil28(s0)) <=> (xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3754,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s0) | (~until27(s0)) | node26(s0)))),
% 16.37/10.89 inference(monotonicity,[status(thm)],[3753])).
% 16.37/10.89 tff(3755,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 16.37/10.89 inference(transitivity,[status(thm)],[3754, 3752])).
% 16.37/10.89 tff(3756,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3757,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3756, 3755])).
% 16.37/10.89 tff(3758,plain,
% 16.37/10.89 (xuntil28(s0) | node26(s0)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3757, 3751, 3741])).
% 16.37/10.89 tff(3759,plain,
% 16.37/10.89 (xuntil28(s0)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3758, 3738])).
% 16.37/10.89 tff(3760,plain,
% 16.37/10.89 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 16.37/10.89 inference(bind,[status(th)],[])).
% 16.37/10.89 tff(3761,plain,
% 16.37/10.89 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 16.37/10.89 inference(quant_intro,[status(thm)],[3760])).
% 16.37/10.89 tff(3762,plain,
% 16.37/10.89 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3763,plain,
% 16.37/10.89 (^[Y: $i, X: $i] : rewrite(((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 16.37/10.89 inference(bind,[status(th)],[])).
% 16.37/10.89 tff(3764,plain,
% 16.37/10.89 (![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 16.37/10.89 inference(quant_intro,[status(thm)],[3763])).
% 16.37/10.89 tff(3765,axiom,(![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty9')).
% 16.37/10.89 tff(3766,plain,
% 16.37/10.89 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3765, 3764])).
% 16.37/10.89 tff(3767,plain,
% 16.37/10.89 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3766, 3762])).
% 16.37/10.89 tff(3768,plain,(
% 16.37/10.89 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 16.37/10.89 inference(skolemize,[status(sab)],[3767])).
% 16.37/10.89 tff(3769,plain,
% 16.37/10.89 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3768, 3761])).
% 16.37/10.89 tff(3770,plain,
% 16.37/10.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3771,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3772,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3771, 3770])).
% 16.37/10.89 tff(3773,plain,
% 16.37/10.89 ((~xuntil28(s0)) | until27(s1)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3772, 98, 3769])).
% 16.37/10.89 tff(3774,plain,
% 16.37/10.89 (until27(s1)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3773, 3759])).
% 16.37/10.89 tff(3775,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3776,plain,
% 16.37/10.89 (((~until27(s1)) | node26(s1) | xuntil28(s1)) <=> (xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3777,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1))))),
% 16.37/10.89 inference(monotonicity,[status(thm)],[3776])).
% 16.37/10.89 tff(3778,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 16.37/10.89 inference(transitivity,[status(thm)],[3777, 3775])).
% 16.37/10.89 tff(3779,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3780,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3779, 3778])).
% 16.37/10.89 tff(3781,plain,
% 16.37/10.89 (xuntil28(s1) | node26(s1)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3780, 3751, 3774])).
% 16.37/10.89 tff(3782,plain,
% 16.37/10.89 (xuntil28(s1)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3781, 3701])).
% 16.37/10.89 tff(3783,plain,
% 16.37/10.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3784,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3785,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 16.37/10.89 tff(3786,plain,
% 16.37/10.89 ((~xuntil28(s1)) | until27(s2)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3785, 344, 3769])).
% 16.37/10.89 tff(3787,plain,
% 16.37/10.89 (until27(s2)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3786, 3782])).
% 16.37/10.89 tff(3788,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3789,plain,
% 16.37/10.89 (((~until27(s2)) | node26(s2) | xuntil28(s2)) <=> (xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3790,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2))))),
% 16.37/10.89 inference(monotonicity,[status(thm)],[3789])).
% 16.37/10.89 tff(3791,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 16.37/10.89 inference(transitivity,[status(thm)],[3790, 3788])).
% 16.37/10.89 tff(3792,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3793,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3792, 3791])).
% 16.37/10.89 tff(3794,plain,
% 16.37/10.89 (xuntil28(s2) | node26(s2)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3793, 3751, 3787])).
% 16.37/10.89 tff(3795,plain,
% 16.37/10.89 (xuntil28(s2)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3794, 3670])).
% 16.37/10.89 tff(3796,plain,
% 16.37/10.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3797,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3798,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3797, 3796])).
% 16.37/10.89 tff(3799,plain,
% 16.37/10.89 ((~xuntil28(s2)) | until27(s3)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3798, 587, 3769])).
% 16.37/10.89 tff(3800,plain,
% 16.37/10.89 (until27(s3)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3799, 3795])).
% 16.37/10.89 tff(3801,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | (~until27(s3)) | node26(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | (~until27(s3)) | node26(s3))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3802,plain,
% 16.37/10.89 (((~until27(s3)) | node26(s3) | xuntil28(s3)) <=> (xuntil28(s3) | (~until27(s3)) | node26(s3))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3803,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | (~until27(s3)) | node26(s3)))),
% 16.37/10.89 inference(monotonicity,[status(thm)],[3802])).
% 16.37/10.89 tff(3804,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | (~until27(s3)) | node26(s3))),
% 16.37/10.89 inference(transitivity,[status(thm)],[3803, 3801])).
% 16.37/10.89 tff(3805,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3806,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | (~until27(s3)) | node26(s3)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3805, 3804])).
% 16.37/10.89 tff(3807,plain,
% 16.37/10.89 (xuntil28(s3) | node26(s3)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3806, 3751, 3800])).
% 16.37/10.89 tff(3808,plain,
% 16.37/10.89 (xuntil28(s3)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3807, 3642])).
% 16.37/10.89 tff(3809,plain,
% 16.37/10.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3810,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3811,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 16.37/10.89 tff(3812,plain,
% 16.37/10.89 ((~xuntil28(s3)) | until27(s4)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3811, 1009, 3769])).
% 16.37/10.89 tff(3813,plain,
% 16.37/10.89 (until27(s4)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3812, 3808])).
% 16.37/10.89 tff(3814,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | (~until27(s4)) | node26(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | (~until27(s4)) | node26(s4))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3815,plain,
% 16.37/10.89 (((~until27(s4)) | node26(s4) | xuntil28(s4)) <=> (xuntil28(s4) | (~until27(s4)) | node26(s4))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3816,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | (~until27(s4)) | node26(s4)))),
% 16.37/10.89 inference(monotonicity,[status(thm)],[3815])).
% 16.37/10.89 tff(3817,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | (~until27(s4)) | node26(s4))),
% 16.37/10.89 inference(transitivity,[status(thm)],[3816, 3814])).
% 16.37/10.89 tff(3818,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3819,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | (~until27(s4)) | node26(s4)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3818, 3817])).
% 16.37/10.89 tff(3820,plain,
% 16.37/10.89 (xuntil28(s4) | node26(s4)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3819, 3751, 3813])).
% 16.37/10.89 tff(3821,plain,
% 16.37/10.89 (xuntil28(s4)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3820, 3314])).
% 16.37/10.89 tff(3822,plain,
% 16.37/10.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3823,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3824,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3823, 3822])).
% 16.37/10.89 tff(3825,plain,
% 16.37/10.89 ((~xuntil28(s4)) | until27(s5)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3824, 1516, 3769])).
% 16.37/10.89 tff(3826,plain,
% 16.37/10.89 (until27(s5)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3825, 3821])).
% 16.37/10.89 tff(3827,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s5) | (~until27(s5)) | node26(s5))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s5) | (~until27(s5)) | node26(s5))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3828,plain,
% 16.37/10.89 (((~until27(s5)) | node26(s5) | xuntil28(s5)) <=> (xuntil28(s5) | (~until27(s5)) | node26(s5))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3829,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s5)) | node26(s5) | xuntil28(s5))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s5) | (~until27(s5)) | node26(s5)))),
% 16.37/10.89 inference(monotonicity,[status(thm)],[3828])).
% 16.37/10.89 tff(3830,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s5)) | node26(s5) | xuntil28(s5))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s5) | (~until27(s5)) | node26(s5))),
% 16.37/10.89 inference(transitivity,[status(thm)],[3829, 3827])).
% 16.37/10.89 tff(3831,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s5)) | node26(s5) | xuntil28(s5))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3832,plain,
% 16.37/10.89 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s5) | (~until27(s5)) | node26(s5)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3831, 3830])).
% 16.37/10.89 tff(3833,plain,
% 16.37/10.89 (xuntil28(s5) | node26(s5)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3832, 3751, 3826])).
% 16.37/10.89 tff(3834,plain,
% 16.37/10.89 (xuntil28(s5)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3833, 3271])).
% 16.37/10.89 tff(3835,plain,
% 16.37/10.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3836,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3837,plain,
% 16.37/10.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3836, 3835])).
% 16.37/10.89 tff(3838,plain,
% 16.37/10.89 ((~xuntil28(s5)) | until27(s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3837, 1597, 3769])).
% 16.37/10.89 tff(3839,plain,
% 16.37/10.89 (until27(s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3838, 3834])).
% 16.37/10.89 tff(3840,assumption,(m_user_v_ack(c_e_h_2, c_u, s6)), introduced(assumption)).
% 16.37/10.89 tff(3841,plain,
% 16.37/10.89 (((~![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_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3842,plain,
% 16.37/10.89 ((~![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_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3843,plain,
% 16.37/10.89 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3842, 3841])).
% 16.37/10.89 tff(3844,plain,
% 16.37/10.89 ($false),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3843, 1864, 3840, 3181])).
% 16.37/10.89 tff(3845,plain,((~m_user_v_ack(c_e_h_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.89 tff(3846,plain,
% 16.37/10.89 (~m_user_v_ack(c_e_h_2, c_u, s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3845, 3171])).
% 16.37/10.89 tff(3847,plain,
% 16.37/10.89 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3848,plain,
% 16.37/10.89 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6)))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3849,plain,
% 16.37/10.89 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3848, 3847])).
% 16.37/10.89 tff(3850,plain,
% 16.37/10.89 (~node25(s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3849, 3213, 3846])).
% 16.37/10.89 tff(3851,assumption,(m_user_v_ack(c_e_h_1, c_u, s6)), introduced(assumption)).
% 16.37/10.89 tff(3852,plain,
% 16.37/10.89 (((~![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))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3853,plain,
% 16.37/10.89 ((~![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))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3854,plain,
% 16.37/10.89 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 16.37/10.89 tff(3855,plain,
% 16.37/10.89 ($false),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3854, 1864, 3851, 1825])).
% 16.37/10.89 tff(3856,plain,((~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.89 tff(3857,plain,
% 16.37/10.89 (~m_user_v_ack(c_e_h_1, c_u, s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3856, 1823])).
% 16.37/10.89 tff(3858,plain,
% 16.37/10.89 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3859,plain,
% 16.37/10.89 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6)))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3860,plain,
% 16.37/10.89 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 16.37/10.89 tff(3861,plain,
% 16.37/10.89 (~node24(s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3860, 1879, 3857])).
% 16.37/10.89 tff(3862,assumption,(~m_user_v_ack(c_e_h_1, c_u, s6)), introduced(assumption)).
% 16.37/10.89 tff(3863,plain,
% 16.37/10.89 (^[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))))),
% 16.37/10.89 inference(bind,[status(th)],[])).
% 16.37/10.89 tff(3864,plain,
% 16.37/10.89 (![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)))),
% 16.37/10.89 inference(quant_intro,[status(thm)],[3863])).
% 16.37/10.89 tff(3865,plain,
% 16.37/10.89 (![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)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3866,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')).
% 16.37/10.89 tff(3867,plain,
% 16.37/10.89 (![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3866, 3865])).
% 16.37/10.89 tff(3868,plain,(
% 16.37/10.89 ![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 16.37/10.89 inference(skolemize,[status(sab)],[3867])).
% 16.37/10.89 tff(3869,plain,
% 16.37/10.89 (![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3868, 3864])).
% 16.37/10.89 tff(3870,plain,
% 16.37/10.89 (((~![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)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3871,plain,
% 16.37/10.89 ((~![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)))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3872,plain,
% 16.37/10.89 ((~![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))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 16.37/10.89 tff(3873,plain,
% 16.37/10.89 (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3872, 3869, 3862])).
% 16.37/10.89 tff(3874,plain,
% 16.37/10.89 (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[1853, 3873, 1826])).
% 16.37/10.89 tff(3875,plain,
% 16.37/10.89 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3876,plain,
% 16.37/10.89 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6)))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3877,plain,
% 16.37/10.89 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3876, 3875])).
% 16.37/10.89 tff(3878,plain,
% 16.37/10.89 (~node23(s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3877, 3252, 3862])).
% 16.37/10.89 tff(3879,assumption,(~node25(s6)), introduced(assumption)).
% 16.37/10.89 tff(3880,assumption,(~node24(s6)), introduced(assumption)).
% 16.37/10.89 tff(3881,plain,
% 16.37/10.89 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s6) | node24(s6) | node25(s6) | (~node26(s6)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s6) | node24(s6) | node25(s6) | (~node26(s6)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3882,plain,
% 16.37/10.89 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s6) | node24(s6) | node25(s6) | (~node26(s6)))),
% 16.37/10.89 inference(quant_inst,[status(thm)],[])).
% 16.37/10.89 tff(3883,plain,
% 16.37/10.89 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s6) | node24(s6) | node25(s6) | (~node26(s6))),
% 16.37/10.89 inference(modus_ponens,[status(thm)],[3882, 3881])).
% 16.37/10.89 tff(3884,plain,
% 16.37/10.89 (node23(s6) | (~node26(s6))),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3883, 3266, 3880, 3879])).
% 16.37/10.89 tff(3885,plain,
% 16.37/10.89 (~node26(s6)),
% 16.37/10.89 inference(unit_resolution,[status(thm)],[3884, 3878])).
% 16.37/10.89 tff(3886,assumption,(until27(s6)), introduced(assumption)).
% 16.37/10.89 tff(3887,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3888,plain,
% 16.37/10.89 (((~until27(s6)) | node26(s6) | xuntil28(s6)) <=> (xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 16.37/10.89 inference(rewrite,[status(thm)],[])).
% 16.37/10.89 tff(3889,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s6)) | node26(s6) | xuntil28(s6))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6))))),
% 16.37/10.89 inference(monotonicity,[status(thm)],[3888])).
% 16.37/10.89 tff(3890,plain,
% 16.37/10.89 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s6)) | node26(s6) | xuntil28(s6))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 16.37/10.90 inference(transitivity,[status(thm)],[3889, 3887])).
% 16.37/10.90 tff(3891,plain,
% 16.37/10.90 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s6)) | node26(s6) | xuntil28(s6))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3892,plain,
% 16.37/10.90 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3891, 3890])).
% 16.37/10.90 tff(3893,plain,
% 16.37/10.90 (xuntil28(s6) | node26(s6)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3892, 3751, 3886])).
% 16.37/10.90 tff(3894,plain,
% 16.37/10.90 (xuntil28(s6)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3893, 3885])).
% 16.37/10.90 tff(3895,plain,
% 16.37/10.90 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3896,plain,
% 16.37/10.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3897,plain,
% 16.37/10.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3896, 3895])).
% 16.37/10.90 tff(3898,plain,
% 16.37/10.90 ((~xuntil28(s6)) | until27(s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3897, 1839, 3769])).
% 16.37/10.90 tff(3899,plain,
% 16.37/10.90 (until27(s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3898, 3894])).
% 16.37/10.90 tff(3900,assumption,(~xuntil28(s7)), introduced(assumption)).
% 16.37/10.90 tff(3901,plain,
% 16.37/10.90 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3902,plain,
% 16.37/10.90 (((~until27(s7)) | node26(s7) | xuntil28(s7)) <=> (xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3903,plain,
% 16.37/10.90 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s7)) | node26(s7) | xuntil28(s7))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7))))),
% 16.37/10.90 inference(monotonicity,[status(thm)],[3902])).
% 16.37/10.90 tff(3904,plain,
% 16.37/10.90 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s7)) | node26(s7) | xuntil28(s7))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 16.37/10.90 inference(transitivity,[status(thm)],[3903, 3901])).
% 16.37/10.90 tff(3905,plain,
% 16.37/10.90 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s7)) | node26(s7) | xuntil28(s7))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3906,plain,
% 16.37/10.90 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 16.37/10.90 tff(3907,plain,
% 16.37/10.90 (node26(s7) | (~until27(s7))),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3906, 3751, 3900])).
% 16.37/10.90 tff(3908,plain,
% 16.37/10.90 (node26(s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3907, 3899])).
% 16.37/10.90 tff(3909,assumption,(~node25(s7)), introduced(assumption)).
% 16.37/10.90 tff(3910,assumption,(~node24(s7)), introduced(assumption)).
% 16.37/10.90 tff(3911,plain,
% 16.37/10.90 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s7) | node24(s7) | node25(s7) | (~node26(s7)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s7) | node24(s7) | node25(s7) | (~node26(s7)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3912,plain,
% 16.37/10.90 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s7) | node24(s7) | node25(s7) | (~node26(s7)))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3913,plain,
% 16.37/10.90 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s7) | node24(s7) | node25(s7) | (~node26(s7))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3912, 3911])).
% 16.37/10.90 tff(3914,plain,
% 16.37/10.90 (node23(s7) | (~node26(s7))),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3913, 3266, 3910, 3909])).
% 16.37/10.90 tff(3915,plain,
% 16.37/10.90 (node23(s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3914, 3908])).
% 16.37/10.90 tff(3916,plain,
% 16.37/10.90 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3917,plain,
% 16.37/10.90 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7)))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3918,plain,
% 16.37/10.90 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 16.37/10.90 tff(3919,plain,
% 16.37/10.90 (m_user_v_ack(c_e_h_1, c_u, s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3918, 3252, 3915])).
% 16.37/10.90 tff(3920,plain,
% 16.37/10.90 ($false),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[1867, 1864, 3919, 3874])).
% 16.37/10.90 tff(3921,plain,(m_user_v_ack(c_e_h_1, c_u, s6) | node24(s7) | node25(s7) | xuntil28(s7) | (~until27(s6)) | node20(c_e_h_1, c_r, s6) | node24(s6) | node25(s6)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.90 tff(3922,plain,
% 16.37/10.90 (node24(s7) | node25(s7) | xuntil28(s7) | (~until27(s6)) | node20(c_e_h_1, c_r, s6) | node25(s6)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3921, 3857, 3861])).
% 16.37/10.90 tff(3923,plain,
% 16.37/10.90 (node24(s7) | node25(s7) | xuntil28(s7) | node20(c_e_h_1, c_r, s6)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3922, 3850, 3839])).
% 16.37/10.90 tff(3924,plain,
% 16.37/10.90 (node24(s7) | xuntil28(s7) | node20(c_e_h_1, c_r, s6)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3923, 3219])).
% 16.37/10.90 tff(3925,plain,
% 16.37/10.90 (xuntil28(s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3924, 1885, 1639])).
% 16.37/10.90 tff(3926,plain,
% 16.37/10.90 (succ(s7, s8) <=> succ(s7, s8)),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3927,axiom,(succ(s7, s8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound8')).
% 16.37/10.90 tff(3928,plain,
% 16.37/10.90 (succ(s7, s8)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 16.37/10.90 tff(3929,plain,
% 16.37/10.90 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3930,plain,
% 16.37/10.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3931,plain,
% 16.37/10.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 16.37/10.90 tff(3932,plain,
% 16.37/10.90 ((~xuntil28(s7)) | until27(s8)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3931, 3928, 3769])).
% 16.37/10.90 tff(3933,plain,
% 16.37/10.90 (until27(s8)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3932, 3925])).
% 16.37/10.90 tff(3934,assumption,(node23(s7)), introduced(assumption)).
% 16.37/10.90 tff(3935,plain,
% 16.37/10.90 (((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s7)) | m_user_v_ack(c_e_h_2, c_u, s7))) <=> ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s7)) | m_user_v_ack(c_e_h_2, c_u, s7))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3936,plain,
% 16.37/10.90 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s7)) | m_user_v_ack(c_e_h_2, c_u, s7))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3937,plain,
% 16.37/10.90 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s7)) | m_user_v_ack(c_e_h_2, c_u, s7)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3936, 3935])).
% 16.37/10.90 tff(3938,plain,
% 16.37/10.90 ($false),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3937, 3729, 3934, 3204])).
% 16.37/10.90 tff(3939,plain,(~node23(s7)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.90 tff(3940,assumption,(~node23(s7)), introduced(assumption)).
% 16.37/10.90 tff(3941,assumption,(node26(s7)), introduced(assumption)).
% 16.37/10.90 tff(3942,plain,
% 16.37/10.90 ($false),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3913, 3266, 3910, 3909, 3941, 3940])).
% 16.37/10.90 tff(3943,plain,((~node26(s7)) | node24(s7) | node25(s7) | node23(s7)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.90 tff(3944,plain,
% 16.37/10.90 ((~node26(s7)) | node24(s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3943, 3219, 3939])).
% 16.37/10.90 tff(3945,plain,
% 16.37/10.90 (~node26(s7)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3944, 1885])).
% 16.37/10.90 tff(3946,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s2)), introduced(assumption)).
% 16.37/10.90 tff(3947,assumption,(node6(c_e_h_1, c_j, s1, s2)), introduced(assumption)).
% 16.37/10.90 tff(3948,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s1)), introduced(assumption)).
% 16.37/10.90 tff(3949,plain,
% 16.37/10.90 (((~![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, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~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, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3950,plain,
% 16.37/10.90 (((~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, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3951,plain,
% 16.37/10.90 (((~![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, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~node6(c_e_h_1, c_j, s1, s2))))),
% 16.37/10.90 inference(monotonicity,[status(thm)],[3950])).
% 16.37/10.90 tff(3952,plain,
% 16.37/10.90 (((~![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, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 16.37/10.90 inference(transitivity,[status(thm)],[3951, 3949])).
% 16.37/10.90 tff(3953,plain,
% 16.37/10.90 ((~![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))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3954,plain,
% 16.37/10.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~node6(c_e_h_1, c_j, s1, s2))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3953, 3952])).
% 16.37/10.90 tff(3955,plain,
% 16.37/10.90 ($false),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3954, 436, 3946, 3948, 3947])).
% 16.37/10.90 tff(3956,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.90 tff(3957,plain,
% 16.37/10.90 ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3956, 481])).
% 16.37/10.90 tff(3958,plain,
% 16.37/10.90 (~node6(c_e_h_1, c_j, s1, s2)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3957, 3946])).
% 16.37/10.90 tff(3959,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s1)), introduced(assumption)).
% 16.37/10.90 tff(3960,assumption,(node21(c_e_h_3, c_q, s0, s1)), introduced(assumption)).
% 16.37/10.90 tff(3961,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s0)), introduced(assumption)).
% 16.37/10.90 tff(3962,plain,
% 16.37/10.90 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3963,plain,
% 16.37/10.90 ($false),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3962, 165, 3961])).
% 16.37/10.90 tff(3964,plain,(~m_c_h_element_v_out(c_e_h_3, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.90 tff(3965,plain,
% 16.37/10.90 (^[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)))),
% 16.37/10.90 inference(bind,[status(th)],[])).
% 16.37/10.90 tff(3966,plain,
% 16.37/10.90 (![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))),
% 16.37/10.90 inference(quant_intro,[status(thm)],[3965])).
% 16.37/10.90 tff(3967,plain,
% 16.37/10.90 (![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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3968,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')).
% 16.37/10.90 tff(3969,plain,
% 16.37/10.90 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 16.37/10.90 tff(3970,plain,(
% 16.37/10.90 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 16.37/10.90 inference(skolemize,[status(sab)],[3969])).
% 16.37/10.90 tff(3971,plain,
% 16.37/10.90 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3970, 3966])).
% 16.37/10.90 tff(3972,plain,
% 16.37/10.90 (((~![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, s0)) | m_c_h_element_v_out(c_e_h_3, 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_3, c_q, s0)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3973,plain,
% 16.37/10.90 ((~![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, s0)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3974,plain,
% 16.37/10.90 ((~![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, s0)) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3973, 3972])).
% 16.37/10.90 tff(3975,plain,
% 16.37/10.90 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s0)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3974, 3971, 3964])).
% 16.37/10.90 tff(3976,plain,
% 16.37/10.90 (((~![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_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, 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_3, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s0))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3977,plain,
% 16.37/10.90 ((~![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_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s0))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3978,plain,
% 16.37/10.90 ((~![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_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s0)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3977, 3976])).
% 16.37/10.90 tff(3979,plain,
% 16.37/10.90 (~node20(c_e_h_3, c_q, s0)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3978, 283, 3975])).
% 16.37/10.90 tff(3980,plain,
% 16.37/10.90 (((~![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, 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)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3981,plain,
% 16.37/10.90 ((~![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, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3982,plain,
% 16.37/10.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1))),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3981, 3980])).
% 16.37/10.90 tff(3983,plain,
% 16.37/10.90 ($false),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3982, 82, 3959, 3979, 3960])).
% 16.37/10.90 tff(3984,plain,((~node21(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,[]))).
% 16.37/10.90 tff(3985,plain,
% 16.37/10.90 (~node21(c_e_h_3, c_q, s0, s1)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3984, 3959])).
% 16.37/10.90 tff(3986,plain,
% 16.37/10.90 (((~![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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3987,plain,
% 16.37/10.90 ((~![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))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3988,plain,
% 16.37/10.90 ((~![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)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3987, 3986])).
% 16.37/10.90 tff(3989,plain,
% 16.37/10.90 (node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3988, 112, 102])).
% 16.37/10.90 tff(3990,plain,
% 16.37/10.90 (node22(c_e_h_3, c_q, s0, s1)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3989, 3985])).
% 16.37/10.90 tff(3991,plain,
% 16.37/10.90 (((~![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, 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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3992,plain,
% 16.37/10.90 ((~![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, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3993,plain,
% 16.37/10.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3992, 3991])).
% 16.37/10.90 tff(3994,plain,
% 16.37/10.90 ($false),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3993, 127, 369, 3959, 3990])).
% 16.37/10.90 tff(3995,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.90 tff(3996,plain,
% 16.37/10.90 (((~![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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(3997,plain,
% 16.37/10.90 ((~![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))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(3998,plain,
% 16.37/10.90 ((~![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)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[3997, 3996])).
% 16.37/10.90 tff(3999,plain,
% 16.37/10.90 (node3(c_e_h_3, c_e_h_1, s1)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[3998, 379, 376])).
% 16.37/10.90 tff(4000,plain,
% 16.37/10.90 (((~![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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(4001,plain,
% 16.37/10.90 ((~![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))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(4002,plain,
% 16.37/10.90 ((~![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)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 16.37/10.90 tff(4003,plain,
% 16.37/10.90 ((~m_cell_v_ack(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[4002, 393, 3999])).
% 16.37/10.90 tff(4004,plain,
% 16.37/10.90 (~m_cell_v_ack(c_e_h_1, s1)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[4003, 3995])).
% 16.37/10.90 tff(4005,plain,
% 16.37/10.90 (((~![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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(4006,plain,
% 16.37/10.90 ((~![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))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(4007,plain,
% 16.37/10.90 ((~![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)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[4006, 4005])).
% 16.37/10.90 tff(4008,plain,
% 16.37/10.90 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[4007, 405, 4004])).
% 16.37/10.90 tff(4009,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s1)), introduced(assumption)).
% 16.37/10.90 tff(4010,assumption,(node21(c_e_h_1, c_l, s0, s1)), introduced(assumption)).
% 16.37/10.90 tff(4011,plain,
% 16.37/10.90 (((~![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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(4012,plain,
% 16.37/10.90 ((~![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))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(4013,plain,
% 16.37/10.90 ((~![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)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[4012, 4011])).
% 16.37/10.90 tff(4014,plain,
% 16.37/10.90 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[4013, 53, 1138])).
% 16.37/10.90 tff(4015,plain,
% 16.37/10.90 (((~![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))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(4016,plain,
% 16.37/10.90 ((~![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))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.90 tff(4017,plain,
% 16.37/10.90 ((~![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)),
% 16.37/10.90 inference(modus_ponens,[status(thm)],[4016, 4015])).
% 16.37/10.90 tff(4018,plain,
% 16.37/10.90 (~node20(c_e_h_1, c_l, s0)),
% 16.37/10.90 inference(unit_resolution,[status(thm)],[4017, 68, 4014])).
% 16.37/10.90 tff(4019,plain,
% 16.37/10.90 (((~![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, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, 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_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(4020,plain,
% 16.37/10.90 ((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))) <=> (node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)))),
% 16.37/10.90 inference(rewrite,[status(thm)],[])).
% 16.37/10.90 tff(4021,plain,
% 16.37/10.90 (((~![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, 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) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1))))),
% 16.37/10.90 inference(monotonicity,[status(thm)],[4020])).
% 16.37/10.90 tff(4022,plain,
% 16.37/10.90 (((~![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, 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) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)))),
% 16.37/10.90 inference(transitivity,[status(thm)],[4021, 4019])).
% 16.37/10.90 tff(4023,plain,
% 16.37/10.90 ((~![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, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))),
% 16.37/10.90 inference(quant_inst,[status(thm)],[])).
% 16.37/10.91 tff(4024,plain,
% 16.37/10.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 16.37/10.91 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 16.37/10.91 tff(4025,plain,
% 16.37/10.91 ($false),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4024, 82, 4018, 4010, 4009])).
% 16.37/10.91 tff(4026,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,[]))).
% 16.37/10.91 tff(4027,plain,
% 16.37/10.91 (~node21(c_e_h_1, c_l, s0, s1)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4026, 4009])).
% 16.37/10.91 tff(4028,plain,
% 16.37/10.91 (((~![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))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4029,plain,
% 16.37/10.91 ((~![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))),
% 16.37/10.91 inference(quant_inst,[status(thm)],[])).
% 16.37/10.91 tff(4030,plain,
% 16.37/10.91 ((~![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)),
% 16.37/10.91 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 16.37/10.91 tff(4031,plain,
% 16.37/10.91 (node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4030, 112, 102])).
% 16.37/10.91 tff(4032,plain,
% 16.37/10.91 (node22(c_e_h_1, c_l, s0, s1)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4031, 4027])).
% 16.37/10.91 tff(4033,plain,
% 16.37/10.91 (((~![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))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4034,plain,
% 16.37/10.91 ((~![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))),
% 16.37/10.91 inference(quant_inst,[status(thm)],[])).
% 16.37/10.91 tff(4035,plain,
% 16.37/10.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 16.37/10.91 inference(modus_ponens,[status(thm)],[4034, 4033])).
% 16.37/10.91 tff(4036,plain,
% 16.37/10.91 ($false),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4035, 127, 4032, 413, 4009])).
% 16.37/10.91 tff(4037,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.91 tff(4038,plain,
% 16.37/10.91 (((~![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))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4039,plain,
% 16.37/10.91 ((~![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))),
% 16.37/10.91 inference(quant_inst,[status(thm)],[])).
% 16.37/10.91 tff(4040,plain,
% 16.37/10.91 ((~![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)),
% 16.37/10.91 inference(modus_ponens,[status(thm)],[4039, 4038])).
% 16.37/10.91 tff(4041,plain,
% 16.37/10.91 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4040, 420, 4037])).
% 16.37/10.91 tff(4042,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)), introduced(assumption)).
% 16.37/10.91 tff(4043,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)), introduced(assumption)).
% 16.37/10.91 tff(4044,assumption,(node5(c_e_h_1, c_j, s1, s2)), introduced(assumption)).
% 16.37/10.91 tff(4045,plain,
% 16.37/10.91 (((~![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_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_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_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_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4046,plain,
% 16.37/10.91 ((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_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_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4047,plain,
% 16.37/10.91 (((~![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_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_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2))))),
% 16.37/10.91 inference(monotonicity,[status(thm)],[4046])).
% 16.37/10.91 tff(4048,plain,
% 16.37/10.91 (((~![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_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_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 16.37/10.91 inference(transitivity,[status(thm)],[4047, 4045])).
% 16.37/10.91 tff(4049,plain,
% 16.37/10.91 ((~![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)))),
% 16.37/10.91 inference(quant_inst,[status(thm)],[])).
% 16.37/10.91 tff(4050,plain,
% 16.37/10.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2))),
% 16.37/10.91 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 16.37/10.91 tff(4051,plain,
% 16.37/10.91 ($false),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4050, 473, 3946, 4044, 4043, 4042])).
% 16.37/10.91 tff(4052,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) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.91 tff(4053,plain,
% 16.37/10.91 ((~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)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4052, 4041])).
% 16.37/10.91 tff(4054,plain,
% 16.37/10.91 ((~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4053, 4008])).
% 16.37/10.91 tff(4055,plain,
% 16.37/10.91 (~node5(c_e_h_1, c_j, s1, s2)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4054, 3946])).
% 16.37/10.91 tff(4056,plain,
% 16.37/10.91 (((~![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))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4057,plain,
% 16.37/10.91 ((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))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4058,plain,
% 16.37/10.91 (((~![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)))),
% 16.37/10.91 inference(monotonicity,[status(thm)],[4057])).
% 16.37/10.91 tff(4059,plain,
% 16.37/10.91 (((~![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))),
% 16.37/10.91 inference(transitivity,[status(thm)],[4058, 4056])).
% 16.37/10.91 tff(4060,plain,
% 16.37/10.91 ((~![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)))),
% 16.37/10.91 inference(quant_inst,[status(thm)],[])).
% 16.37/10.91 tff(4061,plain,
% 16.37/10.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2)),
% 16.37/10.91 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 16.37/10.91 tff(4062,plain,
% 16.37/10.91 (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4061, 455, 348])).
% 16.37/10.91 tff(4063,plain,
% 16.37/10.91 ($false),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4062, 4055, 3958])).
% 16.37/10.91 tff(4064,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 16.37/10.91 tff(4065,plain,
% 16.37/10.91 (((~![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))),
% 16.37/10.91 inference(rewrite,[status(thm)],[])).
% 16.37/10.91 tff(4066,plain,
% 16.37/10.91 ((~![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))),
% 16.37/10.91 inference(quant_inst,[status(thm)],[])).
% 16.37/10.91 tff(4067,plain,
% 16.37/10.91 ((~![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)),
% 16.37/10.91 inference(modus_ponens,[status(thm)],[4066, 4065])).
% 16.37/10.91 tff(4068,plain,
% 16.37/10.91 (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)),
% 16.37/10.91 inference(unit_resolution,[status(thm)],[4067, 195, 4064])).
% 16.37/10.91 tff(4069,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 16.37/10.91 tff(4070,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s2)), introduced(assumption)).
% 16.37/10.91 tff(4071,assumption,(node15(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 16.37/10.91 tff(4072,plain,
% 16.37/10.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(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))),
% 16.45/10.91 inference(rewrite,[status(thm)],[])).
% 16.45/10.91 tff(4073,plain,
% 16.45/10.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(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))),
% 16.45/10.91 inference(quant_inst,[status(thm)],[])).
% 16.45/10.91 tff(4074,plain,
% 16.45/10.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 16.45/10.91 inference(modus_ponens,[status(thm)],[4073, 4072])).
% 16.45/10.91 tff(4075,plain,
% 16.45/10.91 ($false),
% 16.45/10.91 inference(unit_resolution,[status(thm)],[4074, 178, 4070, 4069, 4071])).
% 16.45/10.91 tff(4076,plain,((~node15(c_e_h_1, c_h, s2, s3)) | 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, s3))), inference(lemma,lemma(discharge,[]))).
% 16.45/10.91 tff(4077,plain,
% 16.45/10.91 (~node15(c_e_h_1, c_h, s2, s3)),
% 16.45/10.91 inference(unit_resolution,[status(thm)],[4076, 4070, 4069])).
% 16.45/10.91 tff(4078,assumption,(node18(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 16.45/10.91 tff(4079,plain,
% 16.45/10.91 (((~![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_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~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, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 16.45/10.91 inference(rewrite,[status(thm)],[])).
% 16.45/10.91 tff(4080,plain,
% 16.45/10.91 (((~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))) <=> (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, s3)) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 16.45/10.91 inference(rewrite,[status(thm)],[])).
% 16.45/10.91 tff(4081,plain,
% 16.45/10.91 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3))))),
% 16.45/10.91 inference(monotonicity,[status(thm)],[4080])).
% 16.45/10.91 tff(4082,plain,
% 16.45/10.91 (((~![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_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, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 16.45/10.91 inference(transitivity,[status(thm)],[4081, 4079])).
% 16.45/10.91 tff(4083,plain,
% 16.45/10.91 ((~![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_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)))),
% 16.45/10.91 inference(quant_inst,[status(thm)],[])).
% 16.45/10.91 tff(4084,plain,
% 16.45/10.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3))),
% 16.45/10.91 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 16.45/10.91 tff(4085,plain,
% 16.45/10.91 ($false),
% 16.45/10.91 inference(unit_resolution,[status(thm)],[4084, 560, 4070, 4069, 4078])).
% 16.45/10.91 tff(4086,plain,((~node18(c_e_h_1, c_h, s2, s3)) | 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, s3))), inference(lemma,lemma(discharge,[]))).
% 16.45/10.91 tff(4087,plain,
% 16.45/10.91 (~node18(c_e_h_1, c_h, s2, s3)),
% 16.45/10.91 inference(unit_resolution,[status(thm)],[4086, 4070, 4069])).
% 16.45/10.91 tff(4088,plain,
% 16.45/10.91 (((~![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))),
% 16.45/10.91 inference(rewrite,[status(thm)],[])).
% 16.45/10.91 tff(4089,plain,
% 16.45/10.91 ((~![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))),
% 16.45/10.91 inference(quant_inst,[status(thm)],[])).
% 16.45/10.91 tff(4090,plain,
% 16.45/10.91 ((~![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)),
% 16.45/10.91 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 16.45/10.91 tff(4091,plain,
% 16.45/10.91 (node19(c_e_h_1, c_h, s2, s3)),
% 16.45/10.91 inference(unit_resolution,[status(thm)],[4090, 221, 591])).
% 16.45/10.91 tff(4092,plain,
% 16.45/10.91 (((~![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_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)))),
% 16.45/10.91 inference(rewrite,[status(thm)],[])).
% 16.45/10.91 tff(4093,plain,
% 16.45/10.91 ((~![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_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 16.45/10.91 inference(quant_inst,[status(thm)],[])).
% 16.45/10.91 tff(4094,plain,
% 16.45/10.91 ((~![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_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))),
% 16.45/10.91 inference(modus_ponens,[status(thm)],[4093, 4092])).
% 16.45/10.91 tff(4095,plain,
% 16.45/10.91 (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3)),
% 16.45/10.91 inference(unit_resolution,[status(thm)],[4094, 542, 4091])).
% 16.45/10.91 tff(4096,plain,
% 16.45/10.91 (node17(c_e_h_1, c_h, s2)),
% 16.45/10.91 inference(unit_resolution,[status(thm)],[4095, 4087])).
% 16.45/10.91 tff(4097,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s2)), introduced(assumption)).
% 16.45/10.91 tff(4098,plain,
% 16.45/10.91 (((~![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_h, s2) | (~node17(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)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)))),
% 16.45/10.91 inference(rewrite,[status(thm)],[])).
% 16.45/10.91 tff(4099,plain,
% 16.45/10.91 (((~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))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)))),
% 16.45/10.91 inference(rewrite,[status(thm)],[])).
% 16.45/10.91 tff(4100,plain,
% 16.45/10.91 (((~![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_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)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2))))),
% 16.45/10.92 inference(monotonicity,[status(thm)],[4099])).
% 16.45/10.92 tff(4101,plain,
% 16.45/10.92 (((~![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_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)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)))),
% 16.45/10.92 inference(transitivity,[status(thm)],[4100, 4098])).
% 16.45/10.92 tff(4102,plain,
% 16.45/10.92 ((~![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_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4103,plain,
% 16.45/10.92 ((~![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_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2))),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4102, 4101])).
% 16.45/10.92 tff(4104,plain,
% 16.45/10.92 ((~node17(c_e_h_1, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2))),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4103, 524, 4097])).
% 16.45/10.92 tff(4105,plain,
% 16.45/10.92 (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4104, 4096])).
% 16.45/10.92 tff(4106,plain,
% 16.45/10.92 (((~![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))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4107,plain,
% 16.45/10.92 ((~![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))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4108,plain,
% 16.45/10.92 ((~![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)),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 16.45/10.92 tff(4109,plain,
% 16.45/10.92 ((~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4108, 209, 4097])).
% 16.45/10.92 tff(4110,plain,
% 16.45/10.92 (~node16(c_e_h_1, c_h, s2)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4109, 4105])).
% 16.45/10.92 tff(4111,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s2)), introduced(assumption)).
% 16.45/10.92 tff(4112,assumption,(node14(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 16.45/10.92 tff(4113,plain,
% 16.45/10.92 (((~![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_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)))) | (~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)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4114,plain,
% 16.45/10.92 ((~![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_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)))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4115,plain,
% 16.45/10.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4114, 4113])).
% 16.45/10.92 tff(4116,plain,
% 16.45/10.92 ($false),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4115, 254, 4069, 4112, 4111])).
% 16.45/10.92 tff(4117,plain,((~node14(c_e_h_1, c_h, s2, 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)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.92 tff(4118,plain,
% 16.45/10.92 (~node14(c_e_h_1, c_h, s2, s3)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4117, 4105, 4069])).
% 16.45/10.92 tff(4119,plain,
% 16.45/10.92 (((~![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_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(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)))) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4120,plain,
% 16.45/10.92 ((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))) <=> (node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4121,plain,
% 16.45/10.92 (((~![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_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)))) | (node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))))),
% 16.45/10.92 inference(monotonicity,[status(thm)],[4120])).
% 16.45/10.92 tff(4122,plain,
% 16.45/10.92 (((~![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_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)))) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 16.45/10.92 inference(transitivity,[status(thm)],[4121, 4119])).
% 16.45/10.92 tff(4123,plain,
% 16.45/10.92 ((~![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_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)))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4124,plain,
% 16.45/10.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4123, 4122])).
% 16.45/10.92 tff(4125,plain,
% 16.45/10.92 (node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4124, 235, 4091])).
% 16.45/10.92 tff(4126,plain,
% 16.45/10.92 ($false),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4125, 4118, 4110, 4077])).
% 16.45/10.92 tff(4127,plain,(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, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.92 tff(4128,plain,
% 16.45/10.92 (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, s3))),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4127, 4068])).
% 16.45/10.92 tff(4129,plain,
% 16.45/10.92 (~m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4128, 566])).
% 16.45/10.92 tff(4130,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_i, s3)), introduced(assumption)).
% 16.45/10.92 tff(4131,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 16.45/10.92 tff(4132,plain,
% 16.45/10.92 (((~![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))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4133,plain,
% 16.45/10.92 ((~![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))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4134,plain,
% 16.45/10.92 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4133, 4132])).
% 16.45/10.92 tff(4135,plain,
% 16.45/10.92 ($false),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4134, 269, 4131, 4130])).
% 16.45/10.92 tff(4136,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.92 tff(4137,plain,
% 16.45/10.92 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4136, 4129])).
% 16.45/10.92 tff(4138,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)), introduced(assumption)).
% 16.45/10.92 tff(4139,assumption,(node20(c_e_h_1, c_i, s3)), introduced(assumption)).
% 16.45/10.92 tff(4140,plain,
% 16.45/10.92 (((~![I0: $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))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4141,plain,
% 16.45/10.92 ((~![I0: $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))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4142,plain,
% 16.45/10.92 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 16.45/10.92 tff(4143,plain,
% 16.45/10.92 ($false),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4142, 283, 4139, 4138])).
% 16.45/10.92 tff(4144,plain,((~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.92 tff(4145,plain,
% 16.45/10.92 (~node20(c_e_h_1, c_i, s3)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4144, 4137])).
% 16.45/10.92 tff(4146,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 16.45/10.92 tff(4147,plain,
% 16.45/10.92 (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[615, 612, 604])).
% 16.45/10.92 tff(4148,plain,
% 16.45/10.92 (~m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[1091, 4147])).
% 16.45/10.92 tff(4149,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s4)), introduced(assumption)).
% 16.45/10.92 tff(4150,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 16.45/10.92 tff(4151,assumption,(~node14(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 16.45/10.92 tff(4152,assumption,(node15(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 16.45/10.92 tff(4153,plain,
% 16.45/10.92 (((~![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_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))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4154,plain,
% 16.45/10.92 ((~![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_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4155,plain,
% 16.45/10.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4154, 4153])).
% 16.45/10.92 tff(4156,plain,
% 16.45/10.92 ($false),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4155, 178, 4146, 4150, 4152])).
% 16.45/10.92 tff(4157,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,[]))).
% 16.45/10.92 tff(4158,plain,
% 16.45/10.92 (~node15(c_e_h_1, c_e, s4, s5)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4157, 4150, 4146])).
% 16.45/10.92 tff(4159,plain,
% 16.45/10.92 (((~![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))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4160,plain,
% 16.45/10.92 ((~![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))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4161,plain,
% 16.45/10.92 ((~![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)),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4160, 4159])).
% 16.45/10.92 tff(4162,plain,
% 16.45/10.92 (node19(c_e_h_1, c_e, s4, s5)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4161, 221, 1520])).
% 16.45/10.92 tff(4163,plain,
% 16.45/10.92 (((~![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_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) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4164,plain,
% 16.45/10.92 ((~![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_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)))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4165,plain,
% 16.45/10.92 ((~![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_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))),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4164, 4163])).
% 16.45/10.92 tff(4166,plain,
% 16.45/10.92 (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)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4165, 235, 4162])).
% 16.45/10.92 tff(4167,plain,
% 16.45/10.92 (node16(c_e_h_1, c_e, s4)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4166, 4158, 4151])).
% 16.45/10.92 tff(4168,plain,
% 16.45/10.92 (((~![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_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))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4169,plain,
% 16.45/10.92 ((~![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_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))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4170,plain,
% 16.45/10.92 ((~![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_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)),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 16.45/10.92 tff(4171,plain,
% 16.45/10.92 ((~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4170, 209, 4149])).
% 16.45/10.92 tff(4172,plain,
% 16.45/10.92 (m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4171, 4167])).
% 16.45/10.92 tff(4173,plain,
% 16.45/10.92 (((~![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_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)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4174,plain,
% 16.45/10.92 (((~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)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4175,plain,
% 16.45/10.92 (((~![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, 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))))),
% 16.45/10.92 inference(monotonicity,[status(thm)],[4174])).
% 16.45/10.92 tff(4176,plain,
% 16.45/10.92 (((~![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, 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)))),
% 16.45/10.92 inference(transitivity,[status(thm)],[4175, 4173])).
% 16.45/10.92 tff(4177,plain,
% 16.45/10.92 ((~![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, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4178,plain,
% 16.45/10.92 ((~![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_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))),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 16.45/10.92 tff(4179,plain,
% 16.45/10.92 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4))),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4178, 524, 4149])).
% 16.45/10.92 tff(4180,plain,
% 16.45/10.92 (~node17(c_e_h_1, c_e, s4)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4179, 4172])).
% 16.45/10.92 tff(4181,plain,
% 16.45/10.92 (((~![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_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) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4182,plain,
% 16.45/10.92 ((~![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_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4183,plain,
% 16.45/10.92 ((~![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_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5))),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 16.45/10.92 tff(4184,plain,
% 16.45/10.92 (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4183, 542, 4162])).
% 16.45/10.92 tff(4185,plain,
% 16.45/10.92 (node18(c_e_h_1, c_e, s4, s5)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4184, 4180])).
% 16.45/10.92 tff(4186,plain,
% 16.45/10.92 (((~![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, 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)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4187,plain,
% 16.45/10.92 ((~![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, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 16.45/10.92 inference(quant_inst,[status(thm)],[])).
% 16.45/10.92 tff(4188,plain,
% 16.45/10.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5))),
% 16.45/10.92 inference(modus_ponens,[status(thm)],[4187, 4186])).
% 16.45/10.92 tff(4189,plain,
% 16.45/10.92 ($false),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4188, 560, 4146, 4150, 4185])).
% 16.45/10.92 tff(4190,plain,(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)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.92 tff(4191,plain,
% 16.45/10.92 (node14(c_e_h_1, c_e, s4, s5)),
% 16.45/10.92 inference(unit_resolution,[status(thm)],[4190, 4146, 4150, 4149])).
% 16.45/10.92 tff(4192,plain,
% 16.45/10.92 (((~![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_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~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_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4193,plain,
% 16.45/10.92 (((~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_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 16.45/10.92 inference(rewrite,[status(thm)],[])).
% 16.45/10.92 tff(4194,plain,
% 16.45/10.92 (((~![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_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_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node14(c_e_h_1, c_e, s4, s5))))),
% 16.45/10.92 inference(monotonicity,[status(thm)],[4193])).
% 16.45/10.92 tff(4195,plain,
% 16.45/10.92 (((~![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_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_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 16.45/10.93 inference(transitivity,[status(thm)],[4194, 4192])).
% 16.45/10.93 tff(4196,plain,
% 16.45/10.93 ((~![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_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)))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4197,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node14(c_e_h_1, c_e, s4, s5))),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4196, 4195])).
% 16.45/10.93 tff(4198,plain,
% 16.45/10.93 (m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4197, 254, 4146, 4191])).
% 16.45/10.93 tff(4199,plain,
% 16.45/10.93 (~node17(c_e_h_1, c_e, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4179, 4198])).
% 16.45/10.93 tff(4200,plain,
% 16.45/10.93 (node18(c_e_h_1, c_e, s4, s5)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4184, 4199])).
% 16.45/10.93 tff(4201,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4188, 560, 4146, 4150, 4200])).
% 16.45/10.93 tff(4202,plain,((~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) | m_c_h_element_v_in2(c_e_h_1, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.93 tff(4203,plain,
% 16.45/10.93 (m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4202, 4148, 4146])).
% 16.45/10.93 tff(4204,assumption,(~node20(c_e_h_1, c_i, s3)), introduced(assumption)).
% 16.45/10.93 tff(4205,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 16.45/10.93 tff(4206,assumption,(node22(c_e_h_1, c_i, s3, s4)), introduced(assumption)).
% 16.45/10.93 tff(4207,plain,
% 16.45/10.93 (((~![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_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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4208,plain,
% 16.45/10.93 ((~![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_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4209,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 16.45/10.93 tff(4210,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4209, 127, 4206, 4205, 604])).
% 16.45/10.93 tff(4211,plain,((~node22(c_e_h_1, c_i, s3, s4)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.93 tff(4212,plain,
% 16.45/10.93 (~node22(c_e_h_1, c_i, s3, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4211, 4205, 604])).
% 16.45/10.93 tff(4213,assumption,(node21(c_e_h_1, c_i, s3, s4)), introduced(assumption)).
% 16.45/10.93 tff(4214,plain,
% 16.45/10.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, 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, s4)) | node20(c_e_h_1, c_i, s3) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4215,plain,
% 16.45/10.93 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4216,plain,
% 16.45/10.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3) | (~node21(c_e_h_1, c_i, s3, s4))))),
% 16.45/10.93 inference(monotonicity,[status(thm)],[4215])).
% 16.45/10.93 tff(4217,plain,
% 16.45/10.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 16.45/10.93 inference(transitivity,[status(thm)],[4216, 4214])).
% 16.45/10.93 tff(4218,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4219,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3) | (~node21(c_e_h_1, c_i, s3, s4))),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4218, 4217])).
% 16.45/10.93 tff(4220,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4219, 82, 4213, 4205, 4204])).
% 16.45/10.93 tff(4221,plain,((~node21(c_e_h_1, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.93 tff(4222,plain,
% 16.45/10.93 (~node21(c_e_h_1, c_i, s3, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4221, 4205, 4204])).
% 16.45/10.93 tff(4223,plain,
% 16.45/10.93 (((~![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4224,plain,
% 16.45/10.93 ((~![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))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4225,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4224, 4223])).
% 16.45/10.93 tff(4226,plain,
% 16.45/10.93 (node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4225, 112, 1013])).
% 16.45/10.93 tff(4227,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4226, 4222, 4212])).
% 16.45/10.93 tff(4228,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.93 tff(4229,plain,
% 16.45/10.93 (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4228, 604, 4204])).
% 16.45/10.93 tff(4230,plain,
% 16.45/10.93 (((~![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4231,plain,
% 16.45/10.93 ((~![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))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4232,plain,
% 16.45/10.93 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4231, 4230])).
% 16.45/10.93 tff(4233,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4232, 612, 4229, 4203])).
% 16.45/10.93 tff(4234,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | node20(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.93 tff(4235,plain,
% 16.45/10.93 (m_and_h_gate_v_out(c_e_h_1, c_i, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4234, 4145])).
% 16.45/10.93 tff(4236,plain,
% 16.45/10.93 (~m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4235, 603])).
% 16.45/10.93 tff(4237,plain,
% 16.45/10.93 (((~![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4238,plain,
% 16.45/10.93 ((~![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))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4239,plain,
% 16.45/10.93 ((~![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)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 16.45/10.93 tff(4240,plain,
% 16.45/10.93 (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)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4239, 1099])).
% 16.45/10.93 tff(4241,plain,
% 16.45/10.93 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4240, 4236])).
% 16.45/10.93 tff(4242,plain,
% 16.45/10.93 ((~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)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4228, 4145])).
% 16.45/10.93 tff(4243,plain,
% 16.45/10.93 (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4242, 603])).
% 16.45/10.93 tff(4244,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s3)), introduced(assumption)).
% 16.45/10.93 tff(4245,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s2)), introduced(assumption)).
% 16.45/10.93 tff(4246,assumption,(node21(c_e_h_1, c_l, s1, s2)), introduced(assumption)).
% 16.45/10.93 tff(4247,plain,
% 16.45/10.93 (((~![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4248,plain,
% 16.45/10.93 ((~![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))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4249,plain,
% 16.45/10.93 ((~![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)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4248, 4247])).
% 16.45/10.93 tff(4250,plain,
% 16.45/10.93 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4249, 53, 1309])).
% 16.45/10.93 tff(4251,plain,
% 16.45/10.93 (((~![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4252,plain,
% 16.45/10.93 ((~![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))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4253,plain,
% 16.45/10.93 ((~![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)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4252, 4251])).
% 16.45/10.93 tff(4254,plain,
% 16.45/10.93 (~node20(c_e_h_1, c_l, s1)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4253, 68, 4250])).
% 16.45/10.93 tff(4255,plain,
% 16.45/10.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4256,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4257,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2))),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4256, 4255])).
% 16.45/10.93 tff(4258,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4257, 82, 4254, 4245, 4246])).
% 16.45/10.93 tff(4259,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,[]))).
% 16.45/10.93 tff(4260,plain,
% 16.45/10.93 (~node21(c_e_h_1, c_l, s1, s2)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4259, 4245])).
% 16.45/10.93 tff(4261,plain,
% 16.45/10.93 (((~![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4262,plain,
% 16.45/10.93 ((~![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))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4263,plain,
% 16.45/10.93 ((~![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)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4262, 4261])).
% 16.45/10.93 tff(4264,plain,
% 16.45/10.93 (node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4263, 112, 348])).
% 16.45/10.93 tff(4265,plain,
% 16.45/10.93 (node22(c_e_h_1, c_l, s1, s2)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4264, 4260])).
% 16.45/10.93 tff(4266,plain,
% 16.45/10.93 (((~![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_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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4267,plain,
% 16.45/10.93 ((~![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_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4268,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4267, 4266])).
% 16.45/10.93 tff(4269,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4268, 127, 4037, 4245, 4265])).
% 16.45/10.93 tff(4270,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.93 tff(4271,plain,
% 16.45/10.93 (((~![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4272,plain,
% 16.45/10.93 ((~![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))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4273,plain,
% 16.45/10.93 ((~![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)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4272, 4271])).
% 16.45/10.93 tff(4274,plain,
% 16.45/10.93 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4273, 420, 4270])).
% 16.45/10.93 tff(4275,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s0)), introduced(assumption)).
% 16.45/10.93 tff(4276,plain,
% 16.45/10.93 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4277,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4276, 9, 4275])).
% 16.45/10.93 tff(4278,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.93 tff(4279,plain,
% 16.45/10.93 (^[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)))),
% 16.45/10.93 inference(bind,[status(th)],[])).
% 16.45/10.93 tff(4280,plain,
% 16.45/10.93 (![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))),
% 16.45/10.93 inference(quant_intro,[status(thm)],[4279])).
% 16.45/10.93 tff(4281,plain,
% 16.45/10.93 (![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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4282,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')).
% 16.45/10.93 tff(4283,plain,
% 16.45/10.93 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4282, 4281])).
% 16.45/10.93 tff(4284,plain,(
% 16.45/10.93 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.45/10.93 inference(skolemize,[status(sab)],[4283])).
% 16.45/10.93 tff(4285,plain,
% 16.45/10.93 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4284, 4280])).
% 16.45/10.93 tff(4286,plain,
% 16.45/10.93 (((~![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, s0)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4287,plain,
% 16.45/10.93 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4288,plain,
% 16.45/10.93 ((~![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, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4287, 4286])).
% 16.45/10.93 tff(4289,plain,
% 16.45/10.93 (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4288, 4285, 4278])).
% 16.45/10.93 tff(4290,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s1)), introduced(assumption)).
% 16.45/10.93 tff(4291,assumption,(node15(c_e_h_3, c_f, s0, s1)), introduced(assumption)).
% 16.45/10.93 tff(4292,plain,
% 16.45/10.93 (((~![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_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))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4293,plain,
% 16.45/10.93 ((~![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_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4294,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4293, 4292])).
% 16.45/10.93 tff(4295,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4294, 178, 4290, 3964, 4291])).
% 16.45/10.93 tff(4296,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,[]))).
% 16.45/10.93 tff(4297,plain,
% 16.45/10.93 (~node15(c_e_h_3, c_f, s0, s1)),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4296, 4290])).
% 16.45/10.93 tff(4298,assumption,(node18(c_e_h_3, c_f, s0, s1)), introduced(assumption)).
% 16.45/10.93 tff(4299,plain,
% 16.45/10.93 (((~![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_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, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))),
% 16.45/10.93 inference(rewrite,[status(thm)],[])).
% 16.45/10.93 tff(4300,plain,
% 16.45/10.93 ((~![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_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))),
% 16.45/10.93 inference(quant_inst,[status(thm)],[])).
% 16.45/10.93 tff(4301,plain,
% 16.45/10.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1))),
% 16.45/10.93 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 16.45/10.93 tff(4302,plain,
% 16.45/10.93 ($false),
% 16.45/10.93 inference(unit_resolution,[status(thm)],[4301, 560, 4290, 3964, 4298])).
% 16.45/10.93 tff(4303,plain,((~node18(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,[]))).
% 16.45/10.93 tff(4304,plain,
% 16.45/10.94 (~node18(c_e_h_3, c_f, s0, s1)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4303, 4290])).
% 16.45/10.94 tff(4305,plain,
% 16.45/10.94 (((~![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))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4306,plain,
% 16.45/10.94 ((~![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))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4307,plain,
% 16.45/10.94 ((~![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)),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4306, 4305])).
% 16.45/10.94 tff(4308,plain,
% 16.45/10.94 (node19(c_e_h_3, c_f, s0, s1)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4307, 221, 102])).
% 16.45/10.94 tff(4309,plain,
% 16.45/10.94 (((~![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)) | node17(c_e_h_3, c_f, s0) | node18(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)) | node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4310,plain,
% 16.45/10.94 ((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)) | node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4311,plain,
% 16.45/10.94 (((~![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_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)) | node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1)))),
% 16.45/10.94 inference(monotonicity,[status(thm)],[4310])).
% 16.45/10.94 tff(4312,plain,
% 16.45/10.94 (((~![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_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)) | node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1))),
% 16.45/10.94 inference(transitivity,[status(thm)],[4311, 4309])).
% 16.45/10.94 tff(4313,plain,
% 16.45/10.94 ((~![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_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4314,plain,
% 16.45/10.94 ((~![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)) | node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1)),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 16.45/10.94 tff(4315,plain,
% 16.45/10.94 (node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4314, 542, 4308])).
% 16.45/10.94 tff(4316,plain,
% 16.45/10.94 (node17(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4315, 4304])).
% 16.45/10.94 tff(4317,assumption,(node17(c_e_h_3, c_f, s0)), introduced(assumption)).
% 16.45/10.94 tff(4318,assumption,(node16(c_e_h_3, c_f, s0)), introduced(assumption)).
% 16.45/10.94 tff(4319,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s0)), introduced(assumption)).
% 16.45/10.94 tff(4320,plain,
% 16.45/10.94 (((~![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_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)))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4321,plain,
% 16.45/10.94 ((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)))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4322,plain,
% 16.45/10.94 (((~![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_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))))),
% 16.45/10.94 inference(monotonicity,[status(thm)],[4321])).
% 16.45/10.94 tff(4323,plain,
% 16.45/10.94 (((~![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_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)))),
% 16.45/10.94 inference(transitivity,[status(thm)],[4322, 4320])).
% 16.45/10.94 tff(4324,plain,
% 16.45/10.94 ((~![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_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4325,plain,
% 16.45/10.94 ((~![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_f, s0) | (~node17(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4324, 4323])).
% 16.45/10.94 tff(4326,plain,
% 16.45/10.94 (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))),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4325, 767, 4317])).
% 16.45/10.94 tff(4327,plain,
% 16.45/10.94 (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4326, 4319])).
% 16.45/10.94 tff(4328,plain,
% 16.45/10.94 (((~![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_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))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4329,plain,
% 16.45/10.94 ((~![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_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))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4330,plain,
% 16.45/10.94 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4329, 4328])).
% 16.45/10.94 tff(4331,plain,
% 16.45/10.94 (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4330, 209, 4318])).
% 16.45/10.94 tff(4332,plain,
% 16.45/10.94 ($false),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4331, 4327, 4319])).
% 16.45/10.94 tff(4333,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~node16(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0))), inference(lemma,lemma(discharge,[]))).
% 16.45/10.94 tff(4334,plain,
% 16.45/10.94 (m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4333, 4318, 4317])).
% 16.45/10.94 tff(4335,plain,
% 16.45/10.94 (((~![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_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)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4336,plain,
% 16.45/10.94 ((~![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_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4337,plain,
% 16.45/10.94 ((~![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_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0))),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4336, 4335])).
% 16.45/10.94 tff(4338,plain,
% 16.45/10.94 ((~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)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4337, 524, 4317])).
% 16.45/10.94 tff(4339,plain,
% 16.45/10.94 (m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4338, 4334])).
% 16.45/10.94 tff(4340,plain,
% 16.45/10.94 (((~![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)))) | ((~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)) | (~node16(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)))) | (~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)) | (~node16(c_e_h_3, c_f, s0)))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4341,plain,
% 16.45/10.94 (((~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))) <=> ((~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)) | (~node16(c_e_h_3, c_f, s0)))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4342,plain,
% 16.45/10.94 (((~![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_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)))) | ((~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)) | (~node16(c_e_h_3, c_f, s0))))),
% 16.45/10.94 inference(monotonicity,[status(thm)],[4341])).
% 16.45/10.94 tff(4343,plain,
% 16.45/10.94 (((~![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_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)))) | (~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)) | (~node16(c_e_h_3, c_f, s0)))),
% 16.45/10.94 inference(transitivity,[status(thm)],[4342, 4340])).
% 16.45/10.94 tff(4344,plain,
% 16.45/10.94 ((~![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_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)))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4345,plain,
% 16.45/10.94 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | (~node16(c_e_h_3, c_f, s0))),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4344, 4343])).
% 16.45/10.94 tff(4346,plain,
% 16.45/10.94 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4345, 983, 4318])).
% 16.45/10.94 tff(4347,plain,
% 16.45/10.94 ($false),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4346, 4339, 4334])).
% 16.45/10.94 tff(4348,plain,((~node16(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0))), inference(lemma,lemma(discharge,[]))).
% 16.45/10.94 tff(4349,plain,
% 16.45/10.94 (~node16(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4348, 4316])).
% 16.45/10.94 tff(4350,plain,
% 16.45/10.94 (((~![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_f, s0) | node15(c_e_h_3, c_f, s0, s1) | node14(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) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4351,plain,
% 16.45/10.94 ((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) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4352,plain,
% 16.45/10.94 (((~![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_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) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1))))),
% 16.45/10.94 inference(monotonicity,[status(thm)],[4351])).
% 16.45/10.94 tff(4353,plain,
% 16.45/10.94 (((~![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_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) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 16.45/10.94 inference(transitivity,[status(thm)],[4352, 4350])).
% 16.45/10.94 tff(4354,plain,
% 16.45/10.94 ((~![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_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)))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4355,plain,
% 16.45/10.94 ((~![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_f, s0) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1))),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4354, 4353])).
% 16.45/10.94 tff(4356,plain,
% 16.45/10.94 (node16(c_e_h_3, c_f, s0) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4355, 235, 4308])).
% 16.45/10.94 tff(4357,plain,
% 16.45/10.94 (node14(c_e_h_3, c_f, s0, s1)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4356, 4349, 4297])).
% 16.45/10.94 tff(4358,plain,
% 16.45/10.94 (((~![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_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))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4359,plain,
% 16.45/10.94 (((~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))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4360,plain,
% 16.45/10.94 (((~![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_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)))),
% 16.45/10.94 inference(monotonicity,[status(thm)],[4359])).
% 16.45/10.94 tff(4361,plain,
% 16.45/10.94 (((~![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_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))),
% 16.45/10.94 inference(transitivity,[status(thm)],[4360, 4358])).
% 16.45/10.94 tff(4362,plain,
% 16.45/10.94 ((~![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_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)))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4363,plain,
% 16.45/10.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4362, 4361])).
% 16.45/10.94 tff(4364,plain,
% 16.45/10.94 ($false),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4363, 254, 4290, 4357, 4289])).
% 16.45/10.94 tff(4365,plain,(~m_c_h_element_v_out(c_e_h_3, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.94 tff(4366,plain,
% 16.45/10.94 (((~![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, s1)) | m_c_h_element_v_out(c_e_h_3, 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_3, c_q, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4367,plain,
% 16.45/10.94 ((~![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, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4368,plain,
% 16.45/10.94 ((~![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, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 16.45/10.94 inference(modus_ponens,[status(thm)],[4367, 4366])).
% 16.45/10.94 tff(4369,plain,
% 16.45/10.94 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s1)),
% 16.45/10.94 inference(unit_resolution,[status(thm)],[4368, 3971, 4365])).
% 16.45/10.94 tff(4370,plain,
% 16.45/10.94 (((~![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_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, 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_3, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s1))),
% 16.45/10.94 inference(rewrite,[status(thm)],[])).
% 16.45/10.94 tff(4371,plain,
% 16.45/10.94 ((~![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_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s1))),
% 16.45/10.94 inference(quant_inst,[status(thm)],[])).
% 16.45/10.94 tff(4372,plain,
% 16.45/10.94 ((~![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_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s1)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4371, 4370])).
% 16.45/10.95 tff(4373,plain,
% 16.45/10.95 (~node20(c_e_h_3, c_q, s1)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4372, 283, 4369])).
% 16.45/10.95 tff(4374,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s2)), introduced(assumption)).
% 16.45/10.95 tff(4375,assumption,(node22(c_e_h_3, c_q, s1, s2)), introduced(assumption)).
% 16.45/10.95 tff(4376,plain,
% 16.45/10.95 (((~![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_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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4377,plain,
% 16.45/10.95 ((~![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_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4378,plain,
% 16.45/10.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4377, 4376])).
% 16.45/10.95 tff(4379,plain,
% 16.45/10.95 ($false),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4378, 127, 4374, 4375, 3995])).
% 16.45/10.95 tff(4380,plain,((~node22(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,[]))).
% 16.45/10.95 tff(4381,plain,
% 16.45/10.95 (~node22(c_e_h_3, c_q, s1, s2)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4380, 4374])).
% 16.45/10.95 tff(4382,plain,
% 16.45/10.95 (((~![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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4383,plain,
% 16.45/10.95 ((~![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))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4384,plain,
% 16.45/10.95 ((~![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)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4383, 4382])).
% 16.45/10.95 tff(4385,plain,
% 16.45/10.95 (node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4384, 112, 348])).
% 16.45/10.95 tff(4386,plain,
% 16.45/10.95 (node21(c_e_h_3, c_q, s1, s2)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4385, 4381])).
% 16.45/10.95 tff(4387,plain,
% 16.45/10.95 (((~![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_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)))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4388,plain,
% 16.45/10.95 ((~![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_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4389,plain,
% 16.45/10.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2))),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4388, 4387])).
% 16.45/10.95 tff(4390,plain,
% 16.45/10.95 ($false),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4389, 82, 4374, 4386, 4373])).
% 16.45/10.95 tff(4391,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.95 tff(4392,plain,
% 16.45/10.95 (((~![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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4393,plain,
% 16.45/10.95 ((~![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))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4394,plain,
% 16.45/10.95 ((~![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)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4393, 4392])).
% 16.45/10.95 tff(4395,plain,
% 16.45/10.95 (node3(c_e_h_3, c_e_h_1, s2)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4394, 379, 376])).
% 16.45/10.95 tff(4396,plain,
% 16.45/10.95 (((~![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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4397,plain,
% 16.45/10.95 ((~![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))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4398,plain,
% 16.45/10.95 ((~![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)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4397, 4396])).
% 16.45/10.95 tff(4399,plain,
% 16.45/10.95 ((~m_cell_v_ack(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4398, 393, 4395])).
% 16.45/10.95 tff(4400,plain,
% 16.45/10.95 (~m_cell_v_ack(c_e_h_1, s2)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4399, 4391])).
% 16.45/10.95 tff(4401,plain,
% 16.45/10.95 (((~![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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4402,plain,
% 16.45/10.95 ((~![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))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4403,plain,
% 16.45/10.95 ((~![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)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4402, 4401])).
% 16.45/10.95 tff(4404,plain,
% 16.45/10.95 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4403, 405, 4400])).
% 16.45/10.95 tff(4405,assumption,(node5(c_e_h_1, c_j, s2, s3)), introduced(assumption)).
% 16.45/10.95 tff(4406,plain,
% 16.45/10.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4407,plain,
% 16.45/10.95 ((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)))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4408,plain,
% 16.45/10.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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))))),
% 16.45/10.95 inference(monotonicity,[status(thm)],[4407])).
% 16.45/10.95 tff(4409,plain,
% 16.45/10.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 16.45/10.95 inference(transitivity,[status(thm)],[4408, 4406])).
% 16.45/10.95 tff(4410,plain,
% 16.45/10.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4411,plain,
% 16.45/10.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3))),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4410, 4409])).
% 16.45/10.95 tff(4412,plain,
% 16.45/10.95 ($false),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4411, 473, 4244, 4405, 4404, 4274])).
% 16.45/10.95 tff(4413,plain,((~node5(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,[]))).
% 16.45/10.95 tff(4414,plain,
% 16.45/10.95 (~node5(c_e_h_1, c_j, s2, s3)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4413, 4244])).
% 16.45/10.95 tff(4415,plain,
% 16.45/10.95 (((~![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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4416,plain,
% 16.45/10.95 ((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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4417,plain,
% 16.45/10.95 (((~![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)))),
% 16.45/10.95 inference(monotonicity,[status(thm)],[4416])).
% 16.45/10.95 tff(4418,plain,
% 16.45/10.95 (((~![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))),
% 16.45/10.95 inference(transitivity,[status(thm)],[4417, 4415])).
% 16.45/10.95 tff(4419,plain,
% 16.45/10.95 ((~![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)))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4420,plain,
% 16.45/10.95 ((~![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)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4419, 4418])).
% 16.45/10.95 tff(4421,plain,
% 16.45/10.95 (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4420, 455, 591])).
% 16.45/10.95 tff(4422,plain,
% 16.45/10.95 (node6(c_e_h_1, c_j, s2, s3)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4421, 4414])).
% 16.45/10.95 tff(4423,plain,
% 16.45/10.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_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)))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4424,plain,
% 16.45/10.95 (((~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)))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4425,plain,
% 16.45/10.95 (((~![Y: $i, I0: $i, X: $i, I1: $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))))),
% 16.45/10.95 inference(monotonicity,[status(thm)],[4424])).
% 16.45/10.95 tff(4426,plain,
% 16.45/10.95 (((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.45/10.95 inference(transitivity,[status(thm)],[4425, 4423])).
% 16.45/10.95 tff(4427,plain,
% 16.45/10.95 ((~![Y: $i, I0: $i, X: $i, I1: $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))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4428,plain,
% 16.45/10.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | (~node6(c_e_h_1, c_j, s2, s3))),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4427, 4426])).
% 16.45/10.95 tff(4429,plain,
% 16.45/10.95 ($false),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4428, 436, 4064, 4244, 4422])).
% 16.45/10.95 tff(4430,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.95 tff(4431,plain,
% 16.45/10.95 (((~![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_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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4432,plain,
% 16.45/10.95 ((~![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_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4433,plain,
% 16.45/10.95 ((~![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_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4432, 4431])).
% 16.45/10.95 tff(4434,plain,
% 16.45/10.95 (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4433, 195, 4430])).
% 16.45/10.95 tff(4435,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s3)), introduced(assumption)).
% 16.45/10.95 tff(4436,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s4)), introduced(assumption)).
% 16.45/10.95 tff(4437,assumption,(node18(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 16.45/10.95 tff(4438,plain,
% 16.45/10.95 (((~![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_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, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4439,plain,
% 16.45/10.95 ((~![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_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4440,plain,
% 16.45/10.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4))),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4439, 4438])).
% 16.45/10.95 tff(4441,plain,
% 16.45/10.95 ($false),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4440, 560, 4436, 4437, 4131])).
% 16.45/10.95 tff(4442,plain,((~node18(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_out(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.95 tff(4443,plain,
% 16.45/10.95 (~node18(c_e_h_1, c_h, s3, s4)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4442, 4436, 4131])).
% 16.45/10.95 tff(4444,plain,
% 16.45/10.95 (((~![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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4445,plain,
% 16.45/10.95 ((~![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))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4446,plain,
% 16.45/10.95 ((~![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)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4445, 4444])).
% 16.45/10.95 tff(4447,plain,
% 16.45/10.95 (node19(c_e_h_1, c_h, s3, s4)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4446, 221, 1013])).
% 16.45/10.95 tff(4448,plain,
% 16.45/10.95 (((~![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, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, 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_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4449,plain,
% 16.45/10.95 ((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))) <=> (node18(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))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4450,plain,
% 16.45/10.95 (((~![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_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)))) | (node18(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)))),
% 16.45/10.95 inference(monotonicity,[status(thm)],[4449])).
% 16.45/10.95 tff(4451,plain,
% 16.45/10.95 (((~![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_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)))) | node18(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))),
% 16.45/10.95 inference(transitivity,[status(thm)],[4450, 4448])).
% 16.45/10.95 tff(4452,plain,
% 16.45/10.95 ((~![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_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4453,plain,
% 16.45/10.95 ((~![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, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3)),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4452, 4451])).
% 16.45/10.95 tff(4454,plain,
% 16.45/10.95 (node18(c_e_h_1, c_h, s3, s4) | node17(c_e_h_1, c_h, s3)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4453, 542, 4447])).
% 16.45/10.95 tff(4455,plain,
% 16.45/10.95 (node17(c_e_h_1, c_h, s3)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4454, 4443])).
% 16.45/10.95 tff(4456,plain,
% 16.45/10.95 (((~![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_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)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))),
% 16.45/10.95 inference(rewrite,[status(thm)],[])).
% 16.45/10.95 tff(4457,plain,
% 16.45/10.95 ((~![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_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))),
% 16.45/10.95 inference(quant_inst,[status(thm)],[])).
% 16.45/10.95 tff(4458,plain,
% 16.45/10.95 ((~![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_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3))),
% 16.45/10.95 inference(modus_ponens,[status(thm)],[4457, 4456])).
% 16.45/10.95 tff(4459,plain,
% 16.45/10.95 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3))),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4458, 524, 4435])).
% 16.45/10.95 tff(4460,plain,
% 16.45/10.95 (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 16.45/10.95 inference(unit_resolution,[status(thm)],[4459, 4455])).
% 16.45/10.95 tff(4461,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s3)), introduced(assumption)).
% 16.45/10.95 tff(4462,assumption,(~node15(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 16.45/10.95 tff(4463,plain,
% 16.45/10.95 (((~![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_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))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4464,plain,
% 16.45/10.96 ((~![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_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))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4465,plain,
% 16.45/10.96 ((~![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_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)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4464, 4463])).
% 16.45/10.96 tff(4466,plain,
% 16.45/10.96 ((~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4465, 209, 4435])).
% 16.45/10.96 tff(4467,plain,
% 16.45/10.96 (~node16(c_e_h_1, c_h, s3)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4466, 4461])).
% 16.45/10.96 tff(4468,plain,
% 16.45/10.96 (((~![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)))) | (node14(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, 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_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4469,plain,
% 16.45/10.96 ((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))) <=> (node14(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4470,plain,
% 16.45/10.96 (((~![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_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)))) | (node14(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3)))),
% 16.45/10.96 inference(monotonicity,[status(thm)],[4469])).
% 16.45/10.96 tff(4471,plain,
% 16.45/10.96 (((~![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_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)))) | node14(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3))),
% 16.45/10.96 inference(transitivity,[status(thm)],[4470, 4468])).
% 16.45/10.96 tff(4472,plain,
% 16.45/10.96 ((~![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_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)))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4473,plain,
% 16.45/10.96 ((~![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)))) | node14(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)) | node15(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 16.45/10.96 tff(4474,plain,
% 16.45/10.96 (node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4473, 235, 4447])).
% 16.45/10.96 tff(4475,plain,
% 16.45/10.96 (node14(c_e_h_1, c_h, s3, s4)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4474, 4467, 4462])).
% 16.45/10.96 tff(4476,plain,
% 16.45/10.96 (((~![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_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, 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_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4477,plain,
% 16.45/10.96 (((~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_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)))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4478,plain,
% 16.45/10.96 (((~![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_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_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))))),
% 16.45/10.96 inference(monotonicity,[status(thm)],[4477])).
% 16.45/10.96 tff(4479,plain,
% 16.45/10.96 (((~![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_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_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)))),
% 16.45/10.96 inference(transitivity,[status(thm)],[4478, 4476])).
% 16.45/10.96 tff(4480,plain,
% 16.45/10.96 ((~![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_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)))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4481,plain,
% 16.45/10.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4))),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4480, 4479])).
% 16.45/10.96 tff(4482,plain,
% 16.45/10.96 ($false),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4481, 254, 4436, 4475, 4461])).
% 16.45/10.96 tff(4483,plain,(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)) | node15(c_e_h_1, c_h, s3, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.96 tff(4484,plain,
% 16.45/10.96 (node15(c_e_h_1, c_h, s3, s4)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4483, 4460, 4436, 4435])).
% 16.45/10.96 tff(4485,plain,
% 16.45/10.96 (((~![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_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))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4486,plain,
% 16.45/10.96 ((~![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_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4487,plain,
% 16.45/10.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4486, 4485])).
% 16.45/10.96 tff(4488,plain,
% 16.45/10.96 ($false),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4487, 178, 4436, 4484, 4131])).
% 16.45/10.96 tff(4489,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, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.96 tff(4490,plain,
% 16.45/10.96 ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4489, 4129])).
% 16.45/10.96 tff(4491,plain,
% 16.45/10.96 (~m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4490, 4434])).
% 16.45/10.96 tff(4492,plain,
% 16.45/10.96 (((~![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))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4493,plain,
% 16.45/10.96 ((~![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))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4494,plain,
% 16.45/10.96 ((~![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)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4493, 4492])).
% 16.45/10.96 tff(4495,plain,
% 16.45/10.96 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4494, 269, 4491])).
% 16.45/10.96 tff(4496,plain,
% 16.45/10.96 (((~![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_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))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4497,plain,
% 16.45/10.96 ((~![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_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4498,plain,
% 16.45/10.96 ((~![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_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 16.45/10.96 tff(4499,plain,
% 16.45/10.96 (~node20(c_e_h_1, c_i, s4)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4498, 283, 4495])).
% 16.45/10.96 tff(4500,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 16.45/10.96 tff(4501,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s5)), introduced(assumption)).
% 16.45/10.96 tff(4502,assumption,(node22(c_e_h_1, c_i, s4, s5)), introduced(assumption)).
% 16.45/10.96 tff(4503,plain,
% 16.45/10.96 (((~![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_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))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4504,plain,
% 16.45/10.96 ((~![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_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4505,plain,
% 16.45/10.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4504, 4503])).
% 16.45/10.96 tff(4506,plain,
% 16.45/10.96 ($false),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4505, 127, 4502, 4500, 4501])).
% 16.45/10.96 tff(4507,plain,((~node22(c_e_h_1, c_i, s4, s5)) | 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, s5))), inference(lemma,lemma(discharge,[]))).
% 16.45/10.96 tff(4508,plain,
% 16.45/10.96 (~node22(c_e_h_1, c_i, s4, s5)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4507, 4501, 4500])).
% 16.45/10.96 tff(4509,assumption,(~node20(c_e_h_1, c_i, s4)), introduced(assumption)).
% 16.45/10.96 tff(4510,assumption,(node21(c_e_h_1, c_i, s4, s5)), introduced(assumption)).
% 16.45/10.96 tff(4511,plain,
% 16.45/10.96 (((~![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_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, 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_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4512,plain,
% 16.45/10.96 ((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))) <=> (node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4513,plain,
% 16.45/10.96 (((~![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_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)))) | (node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5))))),
% 16.45/10.96 inference(monotonicity,[status(thm)],[4512])).
% 16.45/10.96 tff(4514,plain,
% 16.45/10.96 (((~![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_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)))) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)))),
% 16.45/10.96 inference(transitivity,[status(thm)],[4513, 4511])).
% 16.45/10.96 tff(4515,plain,
% 16.45/10.96 ((~![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_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4516,plain,
% 16.45/10.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4515, 4514])).
% 16.45/10.96 tff(4517,plain,
% 16.45/10.96 ($false),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4516, 82, 4510, 4501, 4509])).
% 16.45/10.96 tff(4518,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,[]))).
% 16.45/10.96 tff(4519,plain,
% 16.45/10.96 (~node21(c_e_h_1, c_i, s4, s5)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4518, 4501, 4509])).
% 16.45/10.96 tff(4520,plain,
% 16.45/10.96 (((~![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))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4521,plain,
% 16.45/10.96 ((~![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))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4522,plain,
% 16.45/10.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4521, 4520])).
% 16.45/10.96 tff(4523,plain,
% 16.45/10.96 (node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4522, 112, 1520])).
% 16.45/10.96 tff(4524,plain,
% 16.45/10.96 ($false),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4523, 4519, 4508])).
% 16.45/10.96 tff(4525,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,[]))).
% 16.45/10.96 tff(4526,plain,
% 16.45/10.96 (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4525, 4499, 4243])).
% 16.45/10.96 tff(4527,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s5)), introduced(assumption)).
% 16.45/10.96 tff(4528,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s5)), introduced(assumption)).
% 16.45/10.96 tff(4529,plain,
% 16.45/10.96 (((~![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))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4530,plain,
% 16.45/10.96 ((~![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))),
% 16.45/10.96 inference(quant_inst,[status(thm)],[])).
% 16.45/10.96 tff(4531,plain,
% 16.45/10.96 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 16.45/10.96 inference(modus_ponens,[status(thm)],[4530, 4529])).
% 16.45/10.96 tff(4532,plain,
% 16.45/10.96 ($false),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4531, 612, 4528, 4527])).
% 16.45/10.96 tff(4533,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,[]))).
% 16.45/10.96 tff(4534,plain,
% 16.45/10.96 (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 16.45/10.96 inference(unit_resolution,[status(thm)],[4533, 4526])).
% 16.45/10.96 tff(4535,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 16.45/10.96 tff(4536,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s6)), introduced(assumption)).
% 16.45/10.96 tff(4537,assumption,(node18(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 16.45/10.96 tff(4538,plain,
% 16.45/10.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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)))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4539,plain,
% 16.45/10.96 (((~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)))),
% 16.45/10.96 inference(rewrite,[status(thm)],[])).
% 16.45/10.96 tff(4540,plain,
% 16.45/10.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_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))))),
% 16.45/10.97 inference(monotonicity,[status(thm)],[4539])).
% 16.45/10.97 tff(4541,plain,
% 16.45/10.97 (((~![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, 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)))),
% 16.45/10.97 inference(transitivity,[status(thm)],[4540, 4538])).
% 16.45/10.97 tff(4542,plain,
% 16.45/10.97 ((~![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, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4543,plain,
% 16.45/10.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6))),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4542, 4541])).
% 16.45/10.97 tff(4544,plain,
% 16.45/10.97 ($false),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4543, 560, 4535, 4536, 4537])).
% 16.45/10.97 tff(4545,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,[]))).
% 16.45/10.97 tff(4546,plain,
% 16.45/10.97 (~node18(c_e_h_1, c_e, s5, s6)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4545, 4536, 4535])).
% 16.45/10.97 tff(4547,assumption,(node15(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 16.45/10.97 tff(4548,plain,
% 16.45/10.97 (((~![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, 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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4549,plain,
% 16.45/10.97 ((~![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, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4550,plain,
% 16.45/10.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4549, 4548])).
% 16.45/10.97 tff(4551,plain,
% 16.45/10.97 ($false),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4550, 178, 4535, 4536, 4547])).
% 16.45/10.97 tff(4552,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,[]))).
% 16.45/10.97 tff(4553,plain,
% 16.45/10.97 (~node15(c_e_h_1, c_e, s5, s6)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4552, 4536, 4535])).
% 16.45/10.97 tff(4554,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s5)), introduced(assumption)).
% 16.45/10.97 tff(4555,assumption,(node17(c_e_h_1, c_e, s5)), introduced(assumption)).
% 16.45/10.97 tff(4556,plain,
% 16.45/10.97 (((~![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_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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4557,plain,
% 16.45/10.97 ((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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4558,plain,
% 16.45/10.97 (((~![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, 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)))),
% 16.45/10.97 inference(monotonicity,[status(thm)],[4557])).
% 16.45/10.97 tff(4559,plain,
% 16.45/10.97 (((~![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, 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))),
% 16.45/10.97 inference(transitivity,[status(thm)],[4558, 4556])).
% 16.45/10.97 tff(4560,plain,
% 16.45/10.97 ((~![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, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4561,plain,
% 16.45/10.97 ((~![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_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)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4560, 4559])).
% 16.45/10.97 tff(4562,plain,
% 16.45/10.97 ((~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)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4561, 767, 4555])).
% 16.45/10.97 tff(4563,plain,
% 16.45/10.97 (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4562, 4554])).
% 16.45/10.97 tff(4564,assumption,(~node15(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 16.45/10.97 tff(4565,assumption,(node14(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 16.45/10.97 tff(4566,plain,
% 16.45/10.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~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_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4567,plain,
% 16.45/10.97 (((~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_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4568,plain,
% 16.45/10.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~node14(c_e_h_1, c_e, s5, s6))))),
% 16.45/10.97 inference(monotonicity,[status(thm)],[4567])).
% 16.45/10.97 tff(4569,plain,
% 16.45/10.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 16.45/10.97 inference(transitivity,[status(thm)],[4568, 4566])).
% 16.45/10.97 tff(4570,plain,
% 16.45/10.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4571,plain,
% 16.45/10.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~node14(c_e_h_1, c_e, s5, s6))),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4570, 4569])).
% 16.45/10.97 tff(4572,plain,
% 16.45/10.97 ($false),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4571, 254, 4536, 4565, 4554])).
% 16.45/10.97 tff(4573,plain,((~node14(c_e_h_1, c_e, s5, s6)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.97 tff(4574,plain,
% 16.45/10.97 (~node14(c_e_h_1, c_e, s5, s6)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4573, 4554, 4536])).
% 16.45/10.97 tff(4575,plain,
% 16.45/10.97 (((~![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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4576,plain,
% 16.45/10.97 ((~![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))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4577,plain,
% 16.45/10.97 ((~![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)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4576, 4575])).
% 16.45/10.97 tff(4578,plain,
% 16.45/10.97 (node19(c_e_h_1, c_e, s5, s6)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4577, 221, 1601])).
% 16.45/10.97 tff(4579,plain,
% 16.45/10.97 (((~![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)))) | (node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, 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)))) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4580,plain,
% 16.45/10.97 ((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))) <=> (node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4581,plain,
% 16.45/10.97 (((~![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, 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)))) | (node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5)))),
% 16.45/10.97 inference(monotonicity,[status(thm)],[4580])).
% 16.45/10.97 tff(4582,plain,
% 16.45/10.97 (((~![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, 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)))) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(transitivity,[status(thm)],[4581, 4579])).
% 16.45/10.97 tff(4583,plain,
% 16.45/10.97 ((~![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, 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)))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4584,plain,
% 16.45/10.97 ((~![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)))) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4583, 4582])).
% 16.45/10.97 tff(4585,plain,
% 16.45/10.97 (node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4584, 235, 4578])).
% 16.45/10.97 tff(4586,plain,
% 16.45/10.97 (node16(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4585, 4574, 4564])).
% 16.45/10.97 tff(4587,plain,
% 16.45/10.97 (((~![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_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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4588,plain,
% 16.45/10.97 ((~![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_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))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4589,plain,
% 16.45/10.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4588, 4587])).
% 16.45/10.97 tff(4590,plain,
% 16.45/10.97 ($false),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4589, 209, 4586, 4563, 4554])).
% 16.45/10.97 tff(4591,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s5) | node15(c_e_h_1, c_e, s5, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node17(c_e_h_1, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 16.45/10.97 tff(4592,plain,
% 16.45/10.97 (~node17(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4591, 4536, 4554, 4553])).
% 16.45/10.97 tff(4593,plain,
% 16.45/10.97 (((~![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, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node17(c_e_h_1, c_e, 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_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node17(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4594,plain,
% 16.45/10.97 ((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))) <=> (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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4595,plain,
% 16.45/10.97 (((~![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, 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)))) | (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)))),
% 16.45/10.97 inference(monotonicity,[status(thm)],[4594])).
% 16.45/10.97 tff(4596,plain,
% 16.45/10.97 (((~![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, 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)))) | 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))),
% 16.45/10.97 inference(transitivity,[status(thm)],[4595, 4593])).
% 16.45/10.97 tff(4597,plain,
% 16.45/10.97 ((~![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, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4598,plain,
% 16.45/10.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node17(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4597, 4596])).
% 16.45/10.97 tff(4599,plain,
% 16.45/10.97 (node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4598, 542, 4578])).
% 16.45/10.97 tff(4600,plain,
% 16.45/10.97 ($false),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4599, 4592, 4546])).
% 16.45/10.97 tff(4601,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) | m_c_h_element_v_out(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 16.45/10.97 tff(4602,plain,
% 16.45/10.97 (m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4601, 4536, 4535])).
% 16.45/10.97 tff(4603,plain,
% 16.45/10.97 (node17(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4599, 4546])).
% 16.45/10.97 tff(4604,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s5)), introduced(assumption)).
% 16.45/10.97 tff(4605,plain,
% 16.45/10.97 (((~![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, s5)) | (~node17(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] : ((~m_c_h_element_v_in1(I0, I1, X)) | 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)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4606,plain,
% 16.45/10.97 (((~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_in1(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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4607,plain,
% 16.45/10.97 (((~![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, 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)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 16.45/10.97 inference(monotonicity,[status(thm)],[4606])).
% 16.45/10.97 tff(4608,plain,
% 16.45/10.97 (((~![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, 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)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(transitivity,[status(thm)],[4607, 4605])).
% 16.45/10.97 tff(4609,plain,
% 16.45/10.97 ((~![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, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4610,plain,
% 16.45/10.97 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4609, 4608])).
% 16.45/10.97 tff(4611,plain,
% 16.45/10.97 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4610, 524, 4604])).
% 16.45/10.97 tff(4612,plain,
% 16.45/10.97 ($false),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4611, 4603, 4602])).
% 16.45/10.97 tff(4613,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,[]))).
% 16.45/10.97 tff(4614,plain,
% 16.45/10.97 (~m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4613, 4534, 4236])).
% 16.45/10.97 tff(4615,plain,
% 16.45/10.97 (((~![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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4616,plain,
% 16.45/10.97 ((~![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))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4617,plain,
% 16.45/10.97 ((~![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)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4616, 4615])).
% 16.45/10.97 tff(4618,plain,
% 16.45/10.97 (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)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4617, 1099])).
% 16.45/10.97 tff(4619,plain,
% 16.45/10.97 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4618, 4614])).
% 16.45/10.97 tff(4620,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)), introduced(assumption)).
% 16.45/10.97 tff(4621,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)), introduced(assumption)).
% 16.45/10.97 tff(4622,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 16.45/10.97 tff(4623,plain,
% 16.45/10.97 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[1500, 1561])).
% 16.45/10.97 tff(4624,plain,
% 16.45/10.97 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[1535, 4623, 1527, 1502])).
% 16.45/10.97 tff(4625,plain,
% 16.45/10.97 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[1551, 1276, 1502])).
% 16.45/10.97 tff(4626,plain,
% 16.45/10.97 (~node9(c_e_h_1, c_m, s4)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[1557, 1290, 4625])).
% 16.45/10.97 tff(4627,plain,
% 16.45/10.97 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[1582, 1561, 4626])).
% 16.45/10.97 tff(4628,plain,
% 16.45/10.97 (((~![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))),
% 16.45/10.97 inference(rewrite,[status(thm)],[])).
% 16.45/10.97 tff(4629,plain,
% 16.45/10.97 ((~![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))),
% 16.45/10.97 inference(quant_inst,[status(thm)],[])).
% 16.45/10.97 tff(4630,plain,
% 16.45/10.97 ((~![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)),
% 16.45/10.97 inference(modus_ponens,[status(thm)],[4629, 4628])).
% 16.45/10.97 tff(4631,plain,
% 16.45/10.97 (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)),
% 16.45/10.97 inference(unit_resolution,[status(thm)],[4630, 1145])).
% 16.52/10.98 tff(4632,plain,
% 16.52/10.98 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4631, 4627])).
% 16.52/10.98 tff(4633,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)), introduced(assumption)).
% 16.52/10.98 tff(4634,assumption,(node10(c_e_h_1, c_n, s5, s6)), introduced(assumption)).
% 16.52/10.98 tff(4635,plain,
% 16.52/10.98 (((~![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_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)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4636,plain,
% 16.52/10.98 (((~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)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4637,plain,
% 16.52/10.98 (((~![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, 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))))),
% 16.52/10.98 inference(monotonicity,[status(thm)],[4636])).
% 16.52/10.98 tff(4638,plain,
% 16.52/10.98 (((~![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, 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)))),
% 16.52/10.98 inference(transitivity,[status(thm)],[4637, 4635])).
% 16.52/10.98 tff(4639,plain,
% 16.52/10.98 ((~![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, 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))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4640,plain,
% 16.52/10.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6))),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4639, 4638])).
% 16.52/10.98 tff(4641,plain,
% 16.52/10.98 ($false),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4640, 1160, 4621, 4622, 4633, 4634])).
% 16.52/10.98 tff(4642,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,[]))).
% 16.52/10.98 tff(4643,plain,
% 16.52/10.98 (~node10(c_e_h_1, c_n, s5, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4642, 4622, 4633, 4621])).
% 16.52/10.98 tff(4644,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 16.52/10.98 tff(4645,assumption,(node11(c_e_h_1, c_n, s5, s6)), introduced(assumption)).
% 16.52/10.98 tff(4646,plain,
% 16.52/10.98 (((~![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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4647,plain,
% 16.52/10.98 ((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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4648,plain,
% 16.52/10.98 (((~![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, 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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6))))),
% 16.52/10.98 inference(monotonicity,[status(thm)],[4647])).
% 16.52/10.98 tff(4649,plain,
% 16.52/10.98 (((~![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, 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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 16.52/10.98 inference(transitivity,[status(thm)],[4648, 4646])).
% 16.52/10.98 tff(4650,plain,
% 16.52/10.98 ((~![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, 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)))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4651,plain,
% 16.52/10.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6))),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4650, 4649])).
% 16.52/10.98 tff(4652,plain,
% 16.52/10.98 ($false),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4651, 1223, 4644, 4622, 4645])).
% 16.52/10.98 tff(4653,plain,((~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, s6)), inference(lemma,lemma(discharge,[]))).
% 16.52/10.98 tff(4654,plain,
% 16.52/10.98 (~node11(c_e_h_1, c_n, s5, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4653, 4622, 4644])).
% 16.52/10.98 tff(4655,plain,
% 16.52/10.98 (((~![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))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4656,plain,
% 16.52/10.98 ((~![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))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4657,plain,
% 16.52/10.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6)),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 16.52/10.98 tff(4658,plain,
% 16.52/10.98 (node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4657, 1179, 1601])).
% 16.52/10.98 tff(4659,plain,
% 16.52/10.98 ($false),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4658, 4654, 4643])).
% 16.52/10.98 tff(4660,plain,(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)) | (~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))), inference(lemma,lemma(discharge,[]))).
% 16.52/10.98 tff(4661,plain,
% 16.52/10.98 ($false),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4660, 4632, 4624, 4621, 4622])).
% 16.52/10.98 tff(4662,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4) | (~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, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 16.52/10.98 tff(4663,plain,
% 16.52/10.98 ((~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, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4662, 1496])).
% 16.52/10.98 tff(4664,plain,
% 16.52/10.98 ((~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, s4))),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4663, 1460])).
% 16.52/10.98 tff(4665,plain,
% 16.52/10.98 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4664, 1527, 4621])).
% 16.52/10.98 tff(4666,plain,
% 16.52/10.98 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1537, 1527])).
% 16.52/10.98 tff(4667,plain,
% 16.52/10.98 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1541, 1276, 4666])).
% 16.52/10.98 tff(4668,plain,
% 16.52/10.98 (~node9(c_e_h_1, c_m, s5)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1545, 1290, 4667])).
% 16.52/10.98 tff(4669,plain,
% 16.52/10.98 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1615, 4668])).
% 16.52/10.98 tff(4670,plain,
% 16.52/10.98 (((~![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))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4671,plain,
% 16.52/10.98 ((~![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))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4672,plain,
% 16.52/10.98 ((~![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)),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4671, 4670])).
% 16.52/10.98 tff(4673,plain,
% 16.52/10.98 (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)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4672, 1145])).
% 16.52/10.98 tff(4674,plain,
% 16.52/10.98 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4673, 4669])).
% 16.52/10.98 tff(4675,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)), introduced(assumption)).
% 16.52/10.98 tff(4676,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)), introduced(assumption)).
% 16.52/10.98 tff(4677,assumption,(node10(c_e_h_1, c_n, s6, s7)), introduced(assumption)).
% 16.52/10.98 tff(4678,plain,
% 16.52/10.98 (((~![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_in2(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_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_in2(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_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4679,plain,
% 16.52/10.98 (((~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_in2(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_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4680,plain,
% 16.52/10.98 (((~![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, 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_in2(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_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7))))),
% 16.52/10.98 inference(monotonicity,[status(thm)],[4679])).
% 16.52/10.98 tff(4681,plain,
% 16.52/10.98 (((~![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, 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_in2(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_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 16.52/10.98 inference(transitivity,[status(thm)],[4680, 4678])).
% 16.52/10.98 tff(4682,plain,
% 16.52/10.98 ((~![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, 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))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4683,plain,
% 16.52/10.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7))),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4682, 4681])).
% 16.52/10.98 tff(4684,plain,
% 16.52/10.98 ($false),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4683, 1160, 4620, 4676, 4675, 4677])).
% 16.52/10.98 tff(4685,plain,((~node10(c_e_h_1, c_n, s6, s7)) | (~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_in2(c_e_h_1, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 16.52/10.98 tff(4686,plain,
% 16.52/10.98 (~node10(c_e_h_1, c_n, s6, s7)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4685, 4676, 4620, 4675])).
% 16.52/10.98 tff(4687,plain,
% 16.52/10.98 (((~![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))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4688,plain,
% 16.52/10.98 ((~![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))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4689,plain,
% 16.52/10.98 ((~![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)),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4688, 4687])).
% 16.52/10.98 tff(4690,plain,
% 16.52/10.98 (node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4689, 1179, 1843])).
% 16.52/10.98 tff(4691,plain,
% 16.52/10.98 (node11(c_e_h_1, c_n, s6, s7)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4690, 4686])).
% 16.52/10.98 tff(4692,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 16.52/10.98 tff(4693,plain,
% 16.52/10.98 (((~![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, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~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, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4694,plain,
% 16.52/10.98 ((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, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4695,plain,
% 16.52/10.98 (((~![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, 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, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7))))),
% 16.52/10.98 inference(monotonicity,[status(thm)],[4694])).
% 16.52/10.98 tff(4696,plain,
% 16.52/10.98 (((~![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, 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, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 16.52/10.98 inference(transitivity,[status(thm)],[4695, 4693])).
% 16.52/10.98 tff(4697,plain,
% 16.52/10.98 ((~![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, 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)))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4698,plain,
% 16.52/10.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7))),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4697, 4696])).
% 16.52/10.98 tff(4699,plain,
% 16.52/10.98 ($false),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4698, 1223, 4676, 4692, 4691])).
% 16.52/10.98 tff(4700,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,[]))).
% 16.52/10.98 tff(4701,plain,
% 16.52/10.98 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4700, 4674, 4665, 4620])).
% 16.52/10.98 tff(4702,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), introduced(assumption)).
% 16.52/10.98 tff(4703,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 16.52/10.98 tff(4704,plain,
% 16.52/10.98 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4663, 1527, 4621, 1502])).
% 16.52/10.98 tff(4705,plain,
% 16.52/10.98 (((~![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)))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4706,plain,
% 16.52/10.98 ((~![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)))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4707,plain,
% 16.52/10.98 ((~![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))),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4706, 4705])).
% 16.52/10.98 tff(4708,plain,
% 16.52/10.98 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4707, 1276, 4704])).
% 16.52/10.98 tff(4709,plain,
% 16.52/10.98 (((~![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))),
% 16.52/10.98 inference(rewrite,[status(thm)],[])).
% 16.52/10.98 tff(4710,plain,
% 16.52/10.98 ((~![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))),
% 16.52/10.98 inference(quant_inst,[status(thm)],[])).
% 16.52/10.98 tff(4711,plain,
% 16.52/10.98 ((~![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)),
% 16.52/10.98 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 16.52/10.98 tff(4712,plain,
% 16.52/10.98 (~node9(c_e_h_1, c_m, s6)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[4711, 1290, 4708])).
% 16.52/10.98 tff(4713,plain,
% 16.52/10.98 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1553, 1502])).
% 16.52/10.98 tff(4714,plain,
% 16.52/10.98 (~node9(c_e_h_1, c_m, s4)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1557, 1290, 4713])).
% 16.52/10.98 tff(4715,plain,
% 16.52/10.98 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1583, 4714])).
% 16.52/10.98 tff(4716,plain,
% 16.52/10.98 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1536, 1527, 1502])).
% 16.52/10.98 tff(4717,plain,
% 16.52/10.98 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 16.52/10.98 inference(unit_resolution,[status(thm)],[1541, 1276, 4716])).
% 16.52/10.99 tff(4718,plain,
% 16.52/10.99 (~node9(c_e_h_1, c_m, s5)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[1545, 1290, 4717])).
% 16.52/10.99 tff(4719,plain,
% 16.52/10.99 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[1614, 4718, 4715])).
% 16.52/10.99 tff(4720,assumption,(node11(c_e_h_1, c_m, s6, s7)), introduced(assumption)).
% 16.52/10.99 tff(4721,plain,
% 16.52/10.99 (((~![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, 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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4722,plain,
% 16.52/10.99 ((~![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, 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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4723,plain,
% 16.52/10.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4722, 4721])).
% 16.52/10.99 tff(4724,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4723, 1258, 1618, 4703, 4720])).
% 16.52/10.99 tff(4725,plain,((~node11(c_e_h_1, c_m, s6, s7)) | 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, s7))), inference(lemma,lemma(discharge,[]))).
% 16.52/10.99 tff(4726,plain,
% 16.52/10.99 (~node11(c_e_h_1, c_m, s6, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4725, 4703, 1618])).
% 16.52/10.99 tff(4727,assumption,(~node9(c_e_h_1, c_m, s6)), introduced(assumption)).
% 16.52/10.99 tff(4728,assumption,(node10(c_e_h_1, c_m, s6, s7)), introduced(assumption)).
% 16.52/10.99 tff(4729,plain,
% 16.52/10.99 (((~![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, 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)))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4730,plain,
% 16.52/10.99 ((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)))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4731,plain,
% 16.52/10.99 (((~![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, 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))))),
% 16.52/10.99 inference(monotonicity,[status(thm)],[4730])).
% 16.52/10.99 tff(4732,plain,
% 16.52/10.99 (((~![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, 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)))),
% 16.52/10.99 inference(transitivity,[status(thm)],[4731, 4729])).
% 16.52/10.99 tff(4733,plain,
% 16.52/10.99 ((~![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, 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)))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4734,plain,
% 16.52/10.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7))),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4733, 4732])).
% 16.52/10.99 tff(4735,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4734, 1304, 4703, 4728, 4727])).
% 16.52/10.99 tff(4736,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/10.99 tff(4737,plain,
% 16.52/10.99 (~node10(c_e_h_1, c_m, s6, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4736, 4703, 4727])).
% 16.52/10.99 tff(4738,plain,
% 16.52/10.99 (((~![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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4739,plain,
% 16.52/10.99 ((~![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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4740,plain,
% 16.52/10.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4739, 4738])).
% 16.52/10.99 tff(4741,plain,
% 16.52/10.99 (node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4740, 1179, 1843])).
% 16.52/10.99 tff(4742,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4741, 4737, 4726])).
% 16.52/10.99 tff(4743,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,[]))).
% 16.52/10.99 tff(4744,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4743, 4719, 4712, 4703])).
% 16.52/10.99 tff(4745,plain,((~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_m, s7)) | (~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,[]))).
% 16.52/10.99 tff(4746,plain,
% 16.52/10.99 ((~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_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5))),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4745, 1460])).
% 16.52/10.99 tff(4747,plain,
% 16.52/10.99 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4746, 1527, 4621])).
% 16.52/10.99 tff(4748,assumption,(~node9(c_e_h_1, c_m, s7)), introduced(assumption)).
% 16.52/10.99 tff(4749,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 16.52/10.99 tff(4750,assumption,(node11(c_e_h_1, c_m, s7, s8)), introduced(assumption)).
% 16.52/10.99 tff(4751,plain,
% 16.52/10.99 (((~![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, 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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4752,plain,
% 16.52/10.99 ((~![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, 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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4753,plain,
% 16.52/10.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4752, 4751])).
% 16.52/10.99 tff(4754,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4753, 1258, 4702, 4749, 4750])).
% 16.52/10.99 tff(4755,plain,((~node11(c_e_h_1, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 16.52/10.99 tff(4756,plain,
% 16.52/10.99 (~node11(c_e_h_1, c_m, s7, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4755, 4702, 4749])).
% 16.52/10.99 tff(4757,plain,
% 16.52/10.99 (((~![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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4758,plain,
% 16.52/10.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4759,plain,
% 16.52/10.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4758, 4757])).
% 16.52/10.99 tff(4760,plain,
% 16.52/10.99 (trans(s7, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4759, 3928, 95])).
% 16.52/10.99 tff(4761,plain,
% 16.52/10.99 (((~![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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4762,plain,
% 16.52/10.99 ((~![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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4763,plain,
% 16.52/10.99 ((~![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)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4762, 4761])).
% 16.52/10.99 tff(4764,plain,
% 16.52/10.99 (node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4763, 1179, 4760])).
% 16.52/10.99 tff(4765,plain,
% 16.52/10.99 (node10(c_e_h_1, c_m, s7, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4764, 4756])).
% 16.52/10.99 tff(4766,plain,
% 16.52/10.99 (((~![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, 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)))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4767,plain,
% 16.52/10.99 ((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)))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4768,plain,
% 16.52/10.99 (((~![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, 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))))),
% 16.52/10.99 inference(monotonicity,[status(thm)],[4767])).
% 16.52/10.99 tff(4769,plain,
% 16.52/10.99 (((~![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, 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)))),
% 16.52/10.99 inference(transitivity,[status(thm)],[4768, 4766])).
% 16.52/10.99 tff(4770,plain,
% 16.52/10.99 ((~![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, 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)))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4771,plain,
% 16.52/10.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8))),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4770, 4769])).
% 16.52/10.99 tff(4772,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4771, 1304, 4702, 4765, 4748])).
% 16.52/10.99 tff(4773,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 16.52/10.99 tff(4774,plain,
% 16.52/10.99 (node9(c_e_h_1, c_m, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4773, 4747, 4702])).
% 16.52/10.99 tff(4775,plain,
% 16.52/10.99 (((~![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, 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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4776,plain,
% 16.52/10.99 ((~![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, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4777,plain,
% 16.52/10.99 ((~![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, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4776, 4775])).
% 16.52/10.99 tff(4778,plain,
% 16.52/10.99 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4777, 1290, 4774])).
% 16.52/10.99 tff(4779,plain,
% 16.52/10.99 (((~![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, 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)))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4780,plain,
% 16.52/10.99 ((~![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, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4781,plain,
% 16.52/10.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4780, 4779])).
% 16.52/10.99 tff(4782,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4781, 1276, 4778, 4701])).
% 16.52/10.99 tff(4783,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))), inference(lemma,lemma(discharge,[]))).
% 16.52/10.99 tff(4784,plain,
% 16.52/10.99 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4783, 4619, 1104, 4241])).
% 16.52/10.99 tff(4785,plain,
% 16.52/10.99 (((~![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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4786,plain,
% 16.52/10.99 ((~![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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4787,plain,
% 16.52/10.99 ((~![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)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4786, 4785])).
% 16.52/10.99 tff(4788,plain,
% 16.52/10.99 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4787, 1625, 4784])).
% 16.52/10.99 tff(4789,plain,
% 16.52/10.99 (((~![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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4790,plain,
% 16.52/10.99 ((~![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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4791,plain,
% 16.52/10.99 ((~![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)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 16.52/10.99 tff(4792,plain,
% 16.52/10.99 (~node20(c_e_h_1, c_r, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4791, 68, 4788])).
% 16.52/10.99 tff(4793,plain,
% 16.52/10.99 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4746, 4241, 1104])).
% 16.52/10.99 tff(4794,plain,
% 16.52/10.99 (((~![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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4795,plain,
% 16.52/10.99 ((~![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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4796,plain,
% 16.52/10.99 ((~![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)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4795, 4794])).
% 16.52/10.99 tff(4797,plain,
% 16.52/10.99 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4796, 1625, 4793])).
% 16.52/10.99 tff(4798,plain,
% 16.52/10.99 (((~![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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4799,plain,
% 16.52/10.99 ((~![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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4800,plain,
% 16.52/10.99 ((~![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)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4799, 4798])).
% 16.52/10.99 tff(4801,plain,
% 16.52/10.99 (~node20(c_e_h_1, c_r, s7)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4800, 68, 4797])).
% 16.52/10.99 tff(4802,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s8)), introduced(assumption)).
% 16.52/10.99 tff(4803,assumption,(node22(c_e_h_1, c_r, s7, s8)), introduced(assumption)).
% 16.52/10.99 tff(4804,plain,
% 16.52/10.99 (((~![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_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))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4805,plain,
% 16.52/10.99 ((~![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_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))),
% 16.52/10.99 inference(quant_inst,[status(thm)],[])).
% 16.52/10.99 tff(4806,plain,
% 16.52/10.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 16.52/10.99 inference(modus_ponens,[status(thm)],[4805, 4804])).
% 16.52/10.99 tff(4807,plain,
% 16.52/10.99 ($false),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4806, 127, 4803, 1856, 4802])).
% 16.52/10.99 tff(4808,plain,((~node22(c_e_h_1, c_r, s7, s8)) | 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, s8))), inference(lemma,lemma(discharge,[]))).
% 16.52/10.99 tff(4809,plain,
% 16.52/10.99 (~node22(c_e_h_1, c_r, s7, s8)),
% 16.52/10.99 inference(unit_resolution,[status(thm)],[4808, 4802, 1856])).
% 16.52/10.99 tff(4810,assumption,(~node20(c_e_h_1, c_r, s7)), introduced(assumption)).
% 16.52/10.99 tff(4811,assumption,(node21(c_e_h_1, c_r, s7, s8)), introduced(assumption)).
% 16.52/10.99 tff(4812,plain,
% 16.52/10.99 (((~![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_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4813,plain,
% 16.52/10.99 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 16.52/10.99 inference(rewrite,[status(thm)],[])).
% 16.52/10.99 tff(4814,plain,
% 16.52/10.99 (((~![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_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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8))))),
% 16.52/10.99 inference(monotonicity,[status(thm)],[4813])).
% 16.52/10.99 tff(4815,plain,
% 16.52/10.99 (((~![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_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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 16.52/11.00 inference(transitivity,[status(thm)],[4814, 4812])).
% 16.52/11.00 tff(4816,plain,
% 16.52/11.00 ((~![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_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4817,plain,
% 16.52/11.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8))),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 16.52/11.00 tff(4818,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4817, 82, 4811, 4802, 4810])).
% 16.52/11.00 tff(4819,plain,((~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4820,plain,
% 16.52/11.00 (~node21(c_e_h_1, c_r, s7, s8)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4819, 4802, 4810])).
% 16.52/11.00 tff(4821,plain,
% 16.52/11.00 (((~![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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4822,plain,
% 16.52/11.00 ((~![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))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4823,plain,
% 16.52/11.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4822, 4821])).
% 16.52/11.00 tff(4824,plain,
% 16.52/11.00 (node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4823, 112, 4760])).
% 16.52/11.00 tff(4825,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4824, 4820, 4809])).
% 16.52/11.00 tff(4826,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4827,plain,
% 16.52/11.00 (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4826, 4801, 1855])).
% 16.52/11.00 tff(4828,assumption,(~node20(c_e_h_1, c_r, s8)), introduced(assumption)).
% 16.52/11.00 tff(4829,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s9)), introduced(assumption)).
% 16.52/11.00 tff(4830,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s8)), introduced(assumption)).
% 16.52/11.00 tff(4831,assumption,(node22(c_e_h_1, c_r, s8, s9)), introduced(assumption)).
% 16.52/11.00 tff(4832,plain,
% 16.52/11.00 (((~![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_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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4833,plain,
% 16.52/11.00 ((~![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_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4834,plain,
% 16.52/11.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4833, 4832])).
% 16.52/11.00 tff(4835,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4834, 127, 4831, 4830, 4829])).
% 16.52/11.00 tff(4836,plain,((~node22(c_e_h_1, c_r, s8, s9)) | 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, s9))), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4837,plain,
% 16.52/11.00 (~node22(c_e_h_1, c_r, s8, s9)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4836, 4829, 4830])).
% 16.52/11.00 tff(4838,plain,
% 16.52/11.00 (succ(s8, s9) <=> succ(s8, s9)),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4839,axiom,(succ(s8, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound9')).
% 16.52/11.00 tff(4840,plain,
% 16.52/11.00 (succ(s8, s9)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4839, 4838])).
% 16.52/11.00 tff(4841,plain,
% 16.52/11.00 (((~![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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4842,plain,
% 16.52/11.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4843,plain,
% 16.52/11.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4842, 4841])).
% 16.52/11.00 tff(4844,plain,
% 16.52/11.00 (trans(s8, s9)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4843, 4840, 95])).
% 16.52/11.00 tff(4845,plain,
% 16.52/11.00 (((~![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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4846,plain,
% 16.52/11.00 ((~![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))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4847,plain,
% 16.52/11.00 ((~![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)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4846, 4845])).
% 16.52/11.00 tff(4848,plain,
% 16.52/11.00 (node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4847, 112, 4844])).
% 16.52/11.00 tff(4849,plain,
% 16.52/11.00 (node21(c_e_h_1, c_r, s8, s9)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4848, 4837])).
% 16.52/11.00 tff(4850,plain,
% 16.52/11.00 (((~![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_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)))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4851,plain,
% 16.52/11.00 ((~![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_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4852,plain,
% 16.52/11.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9))),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4851, 4850])).
% 16.52/11.00 tff(4853,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4852, 82, 4849, 4829, 4828])).
% 16.52/11.00 tff(4854,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4855,plain,
% 16.52/11.00 (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4854, 4792, 4827])).
% 16.52/11.00 tff(4856,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s9)), introduced(assumption)).
% 16.52/11.00 tff(4857,assumption,(m_user_v_ack(c_e_h_1, c_u, s9)), introduced(assumption)).
% 16.52/11.00 tff(4858,plain,
% 16.52/11.00 (((~![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, s9)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_u, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4859,plain,
% 16.52/11.00 ((~![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, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4860,plain,
% 16.52/11.00 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4859, 4858])).
% 16.52/11.00 tff(4861,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4860, 1864, 4857, 4856])).
% 16.52/11.00 tff(4862,plain,((~m_user_v_ack(c_e_h_1, c_u, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4863,plain,
% 16.52/11.00 (~m_user_v_ack(c_e_h_1, c_u, s9)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4862, 4855])).
% 16.52/11.00 tff(4864,plain,
% 16.52/11.00 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s9)) | m_user_v_ack(c_e_h_1, c_u, s9))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s9)) | m_user_v_ack(c_e_h_1, c_u, s9))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4865,plain,
% 16.52/11.00 ((m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9))) <=> ((~node23(s9)) | m_user_v_ack(c_e_h_1, c_u, s9))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4866,plain,
% 16.52/11.00 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s9)) | m_user_v_ack(c_e_h_1, c_u, s9)))),
% 16.52/11.00 inference(monotonicity,[status(thm)],[4865])).
% 16.52/11.00 tff(4867,plain,
% 16.52/11.00 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s9)) | m_user_v_ack(c_e_h_1, c_u, s9))),
% 16.52/11.00 inference(transitivity,[status(thm)],[4866, 4864])).
% 16.52/11.00 tff(4868,plain,
% 16.52/11.00 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9)))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4869,plain,
% 16.52/11.00 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s9)) | m_user_v_ack(c_e_h_1, c_u, s9)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4868, 4867])).
% 16.52/11.00 tff(4870,plain,
% 16.52/11.00 (~node23(s9)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4869, 3252, 4863])).
% 16.52/11.00 tff(4871,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), introduced(assumption)).
% 16.52/11.00 tff(4872,assumption,(node11(c_e_h_2, c_m, s6, s7)), introduced(assumption)).
% 16.52/11.00 tff(4873,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), introduced(assumption)).
% 16.52/11.00 tff(4874,plain,
% 16.52/11.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4875,plain,
% 16.52/11.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, 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))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4876,plain,
% 16.52/11.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node11(c_e_h_2, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4875, 4874])).
% 16.52/11.00 tff(4877,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4876, 1258, 4871, 4873, 4872])).
% 16.52/11.00 tff(4878,plain,((~node11(c_e_h_2, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4879,plain,
% 16.52/11.00 ((~node11(c_e_h_2, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4878, 2975])).
% 16.52/11.00 tff(4880,plain,
% 16.52/11.00 (~node11(c_e_h_2, c_m, s6, s7)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4879, 4871])).
% 16.52/11.00 tff(4881,assumption,(m_or_h_gate_v_out(c_e_h_2, c_g, s0)), introduced(assumption)).
% 16.52/11.00 tff(4882,plain,
% 16.52/11.00 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4883,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4882, 141, 4881])).
% 16.52/11.00 tff(4884,plain,(~m_or_h_gate_v_out(c_e_h_2, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4885,assumption,(m_or_h_gate_v_out(c_e_h_2, c_g, s1)), introduced(assumption)).
% 16.52/11.00 tff(4886,plain,
% 16.52/11.00 (^[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)))),
% 16.52/11.00 inference(bind,[status(th)],[])).
% 16.52/11.00 tff(4887,plain,
% 16.52/11.00 (![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))),
% 16.52/11.00 inference(quant_intro,[status(thm)],[4886])).
% 16.52/11.00 tff(4888,plain,
% 16.52/11.00 (![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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4889,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')).
% 16.52/11.00 tff(4890,plain,
% 16.52/11.00 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4889, 4888])).
% 16.52/11.00 tff(4891,plain,(
% 16.52/11.00 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 16.52/11.00 inference(skolemize,[status(sab)],[4890])).
% 16.52/11.00 tff(4892,plain,
% 16.52/11.00 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4891, 4887])).
% 16.52/11.00 tff(4893,plain,
% 16.52/11.00 (((~![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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4894,plain,
% 16.52/11.00 ((~![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))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4895,plain,
% 16.52/11.00 ((~![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)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4894, 4893])).
% 16.52/11.00 tff(4896,plain,
% 16.52/11.00 (~m_or_h_gate_v_in1(c_e_h_2, c_g, s0)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4895, 4892, 2256])).
% 16.52/11.00 tff(4897,assumption,(m_and_h_gate_v_out(c_e_h_2, c_d, s0)), introduced(assumption)).
% 16.52/11.00 tff(4898,plain,
% 16.52/11.00 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4899,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4898, 9, 4897])).
% 16.52/11.00 tff(4900,plain,(~m_and_h_gate_v_out(c_e_h_2, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.00 tff(4901,plain,
% 16.52/11.00 (^[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)))),
% 16.52/11.00 inference(bind,[status(th)],[])).
% 16.52/11.00 tff(4902,plain,
% 16.52/11.00 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.52/11.00 inference(quant_intro,[status(thm)],[4901])).
% 16.52/11.00 tff(4903,plain,
% 16.52/11.00 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4904,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')).
% 16.52/11.00 tff(4905,plain,
% 16.52/11.00 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4904, 4903])).
% 16.52/11.00 tff(4906,plain,(
% 16.52/11.00 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.52/11.00 inference(skolemize,[status(sab)],[4905])).
% 16.52/11.00 tff(4907,plain,
% 16.52/11.00 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4906, 4902])).
% 16.52/11.00 tff(4908,plain,
% 16.52/11.00 (((~![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_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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4909,plain,
% 16.52/11.00 ((~![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_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4910,plain,
% 16.52/11.00 ((~![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_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0)),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4909, 4908])).
% 16.52/11.00 tff(4911,plain,
% 16.52/11.00 (~m_or_h_gate_v_in2(c_e_h_2, c_g, s0)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4910, 4907, 4900])).
% 16.52/11.00 tff(4912,assumption,(node5(c_e_h_2, c_g, s0, s1)), introduced(assumption)).
% 16.52/11.00 tff(4913,plain,
% 16.52/11.00 (((~![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_2, c_g, s0) | m_or_h_gate_v_in1(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_in2(c_e_h_2, c_g, s0) | m_or_h_gate_v_in1(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)))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4914,plain,
% 16.52/11.00 ((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_in2(c_e_h_2, c_g, s0) | m_or_h_gate_v_in1(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)))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4915,plain,
% 16.52/11.00 (((~![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_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_in2(c_e_h_2, c_g, s0) | m_or_h_gate_v_in1(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))))),
% 16.52/11.00 inference(monotonicity,[status(thm)],[4914])).
% 16.52/11.00 tff(4916,plain,
% 16.52/11.00 (((~![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_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_in2(c_e_h_2, c_g, s0) | m_or_h_gate_v_in1(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)))),
% 16.52/11.00 inference(transitivity,[status(thm)],[4915, 4913])).
% 16.52/11.00 tff(4917,plain,
% 16.52/11.00 ((~![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_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)))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4918,plain,
% 16.52/11.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1))),
% 16.52/11.00 inference(modus_ponens,[status(thm)],[4917, 4916])).
% 16.52/11.00 tff(4919,plain,
% 16.52/11.00 ($false),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4918, 473, 4912, 4911, 4885, 4896])).
% 16.52/11.00 tff(4920,plain,((~node5(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,[]))).
% 16.52/11.00 tff(4921,plain,
% 16.52/11.00 (~node5(c_e_h_2, c_g, s0, s1)),
% 16.52/11.00 inference(unit_resolution,[status(thm)],[4920, 4885])).
% 16.52/11.00 tff(4922,plain,
% 16.52/11.00 (((~![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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4923,plain,
% 16.52/11.00 ((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))),
% 16.52/11.00 inference(rewrite,[status(thm)],[])).
% 16.52/11.00 tff(4924,plain,
% 16.52/11.00 (((~![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_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)))),
% 16.52/11.00 inference(monotonicity,[status(thm)],[4923])).
% 16.52/11.00 tff(4925,plain,
% 16.52/11.00 (((~![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_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))),
% 16.52/11.00 inference(transitivity,[status(thm)],[4924, 4922])).
% 16.52/11.00 tff(4926,plain,
% 16.52/11.00 ((~![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_2, c_g, s0, s1) | node5(c_e_h_2, c_g, s0, s1) | (~trans(s0, s1)))),
% 16.52/11.00 inference(quant_inst,[status(thm)],[])).
% 16.52/11.00 tff(4927,plain,
% 16.52/11.00 ((~![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)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4926, 4925])).
% 16.52/11.01 tff(4928,plain,
% 16.52/11.01 (node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4927, 455, 102])).
% 16.52/11.01 tff(4929,plain,
% 16.52/11.01 (node6(c_e_h_2, c_g, s0, s1)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4928, 4921])).
% 16.52/11.01 tff(4930,plain,
% 16.52/11.01 (((~![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_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | (~node6(c_e_h_2, 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_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | (~node6(c_e_h_2, c_g, s0, s1)))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4931,plain,
% 16.52/11.01 (((~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)) <=> (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)) | (~node6(c_e_h_2, c_g, s0, s1)))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4932,plain,
% 16.52/11.01 (((~![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_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))) | (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)) | (~node6(c_e_h_2, c_g, s0, s1))))),
% 16.52/11.01 inference(monotonicity,[status(thm)],[4931])).
% 16.52/11.01 tff(4933,plain,
% 16.52/11.01 (((~![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_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))) | 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)) | (~node6(c_e_h_2, c_g, s0, s1)))),
% 16.52/11.01 inference(transitivity,[status(thm)],[4932, 4930])).
% 16.52/11.01 tff(4934,plain,
% 16.52/11.01 ((~![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_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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4935,plain,
% 16.52/11.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | (~node6(c_e_h_2, c_g, s0, s1))),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4934, 4933])).
% 16.52/11.01 tff(4936,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4935, 436, 4929, 4885, 4884])).
% 16.52/11.01 tff(4937,plain,(~m_or_h_gate_v_out(c_e_h_2, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.01 tff(4938,assumption,(m_or_h_gate_v_out(c_e_h_2, c_g, s2)), introduced(assumption)).
% 16.52/11.01 tff(4939,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_g, s1)), introduced(assumption)).
% 16.52/11.01 tff(4940,plain,
% 16.52/11.01 (((~![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))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4941,plain,
% 16.52/11.01 ((~![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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4942,plain,
% 16.52/11.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4941, 4940])).
% 16.52/11.01 tff(4943,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4942, 4892, 2273, 4939])).
% 16.52/11.01 tff(4944,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.01 tff(4945,plain,
% 16.52/11.01 (~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4944, 2271])).
% 16.52/11.01 tff(4946,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)), introduced(assumption)).
% 16.52/11.01 tff(4947,assumption,(m_mutex_h_half_v_out(c_e_h_2, c_b, s0)), introduced(assumption)).
% 16.52/11.01 tff(4948,plain,
% 16.52/11.01 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_2, c_b, s0))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4949,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4948, 629, 4947])).
% 16.52/11.01 tff(4950,plain,(~m_mutex_h_half_v_out(c_e_h_2, c_b, s0)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.01 tff(4951,plain,
% 16.52/11.01 (^[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)))),
% 16.52/11.01 inference(bind,[status(th)],[])).
% 16.52/11.01 tff(4952,plain,
% 16.52/11.01 (![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))),
% 16.52/11.01 inference(quant_intro,[status(thm)],[4951])).
% 16.52/11.01 tff(4953,plain,
% 16.52/11.01 (![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))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4954,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')).
% 16.52/11.01 tff(4955,plain,
% 16.52/11.01 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4954, 4953])).
% 16.52/11.01 tff(4956,plain,(
% 16.52/11.01 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 16.52/11.01 inference(skolemize,[status(sab)],[4955])).
% 16.52/11.01 tff(4957,plain,
% 16.52/11.01 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4956, 4952])).
% 16.52/11.01 tff(4958,plain,
% 16.52/11.01 (((~![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))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4959,plain,
% 16.52/11.01 ((~![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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4960,plain,
% 16.52/11.01 ((~![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)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4959, 4958])).
% 16.52/11.01 tff(4961,plain,
% 16.52/11.01 (~m_and_h_gate_v_in1(c_e_h_2, c_d, s0)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4960, 4957, 4950])).
% 16.52/11.01 tff(4962,plain,
% 16.52/11.01 (((~![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))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4963,plain,
% 16.52/11.01 ((~![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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4964,plain,
% 16.52/11.01 ((~![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)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4963, 4962])).
% 16.52/11.01 tff(4965,plain,
% 16.52/11.01 (~node20(c_e_h_2, c_d, s0)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4964, 283, 4961])).
% 16.52/11.01 tff(4966,assumption,(m_and_h_gate_v_out(c_e_h_2, c_d, s1)), introduced(assumption)).
% 16.52/11.01 tff(4967,assumption,(node22(c_e_h_2, c_d, s0, s1)), introduced(assumption)).
% 16.52/11.01 tff(4968,plain,
% 16.52/11.01 (((~![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_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))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4969,plain,
% 16.52/11.01 ((~![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_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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4970,plain,
% 16.52/11.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node22(c_e_h_2, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4969, 4968])).
% 16.52/11.01 tff(4971,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4970, 127, 4900, 4967, 4966])).
% 16.52/11.01 tff(4972,plain,((~node22(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,[]))).
% 16.52/11.01 tff(4973,plain,
% 16.52/11.01 (~node22(c_e_h_2, c_d, s0, s1)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4972, 4966])).
% 16.52/11.01 tff(4974,plain,
% 16.52/11.01 (((~![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))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4975,plain,
% 16.52/11.01 ((~![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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4976,plain,
% 16.52/11.01 ((~![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)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4975, 4974])).
% 16.52/11.01 tff(4977,plain,
% 16.52/11.01 (node21(c_e_h_2, c_d, s0, s1) | node22(c_e_h_2, c_d, s0, s1)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4976, 112, 102])).
% 16.52/11.01 tff(4978,plain,
% 16.52/11.01 (node21(c_e_h_2, c_d, s0, s1)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4977, 4973])).
% 16.52/11.01 tff(4979,plain,
% 16.52/11.01 (((~![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_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)))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4980,plain,
% 16.52/11.01 ((~![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_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)))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4981,plain,
% 16.52/11.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node21(c_e_h_2, c_d, s0, s1))),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4980, 4979])).
% 16.52/11.01 tff(4982,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4981, 82, 4978, 4966, 4965])).
% 16.52/11.01 tff(4983,plain,(~m_and_h_gate_v_out(c_e_h_2, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.01 tff(4984,plain,
% 16.52/11.01 (((~![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))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4985,plain,
% 16.52/11.01 ((~![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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4986,plain,
% 16.52/11.01 ((~![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)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4985, 4984])).
% 16.52/11.01 tff(4987,plain,
% 16.52/11.01 (~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4986, 4907, 4983])).
% 16.52/11.01 tff(4988,assumption,(node5(c_e_h_2, c_g, s1, s2)), introduced(assumption)).
% 16.52/11.01 tff(4989,plain,
% 16.52/11.01 (((~![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_2, c_g, s2)) | 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)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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, s2)) | 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)))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4990,plain,
% 16.52/11.01 ((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_out(c_e_h_2, c_g, s2)) | 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)))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(4991,plain,
% 16.52/11.01 (((~![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_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_out(c_e_h_2, c_g, s2)) | 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))))),
% 16.52/11.01 inference(monotonicity,[status(thm)],[4990])).
% 16.52/11.01 tff(4992,plain,
% 16.52/11.01 (((~![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_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_out(c_e_h_2, c_g, s2)) | 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)))),
% 16.52/11.01 inference(transitivity,[status(thm)],[4991, 4989])).
% 16.52/11.01 tff(4993,plain,
% 16.52/11.01 ((~![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_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)))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(4994,plain,
% 16.52/11.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2))),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[4993, 4992])).
% 16.52/11.01 tff(4995,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4994, 473, 4988, 4938, 4987, 4946])).
% 16.52/11.01 tff(4996,plain,((~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_in1(c_e_h_2, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.01 tff(4997,plain,
% 16.52/11.01 ((~node5(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2))),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4996, 4945])).
% 16.52/11.01 tff(4998,plain,
% 16.52/11.01 (~node5(c_e_h_2, c_g, s1, s2)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[4997, 4938])).
% 16.52/11.01 tff(4999,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_g, s1)), introduced(assumption)).
% 16.52/11.01 tff(5000,assumption,(node6(c_e_h_2, c_g, s1, s2)), introduced(assumption)).
% 16.52/11.01 tff(5001,plain,
% 16.52/11.01 (((~![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_g, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~node6(c_e_h_2, c_g, s1, s2)))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(5002,plain,
% 16.52/11.01 (((~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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~node6(c_e_h_2, c_g, s1, s2)))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(5003,plain,
% 16.52/11.01 (((~![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_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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~node6(c_e_h_2, c_g, s1, s2))))),
% 16.52/11.01 inference(monotonicity,[status(thm)],[5002])).
% 16.52/11.01 tff(5004,plain,
% 16.52/11.01 (((~![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_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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~node6(c_e_h_2, c_g, s1, s2)))),
% 16.52/11.01 inference(transitivity,[status(thm)],[5003, 5001])).
% 16.52/11.01 tff(5005,plain,
% 16.52/11.01 ((~![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_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))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(5006,plain,
% 16.52/11.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~node6(c_e_h_2, c_g, s1, s2))),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[5005, 5004])).
% 16.52/11.01 tff(5007,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[5006, 436, 5000, 4938, 4999])).
% 16.52/11.01 tff(5008,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.01 tff(5009,plain,
% 16.52/11.01 (~node6(c_e_h_2, c_g, s1, s2)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[5008, 4938, 4999])).
% 16.52/11.01 tff(5010,plain,
% 16.52/11.01 (((~![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_g, s1, s2) | node5(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)) | node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(5011,plain,
% 16.52/11.01 ((node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(5012,plain,
% 16.52/11.01 (((~![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_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)) | node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2)))),
% 16.52/11.01 inference(monotonicity,[status(thm)],[5011])).
% 16.52/11.01 tff(5013,plain,
% 16.52/11.01 (((~![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_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)) | node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2))),
% 16.52/11.01 inference(transitivity,[status(thm)],[5012, 5010])).
% 16.52/11.01 tff(5014,plain,
% 16.52/11.01 ((~![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_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2) | (~trans(s1, s2)))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(5015,plain,
% 16.52/11.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 16.52/11.01 tff(5016,plain,
% 16.52/11.01 (node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[5015, 455, 348])).
% 16.52/11.01 tff(5017,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[5016, 5009, 4998])).
% 16.52/11.01 tff(5018,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.01 tff(5019,plain,
% 16.52/11.01 (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[5018, 4937])).
% 16.52/11.01 tff(5020,assumption,(m_c_h_element_v_in1(c_e_h_2, c_h, s2)), introduced(assumption)).
% 16.52/11.01 tff(5021,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_g, s2)), introduced(assumption)).
% 16.52/11.01 tff(5022,plain,
% 16.52/11.01 (((~![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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2))) <=> ((~![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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2))),
% 16.52/11.01 inference(rewrite,[status(thm)],[])).
% 16.52/11.01 tff(5023,plain,
% 16.52/11.01 ((~![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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2))),
% 16.52/11.01 inference(quant_inst,[status(thm)],[])).
% 16.52/11.01 tff(5024,plain,
% 16.52/11.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2)),
% 16.52/11.01 inference(modus_ponens,[status(thm)],[5023, 5022])).
% 16.52/11.01 tff(5025,plain,
% 16.52/11.01 ($false),
% 16.52/11.01 inference(unit_resolution,[status(thm)],[5024, 151, 5021, 5020])).
% 16.52/11.02 tff(5026,plain,((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.02 tff(5027,plain,
% 16.52/11.02 (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5026, 5019])).
% 16.52/11.02 tff(5028,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s3)), introduced(assumption)).
% 16.52/11.02 tff(5029,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s2)), introduced(assumption)).
% 16.52/11.02 tff(5030,assumption,(node14(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 16.52/11.02 tff(5031,plain,
% 16.52/11.02 (((~![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_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~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_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5032,plain,
% 16.52/11.02 (((~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_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5033,plain,
% 16.52/11.02 (((~![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_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_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node14(c_e_h_2, c_h, s2, s3))))),
% 16.52/11.02 inference(monotonicity,[status(thm)],[5032])).
% 16.52/11.02 tff(5034,plain,
% 16.52/11.02 (((~![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_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_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 16.52/11.02 inference(transitivity,[status(thm)],[5033, 5031])).
% 16.52/11.02 tff(5035,plain,
% 16.52/11.02 ((~![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_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)))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5036,plain,
% 16.52/11.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node14(c_e_h_2, c_h, s2, s3))),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5035, 5034])).
% 16.52/11.02 tff(5037,plain,
% 16.52/11.02 ($false),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5036, 254, 5028, 5030, 5029])).
% 16.52/11.02 tff(5038,plain,((~node14(c_e_h_2, c_h, s2, 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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.02 tff(5039,plain,
% 16.52/11.02 (~node14(c_e_h_2, c_h, s2, s3)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5038, 5029, 5028])).
% 16.52/11.02 tff(5040,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s2)), introduced(assumption)).
% 16.52/11.02 tff(5041,assumption,(~node14(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 16.52/11.02 tff(5042,assumption,(node15(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 16.52/11.02 tff(5043,plain,
% 16.52/11.02 (((~![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_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))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5044,plain,
% 16.52/11.02 ((~![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_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))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5045,plain,
% 16.52/11.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 16.52/11.02 tff(5046,plain,
% 16.52/11.02 ($false),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5045, 178, 5040, 5028, 5042])).
% 16.52/11.02 tff(5047,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,[]))).
% 16.52/11.02 tff(5048,plain,
% 16.52/11.02 (~node15(c_e_h_2, c_h, s2, s3)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5047, 5040, 5028])).
% 16.52/11.02 tff(5049,plain,
% 16.52/11.02 (((~![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))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5050,plain,
% 16.52/11.02 ((~![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))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5051,plain,
% 16.52/11.02 ((~![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)),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5050, 5049])).
% 16.52/11.02 tff(5052,plain,
% 16.52/11.02 (node19(c_e_h_2, c_h, s2, s3)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5051, 221, 591])).
% 16.52/11.02 tff(5053,plain,
% 16.52/11.02 (((~![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_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(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)))) | 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) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5054,plain,
% 16.52/11.02 ((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))) <=> (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) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5055,plain,
% 16.52/11.02 (((~![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_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)))) | (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) | (~node19(c_e_h_2, c_h, s2, s3))))),
% 16.52/11.02 inference(monotonicity,[status(thm)],[5054])).
% 16.52/11.02 tff(5056,plain,
% 16.52/11.02 (((~![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_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)))) | 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) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 16.52/11.02 inference(transitivity,[status(thm)],[5055, 5053])).
% 16.52/11.02 tff(5057,plain,
% 16.52/11.02 ((~![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_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)))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5058,plain,
% 16.52/11.02 ((~![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_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3))),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5057, 5056])).
% 16.52/11.02 tff(5059,plain,
% 16.52/11.02 (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)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5058, 235, 5052])).
% 16.52/11.02 tff(5060,plain,
% 16.52/11.02 (node16(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5059, 5048, 5041])).
% 16.52/11.02 tff(5061,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s2)), introduced(assumption)).
% 16.52/11.02 tff(5062,plain,
% 16.52/11.02 (((~![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_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))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5063,plain,
% 16.52/11.02 ((~![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_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))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5064,plain,
% 16.52/11.02 ((~![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_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)),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5063, 5062])).
% 16.52/11.02 tff(5065,plain,
% 16.52/11.02 ((~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5064, 209, 5061])).
% 16.52/11.02 tff(5066,plain,
% 16.52/11.02 (m_c_h_element_v_in1(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5065, 5060])).
% 16.52/11.02 tff(5067,plain,
% 16.52/11.02 (((~![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_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_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)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5068,plain,
% 16.52/11.02 ((~![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_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)))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5069,plain,
% 16.52/11.02 ((~![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_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))),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5068, 5067])).
% 16.52/11.02 tff(5070,plain,
% 16.52/11.02 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | (~node17(c_e_h_2, c_h, s2))),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5069, 524, 5061])).
% 16.52/11.02 tff(5071,plain,
% 16.52/11.02 (~node17(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5070, 5066])).
% 16.52/11.02 tff(5072,plain,
% 16.52/11.02 (((~![Y: $i, 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)))) | 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)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5073,plain,
% 16.52/11.02 ((~![Y: $i, 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)))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5074,plain,
% 16.52/11.02 ((~![Y: $i, 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))),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5073, 5072])).
% 16.52/11.02 tff(5075,plain,
% 16.52/11.02 (node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5074, 542, 5052])).
% 16.52/11.02 tff(5076,plain,
% 16.52/11.02 (node18(c_e_h_2, c_h, s2, s3)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5075, 5071])).
% 16.52/11.02 tff(5077,plain,
% 16.52/11.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5078,plain,
% 16.52/11.02 (((~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)))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5079,plain,
% 16.52/11.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))))),
% 16.52/11.02 inference(monotonicity,[status(thm)],[5078])).
% 16.52/11.02 tff(5080,plain,
% 16.52/11.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 16.52/11.02 inference(transitivity,[status(thm)],[5079, 5077])).
% 16.52/11.02 tff(5081,plain,
% 16.52/11.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5082,plain,
% 16.52/11.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3))),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5081, 5080])).
% 16.52/11.02 tff(5083,plain,
% 16.52/11.02 ($false),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5082, 560, 5040, 5028, 5076])).
% 16.52/11.02 tff(5084,plain,(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)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.02 tff(5085,plain,
% 16.52/11.02 (m_c_h_element_v_in2(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5084, 5040, 5028, 5039])).
% 16.52/11.02 tff(5086,plain,
% 16.52/11.02 (((~![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_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))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5087,plain,
% 16.52/11.02 ((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))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5088,plain,
% 16.52/11.02 (((~![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_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)))),
% 16.52/11.02 inference(monotonicity,[status(thm)],[5087])).
% 16.52/11.02 tff(5089,plain,
% 16.52/11.02 (((~![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_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))),
% 16.52/11.02 inference(transitivity,[status(thm)],[5088, 5086])).
% 16.52/11.02 tff(5090,plain,
% 16.52/11.02 ((~![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_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)))),
% 16.52/11.02 inference(quant_inst,[status(thm)],[])).
% 16.52/11.02 tff(5091,plain,
% 16.52/11.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | (~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(modus_ponens,[status(thm)],[5090, 5089])).
% 16.52/11.02 tff(5092,plain,
% 16.52/11.02 (~node17(c_e_h_2, c_h, s2)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5091, 767, 5029, 5085])).
% 16.52/11.02 tff(5093,plain,
% 16.52/11.02 (node18(c_e_h_2, c_h, s2, s3)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5075, 5092])).
% 16.52/11.02 tff(5094,plain,
% 16.52/11.02 ($false),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5082, 560, 5040, 5028, 5093])).
% 16.52/11.02 tff(5095,plain,(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)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.02 tff(5096,plain,
% 16.52/11.02 (~m_c_h_element_v_out(c_e_h_2, c_h, s3)),
% 16.52/11.02 inference(unit_resolution,[status(thm)],[5095, 5027, 2086])).
% 16.52/11.02 tff(5097,plain,
% 16.52/11.02 (((~![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))),
% 16.52/11.02 inference(rewrite,[status(thm)],[])).
% 16.52/11.02 tff(5098,plain,
% 16.52/11.02 ((~![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))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5099,plain,
% 16.52/11.03 ((~![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)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5098, 5097])).
% 16.52/11.03 tff(5100,plain,
% 16.52/11.03 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5099, 269, 5096])).
% 16.52/11.03 tff(5101,plain,
% 16.52/11.03 (((~![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))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5102,plain,
% 16.52/11.03 ((~![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))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5103,plain,
% 16.52/11.03 ((~![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)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5102, 5101])).
% 16.52/11.03 tff(5104,plain,
% 16.52/11.03 (~node20(c_e_h_2, c_i, s3)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5103, 283, 5100])).
% 16.52/11.03 tff(5105,assumption,(~node20(c_e_h_2, c_i, s3)), introduced(assumption)).
% 16.52/11.03 tff(5106,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s4)), introduced(assumption)).
% 16.52/11.03 tff(5107,assumption,(node22(c_e_h_2, c_i, s3, s4)), introduced(assumption)).
% 16.52/11.03 tff(5108,plain,
% 16.52/11.03 (((~![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_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))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5109,plain,
% 16.52/11.03 ((~![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_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))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5110,plain,
% 16.52/11.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5109, 5108])).
% 16.52/11.03 tff(5111,plain,
% 16.52/11.03 ($false),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5110, 127, 5107, 5106, 2178])).
% 16.52/11.03 tff(5112,plain,((~node22(c_e_h_2, c_i, s3, s4)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.03 tff(5113,plain,
% 16.52/11.03 (~node22(c_e_h_2, c_i, s3, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5112, 5106, 2178])).
% 16.52/11.03 tff(5114,plain,
% 16.52/11.03 (((~![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_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))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5115,plain,
% 16.52/11.03 ((~![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_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5116,plain,
% 16.52/11.03 ((~![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_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5115, 5114])).
% 16.52/11.03 tff(5117,plain,
% 16.52/11.03 (node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5116, 112, 1013])).
% 16.52/11.03 tff(5118,plain,
% 16.52/11.03 (node21(c_e_h_2, c_i, s3, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5117, 5113])).
% 16.52/11.03 tff(5119,plain,
% 16.52/11.03 (((~![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_i, s3) | (~node21(c_e_h_2, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, 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_i, s3) | (~node21(c_e_h_2, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5120,plain,
% 16.52/11.03 ((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))) <=> (node20(c_e_h_2, c_i, s3) | (~node21(c_e_h_2, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5121,plain,
% 16.52/11.03 (((~![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_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)))) | (node20(c_e_h_2, c_i, s3) | (~node21(c_e_h_2, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4))))),
% 16.52/11.03 inference(monotonicity,[status(thm)],[5120])).
% 16.52/11.03 tff(5122,plain,
% 16.52/11.03 (((~![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_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)))) | node20(c_e_h_2, c_i, s3) | (~node21(c_e_h_2, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)))),
% 16.52/11.03 inference(transitivity,[status(thm)],[5121, 5119])).
% 16.52/11.03 tff(5123,plain,
% 16.52/11.03 ((~![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_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5124,plain,
% 16.52/11.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s3) | (~node21(c_e_h_2, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5123, 5122])).
% 16.52/11.03 tff(5125,plain,
% 16.52/11.03 ($false),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5124, 82, 5118, 5106, 5105])).
% 16.52/11.03 tff(5126,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | node20(c_e_h_2, c_i, s3) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.03 tff(5127,plain,
% 16.52/11.03 (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5126, 5104, 2176])).
% 16.52/11.03 tff(5128,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s4)), introduced(assumption)).
% 16.52/11.03 tff(5129,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s4)), introduced(assumption)).
% 16.52/11.03 tff(5130,plain,
% 16.52/11.03 (((~![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_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))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5131,plain,
% 16.52/11.03 ((~![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_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5132,plain,
% 16.52/11.03 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5131, 5130])).
% 16.52/11.03 tff(5133,plain,
% 16.52/11.03 ($false),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5132, 612, 5129, 5128])).
% 16.52/11.03 tff(5134,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,[]))).
% 16.52/11.03 tff(5135,plain,
% 16.52/11.03 (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5134, 5127])).
% 16.52/11.03 tff(5136,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s4)), introduced(assumption)).
% 16.52/11.03 tff(5137,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s5)), introduced(assumption)).
% 16.52/11.03 tff(5138,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s4)), introduced(assumption)).
% 16.52/11.03 tff(5139,assumption,(node15(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 16.52/11.03 tff(5140,plain,
% 16.52/11.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5141,plain,
% 16.52/11.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5142,plain,
% 16.52/11.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5141, 5140])).
% 16.52/11.03 tff(5143,plain,
% 16.52/11.03 ($false),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5142, 178, 5137, 5138, 5139])).
% 16.52/11.03 tff(5144,plain,((~node15(c_e_h_2, c_e, s4, s5)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.03 tff(5145,plain,
% 16.52/11.03 (~node15(c_e_h_2, c_e, s4, s5)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5144, 5137, 5138])).
% 16.52/11.03 tff(5146,assumption,(~node15(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 16.52/11.03 tff(5147,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s4)), introduced(assumption)).
% 16.52/11.03 tff(5148,plain,
% 16.52/11.03 (((~![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))) | ((~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))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5149,plain,
% 16.52/11.03 ((~![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))) | ((~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))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5150,plain,
% 16.52/11.03 ((~![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))) | (~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)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5149, 5148])).
% 16.52/11.03 tff(5151,plain,
% 16.52/11.03 ((~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5150, 209, 5136])).
% 16.52/11.03 tff(5152,plain,
% 16.52/11.03 (~node16(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5151, 5147])).
% 16.52/11.03 tff(5153,assumption,(node14(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 16.52/11.03 tff(5154,plain,
% 16.52/11.03 (((~![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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~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_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5155,plain,
% 16.52/11.03 (((~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_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5156,plain,
% 16.52/11.03 (((~![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_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_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5))))),
% 16.52/11.03 inference(monotonicity,[status(thm)],[5155])).
% 16.52/11.03 tff(5157,plain,
% 16.52/11.03 (((~![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_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_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)))),
% 16.52/11.03 inference(transitivity,[status(thm)],[5156, 5154])).
% 16.52/11.03 tff(5158,plain,
% 16.52/11.03 ((~![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_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)))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5159,plain,
% 16.52/11.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5))),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5158, 5157])).
% 16.52/11.03 tff(5160,plain,
% 16.52/11.03 ($false),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5159, 254, 5137, 5153, 5147])).
% 16.52/11.03 tff(5161,plain,((~node14(c_e_h_2, c_e, s4, s5)) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.03 tff(5162,plain,
% 16.52/11.03 (~node14(c_e_h_2, c_e, s4, s5)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5161, 5147, 5137])).
% 16.52/11.03 tff(5163,plain,
% 16.52/11.03 (((~![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))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5164,plain,
% 16.52/11.03 ((~![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))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5165,plain,
% 16.52/11.03 ((~![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)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 16.52/11.03 tff(5166,plain,
% 16.52/11.03 (node19(c_e_h_2, c_e, s4, s5)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5165, 221, 1520])).
% 16.52/11.03 tff(5167,plain,
% 16.52/11.03 (((~![Y: $i, I0: $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_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node14(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, 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_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node14(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5168,plain,
% 16.52/11.03 ((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))) <=> ((~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node14(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5169,plain,
% 16.52/11.03 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | ((~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node14(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4)))),
% 16.52/11.03 inference(monotonicity,[status(thm)],[5168])).
% 16.52/11.03 tff(5170,plain,
% 16.52/11.03 (((~![Y: $i, I0: $i, X: $i, I1: $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)))) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node14(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(transitivity,[status(thm)],[5169, 5167])).
% 16.52/11.03 tff(5171,plain,
% 16.52/11.03 ((~![Y: $i, I0: $i, X: $i, I1: $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)))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5172,plain,
% 16.52/11.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node14(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5171, 5170])).
% 16.52/11.03 tff(5173,plain,
% 16.52/11.03 (node15(c_e_h_2, c_e, s4, s5) | node14(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5172, 235, 5166])).
% 16.52/11.03 tff(5174,plain,
% 16.52/11.03 ($false),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5173, 5162, 5152, 5146])).
% 16.52/11.03 tff(5175,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s4) | node15(c_e_h_2, c_e, s4, s5) | (~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)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.03 tff(5176,plain,
% 16.52/11.03 (m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5175, 5145, 5137, 5136])).
% 16.52/11.03 tff(5177,plain,
% 16.52/11.03 (((~![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_2, c_e, s4)) | (~node17(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)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5178,plain,
% 16.52/11.03 (((~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))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5179,plain,
% 16.52/11.03 (((~![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_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)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)))),
% 16.52/11.03 inference(monotonicity,[status(thm)],[5178])).
% 16.52/11.03 tff(5180,plain,
% 16.52/11.03 (((~![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_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)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(transitivity,[status(thm)],[5179, 5177])).
% 16.52/11.03 tff(5181,plain,
% 16.52/11.03 ((~![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_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)))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5182,plain,
% 16.52/11.03 ((~![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_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(modus_ponens,[status(thm)],[5181, 5180])).
% 16.52/11.03 tff(5183,plain,
% 16.52/11.03 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5182, 524, 5136])).
% 16.52/11.03 tff(5184,plain,
% 16.52/11.03 (~node17(c_e_h_2, c_e, s4)),
% 16.52/11.03 inference(unit_resolution,[status(thm)],[5183, 5176])).
% 16.52/11.03 tff(5185,plain,
% 16.52/11.03 (((~![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_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, 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_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5186,plain,
% 16.52/11.03 ((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))) <=> ((~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(rewrite,[status(thm)],[])).
% 16.52/11.03 tff(5187,plain,
% 16.52/11.03 (((~![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_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)))) | ((~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4)))),
% 16.52/11.03 inference(monotonicity,[status(thm)],[5186])).
% 16.52/11.03 tff(5188,plain,
% 16.52/11.03 (((~![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_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)))) | (~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4))),
% 16.52/11.03 inference(transitivity,[status(thm)],[5187, 5185])).
% 16.52/11.03 tff(5189,plain,
% 16.52/11.03 ((~![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_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))),
% 16.52/11.03 inference(quant_inst,[status(thm)],[])).
% 16.52/11.03 tff(5190,plain,
% 16.52/11.03 ((~![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_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5189, 5188])).
% 16.52/11.04 tff(5191,plain,
% 16.52/11.04 (node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5190, 542, 5166])).
% 16.52/11.04 tff(5192,plain,
% 16.52/11.04 (node18(c_e_h_2, c_e, s4, s5)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5191, 5184])).
% 16.52/11.04 tff(5193,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5194,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, 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)))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5195,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5))),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5194, 5193])).
% 16.52/11.04 tff(5196,plain,
% 16.52/11.04 ($false),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5195, 560, 5137, 5138, 5192])).
% 16.52/11.04 tff(5197,plain,((~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) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.04 tff(5198,plain,
% 16.52/11.04 (~m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5197, 5135, 2593])).
% 16.52/11.04 tff(5199,plain,
% 16.52/11.04 (((~![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))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5200,plain,
% 16.52/11.04 ((~![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))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5201,plain,
% 16.52/11.04 ((~![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)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5200, 5199])).
% 16.52/11.04 tff(5202,plain,
% 16.52/11.04 (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)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5201, 1099])).
% 16.52/11.04 tff(5203,plain,
% 16.52/11.04 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5202, 5198])).
% 16.52/11.04 tff(5204,plain,
% 16.52/11.04 (((~![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))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5205,plain,
% 16.52/11.04 ((~![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))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5206,plain,
% 16.52/11.04 ((~![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)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5205, 5204])).
% 16.52/11.04 tff(5207,plain,
% 16.52/11.04 (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)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5206, 1145])).
% 16.52/11.04 tff(5208,plain,
% 16.52/11.04 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5207, 2950])).
% 16.52/11.04 tff(5209,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)), introduced(assumption)).
% 16.52/11.04 tff(5210,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)), introduced(assumption)).
% 16.52/11.04 tff(5211,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), introduced(assumption)).
% 16.52/11.04 tff(5212,assumption,(node10(c_e_h_2, c_n, s5, s6)), introduced(assumption)).
% 16.52/11.04 tff(5213,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_2, c_n, s5)) | (~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_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_in1(c_e_h_2, c_n, s5)) | (~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_n, s6) | (~node10(c_e_h_2, c_n, s5, s6)))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5214,plain,
% 16.52/11.04 (((~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_in1(c_e_h_2, c_n, s5)) | (~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_n, s6) | (~node10(c_e_h_2, c_n, s5, s6)))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5215,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_in1(c_e_h_2, c_n, s5)) | (~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_n, s6) | (~node10(c_e_h_2, c_n, s5, s6))))),
% 16.52/11.04 inference(monotonicity,[status(thm)],[5214])).
% 16.52/11.04 tff(5216,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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_in1(c_e_h_2, c_n, s5)) | (~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_n, s6) | (~node10(c_e_h_2, c_n, s5, s6)))),
% 16.52/11.04 inference(transitivity,[status(thm)],[5215, 5213])).
% 16.52/11.04 tff(5217,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5218,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node10(c_e_h_2, c_n, s5, s6))),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5217, 5216])).
% 16.52/11.04 tff(5219,plain,
% 16.52/11.04 ($false),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5218, 1160, 5209, 5210, 5211, 5212])).
% 16.52/11.04 tff(5220,plain,((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~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_n, s6)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.04 tff(5221,plain,
% 16.52/11.04 (~node10(c_e_h_2, c_n, s5, s6)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5220, 5211, 5210, 5209])).
% 16.52/11.04 tff(5222,plain,
% 16.52/11.04 (((~![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))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5223,plain,
% 16.52/11.04 ((~![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))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5224,plain,
% 16.52/11.04 ((~![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)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 16.52/11.04 tff(5225,plain,
% 16.52/11.04 (node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5224, 1179, 1601])).
% 16.52/11.04 tff(5226,plain,
% 16.52/11.04 (node11(c_e_h_2, c_n, s5, s6)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5225, 5221])).
% 16.52/11.04 tff(5227,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)), introduced(assumption)).
% 16.52/11.04 tff(5228,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5229,plain,
% 16.52/11.04 ((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)))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5230,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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))))),
% 16.52/11.04 inference(monotonicity,[status(thm)],[5229])).
% 16.52/11.04 tff(5231,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.52/11.04 inference(transitivity,[status(thm)],[5230, 5228])).
% 16.52/11.04 tff(5232,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, 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)))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5233,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6))),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5232, 5231])).
% 16.52/11.04 tff(5234,plain,
% 16.52/11.04 ($false),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5233, 1223, 5227, 5211, 5226])).
% 16.52/11.04 tff(5235,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~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, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 16.52/11.04 tff(5236,plain,
% 16.52/11.04 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~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, s5))),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5235, 5208])).
% 16.52/11.04 tff(5237,plain,
% 16.52/11.04 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5236, 5203, 2900])).
% 16.52/11.04 tff(5238,plain,
% 16.52/11.04 (((~![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)))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5239,plain,
% 16.52/11.04 ((~![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)))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5240,plain,
% 16.52/11.04 ((~![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))),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5239, 5238])).
% 16.52/11.04 tff(5241,plain,
% 16.52/11.04 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5240, 1276, 5237])).
% 16.52/11.04 tff(5242,plain,
% 16.52/11.04 (((~![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))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5243,plain,
% 16.52/11.04 ((~![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))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5244,plain,
% 16.52/11.04 ((~![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)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 16.52/11.04 tff(5245,plain,
% 16.52/11.04 (~node9(c_e_h_2, c_m, s6)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5244, 1290, 5241])).
% 16.52/11.04 tff(5246,assumption,(~node9(c_e_h_2, c_m, s6)), introduced(assumption)).
% 16.52/11.04 tff(5247,assumption,(node10(c_e_h_2, c_m, s6, s7)), introduced(assumption)).
% 16.52/11.04 tff(5248,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, 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, s7)) | (~node10(c_e_h_2, c_m, s6, s7)) | node9(c_e_h_2, 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)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)) | node9(c_e_h_2, c_m, s6))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5249,plain,
% 16.52/11.04 ((node9(c_e_h_2, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)) | node9(c_e_h_2, c_m, s6))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5250,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, 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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, 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_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)) | node9(c_e_h_2, c_m, s6)))),
% 16.52/11.04 inference(monotonicity,[status(thm)],[5249])).
% 16.52/11.04 tff(5251,plain,
% 16.52/11.04 (((~![Y: $i, I0: $i, 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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, 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_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)) | node9(c_e_h_2, c_m, s6))),
% 16.52/11.04 inference(transitivity,[status(thm)],[5250, 5248])).
% 16.52/11.04 tff(5252,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, 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, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5253,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)) | node9(c_e_h_2, c_m, s6)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5252, 5251])).
% 16.52/11.04 tff(5254,plain,
% 16.52/11.04 ($false),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5253, 1304, 4871, 5247, 5246])).
% 16.52/11.04 tff(5255,plain,((~node10(c_e_h_2, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.04 tff(5256,plain,
% 16.52/11.04 ((~node10(c_e_h_2, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5255, 5245])).
% 16.52/11.04 tff(5257,plain,
% 16.52/11.04 (~node10(c_e_h_2, c_m, s6, s7)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5256, 4871])).
% 16.52/11.04 tff(5258,plain,
% 16.52/11.04 (((~![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_2, c_m, s6, s7) | node11(c_e_h_2, 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_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5259,plain,
% 16.52/11.04 ((~![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_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5260,plain,
% 16.52/11.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5259, 5258])).
% 16.52/11.04 tff(5261,plain,
% 16.52/11.04 (node10(c_e_h_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5260, 1179, 1843])).
% 16.52/11.04 tff(5262,plain,
% 16.52/11.04 ($false),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5261, 5257, 4880])).
% 16.52/11.04 tff(5263,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.04 tff(5264,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_r, s7)), introduced(assumption)).
% 16.52/11.04 tff(5265,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), introduced(assumption)).
% 16.52/11.04 tff(5266,plain,
% 16.52/11.04 (((~![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_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, 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_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5267,plain,
% 16.52/11.04 ((~![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_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5268,plain,
% 16.52/11.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5267, 5266])).
% 16.52/11.04 tff(5269,plain,
% 16.52/11.04 ($false),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5268, 1625, 5265, 5264])).
% 16.52/11.04 tff(5270,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 16.52/11.04 tff(5271,plain,
% 16.52/11.04 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5270, 5263])).
% 16.52/11.04 tff(5272,assumption,(~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)), introduced(assumption)).
% 16.52/11.04 tff(5273,assumption,(node20(c_e_h_2, c_r, s7)), introduced(assumption)).
% 16.52/11.04 tff(5274,plain,
% 16.52/11.04 (((~![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_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, 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_2, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s7))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5275,plain,
% 16.52/11.04 ((~![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_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s7))),
% 16.52/11.04 inference(quant_inst,[status(thm)],[])).
% 16.52/11.04 tff(5276,plain,
% 16.52/11.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s7)),
% 16.52/11.04 inference(modus_ponens,[status(thm)],[5275, 5274])).
% 16.52/11.04 tff(5277,plain,
% 16.52/11.04 ($false),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5276, 68, 5273, 5272])).
% 16.52/11.04 tff(5278,plain,(m_and_h_gate_v_in2(c_e_h_2, c_r, s7) | (~node20(c_e_h_2, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 16.52/11.04 tff(5279,plain,
% 16.52/11.04 (~node20(c_e_h_2, c_r, s7)),
% 16.52/11.04 inference(unit_resolution,[status(thm)],[5278, 5271])).
% 16.52/11.04 tff(5280,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s8)), introduced(assumption)).
% 16.52/11.04 tff(5281,assumption,(~node20(c_e_h_2, c_r, s7)), introduced(assumption)).
% 16.52/11.04 tff(5282,assumption,(node21(c_e_h_2, c_r, s7, s8)), introduced(assumption)).
% 16.52/11.04 tff(5283,plain,
% 16.52/11.04 (((~![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_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, 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_2, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, c_r, s7, s8)))),
% 16.52/11.04 inference(rewrite,[status(thm)],[])).
% 16.52/11.04 tff(5284,plain,
% 16.52/11.04 ((~![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_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, c_r, s7, s8)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5285,plain,
% 16.52/11.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, c_r, s7, s8))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5284, 5283])).
% 16.52/11.05 tff(5286,plain,
% 16.52/11.05 ($false),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5285, 82, 5282, 5281, 5280])).
% 16.52/11.05 tff(5287,plain,((~node21(c_e_h_2, c_r, s7, s8)) | node20(c_e_h_2, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8))), inference(lemma,lemma(discharge,[]))).
% 16.52/11.05 tff(5288,plain,
% 16.52/11.05 (~node21(c_e_h_2, c_r, s7, s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5287, 5280, 5281])).
% 16.52/11.05 tff(5289,plain,
% 16.52/11.05 (((~![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_r, s7, s8) | node22(c_e_h_2, 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_2, c_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5290,plain,
% 16.52/11.05 ((~![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_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5291,plain,
% 16.52/11.05 ((~![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_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8)),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 16.52/11.05 tff(5292,plain,
% 16.52/11.05 (node21(c_e_h_2, c_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5291, 112, 4760])).
% 16.52/11.05 tff(5293,plain,
% 16.52/11.05 (node22(c_e_h_2, c_r, s7, s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5292, 5288])).
% 16.52/11.05 tff(5294,plain,
% 16.52/11.05 (((~![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_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5295,plain,
% 16.52/11.05 ((~![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_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5296,plain,
% 16.52/11.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7)),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 16.52/11.05 tff(5297,plain,
% 16.52/11.05 ($false),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5296, 127, 5293, 3198, 5280])).
% 16.52/11.05 tff(5298,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7) | node20(c_e_h_2, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.05 tff(5299,plain,
% 16.52/11.05 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | node20(c_e_h_2, c_r, s7)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5298, 3196])).
% 16.52/11.05 tff(5300,plain,
% 16.52/11.05 (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5299, 5279])).
% 16.52/11.05 tff(5301,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s8)), introduced(assumption)).
% 16.52/11.05 tff(5302,assumption,(m_user_v_ack(c_e_h_2, c_u, s8)), introduced(assumption)).
% 16.52/11.05 tff(5303,plain,
% 16.52/11.05 (((~![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_2, c_u, s8)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5304,plain,
% 16.52/11.05 ((~![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_2, c_u, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5305,plain,
% 16.52/11.05 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5304, 5303])).
% 16.52/11.05 tff(5306,plain,
% 16.52/11.05 ($false),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5305, 1864, 5302, 5301])).
% 16.52/11.05 tff(5307,plain,((~m_user_v_ack(c_e_h_2, c_u, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.05 tff(5308,plain,
% 16.52/11.05 (~m_user_v_ack(c_e_h_2, c_u, s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5307, 5300])).
% 16.52/11.05 tff(5309,plain,
% 16.52/11.05 (((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s8)) | m_user_v_ack(c_e_h_2, c_u, s8))) <=> ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s8)) | m_user_v_ack(c_e_h_2, c_u, s8))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5310,plain,
% 16.52/11.05 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | ((~node23(s8)) | m_user_v_ack(c_e_h_2, c_u, s8))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5311,plain,
% 16.52/11.05 ((~![X: $i] : ((~node23(X)) | m_user_v_ack(c_e_h_2, c_u, X))) | (~node23(s8)) | m_user_v_ack(c_e_h_2, c_u, s8)),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5310, 5309])).
% 16.52/11.05 tff(5312,plain,
% 16.52/11.05 (~node23(s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5311, 3729, 5308])).
% 16.52/11.05 tff(5313,plain,
% 16.52/11.05 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s8) | (~node25(s8)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s8) | (~node25(s8)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5314,plain,
% 16.52/11.05 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s8) | (~node25(s8)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5315,plain,
% 16.52/11.05 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s8) | (~node25(s8))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5314, 5313])).
% 16.52/11.05 tff(5316,plain,
% 16.52/11.05 (~node25(s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5315, 3213, 5308])).
% 16.52/11.05 tff(5317,plain,
% 16.52/11.05 (~node23(s6)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[3877, 3252, 3857])).
% 16.52/11.05 tff(5318,plain,
% 16.52/11.05 (node25(s6) | (~node26(s6))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[3883, 3266, 3861, 5317])).
% 16.52/11.05 tff(5319,plain,
% 16.52/11.05 (~node26(s6)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5318, 3850])).
% 16.52/11.05 tff(5320,assumption,(~node26(s6)), introduced(assumption)).
% 16.52/11.05 tff(5321,assumption,(until27(s8)), introduced(assumption)).
% 16.52/11.05 tff(5322,assumption,(~node26(s7)), introduced(assumption)).
% 16.52/11.05 tff(5323,assumption,(~node26(s5)), introduced(assumption)).
% 16.52/11.05 tff(5324,assumption,(m_user_v_ack(c_e_h_1, c_u, s8)), introduced(assumption)).
% 16.52/11.05 tff(5325,plain,
% 16.52/11.05 (((~![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, s8)) | m_and_h_gate_v_out(c_e_h_1, 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_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5326,plain,
% 16.52/11.05 ((~![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, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5327,plain,
% 16.52/11.05 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5326, 5325])).
% 16.52/11.05 tff(5328,plain,
% 16.52/11.05 ($false),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5327, 1864, 5324, 4830])).
% 16.52/11.05 tff(5329,plain,((~m_user_v_ack(c_e_h_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 16.52/11.05 tff(5330,plain,
% 16.52/11.05 (~m_user_v_ack(c_e_h_1, c_u, s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5329, 4830])).
% 16.52/11.05 tff(5331,plain,
% 16.52/11.05 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5332,plain,
% 16.52/11.05 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5333,plain,
% 16.52/11.05 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5332, 5331])).
% 16.52/11.05 tff(5334,plain,
% 16.52/11.05 (~node24(s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5333, 1879, 5330])).
% 16.52/11.05 tff(5335,assumption,(~node23(s8)), introduced(assumption)).
% 16.52/11.05 tff(5336,assumption,(~node25(s8)), introduced(assumption)).
% 16.52/11.05 tff(5337,plain,
% 16.52/11.05 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s8) | node24(s8) | node25(s8) | (~node26(s8)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s8) | node24(s8) | node25(s8) | (~node26(s8)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5338,plain,
% 16.52/11.05 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s8) | node24(s8) | node25(s8) | (~node26(s8)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5339,plain,
% 16.52/11.05 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s8) | node24(s8) | node25(s8) | (~node26(s8))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 16.52/11.05 tff(5340,plain,
% 16.52/11.05 (node24(s8) | (~node26(s8))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5339, 3266, 5336, 5335])).
% 16.52/11.05 tff(5341,plain,
% 16.52/11.05 (~node26(s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5340, 5334])).
% 16.52/11.05 tff(5342,plain,
% 16.52/11.05 (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[4854, 4830, 4828])).
% 16.52/11.05 tff(5343,plain,
% 16.52/11.05 (~m_user_v_ack(c_e_h_1, c_u, s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[4862, 5342])).
% 16.52/11.05 tff(5344,plain,
% 16.52/11.05 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5345,plain,
% 16.52/11.05 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5346,plain,
% 16.52/11.05 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5345, 5344])).
% 16.52/11.05 tff(5347,plain,
% 16.52/11.05 (~node24(s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5346, 1879, 5343])).
% 16.52/11.05 tff(5348,assumption,(~node23(s9)), introduced(assumption)).
% 16.52/11.05 tff(5349,assumption,(~node25(s9)), introduced(assumption)).
% 16.52/11.05 tff(5350,plain,
% 16.52/11.05 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s9) | node24(s9) | node25(s9) | (~node26(s9)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s9) | node24(s9) | node25(s9) | (~node26(s9)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5351,plain,
% 16.52/11.05 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s9) | node24(s9) | node25(s9) | (~node26(s9)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5352,plain,
% 16.52/11.05 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s9) | node24(s9) | node25(s9) | (~node26(s9))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5351, 5350])).
% 16.52/11.05 tff(5353,plain,
% 16.52/11.05 (node24(s9) | (~node26(s9))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5352, 3266, 5349, 5348])).
% 16.52/11.05 tff(5354,plain,
% 16.52/11.05 (~node26(s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5353, 5347])).
% 16.52/11.05 tff(5355,assumption,(~node26(s9)), introduced(assumption)).
% 16.52/11.05 tff(5356,assumption,(~node26(s8)), introduced(assumption)).
% 16.52/11.05 tff(5357,assumption,(until27(s9)), introduced(assumption)).
% 16.52/11.05 tff(5358,plain,
% 16.52/11.05 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5359,plain,
% 16.52/11.05 (((~until27(s9)) | node26(s9) | xuntil28(s9)) <=> (xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5360,plain,
% 16.52/11.05 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s9)) | node26(s9) | xuntil28(s9))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9))))),
% 16.52/11.05 inference(monotonicity,[status(thm)],[5359])).
% 16.52/11.05 tff(5361,plain,
% 16.52/11.05 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s9)) | node26(s9) | xuntil28(s9))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 16.52/11.05 inference(transitivity,[status(thm)],[5360, 5358])).
% 16.52/11.05 tff(5362,plain,
% 16.52/11.05 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s9)) | node26(s9) | xuntil28(s9))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5363,plain,
% 16.52/11.05 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5362, 5361])).
% 16.52/11.05 tff(5364,plain,
% 16.52/11.05 (xuntil28(s9) | node26(s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5363, 3751, 5357])).
% 16.52/11.05 tff(5365,plain,
% 16.52/11.05 (xuntil28(s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5364, 5355])).
% 16.52/11.05 tff(5366,plain,
% 16.52/11.05 (^[X: $i] : refl(((~last(X)) | (~xuntil2p30(X))) <=> ((~last(X)) | (~xuntil2p30(X))))),
% 16.52/11.05 inference(bind,[status(th)],[])).
% 16.52/11.05 tff(5367,plain,
% 16.52/11.05 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(quant_intro,[status(thm)],[5366])).
% 16.52/11.05 tff(5368,plain,
% 16.52/11.05 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5369,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty14')).
% 16.52/11.05 tff(5370,plain,
% 16.52/11.05 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5369, 5368])).
% 16.52/11.05 tff(5371,plain,(
% 16.52/11.05 ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(skolemize,[status(sab)],[5370])).
% 16.52/11.05 tff(5372,plain,
% 16.52/11.05 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5371, 5367])).
% 16.52/11.05 tff(5373,plain,
% 16.52/11.05 (last(s9) <=> last(s9)),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5374,axiom,(last(s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound10')).
% 16.52/11.05 tff(5375,plain,
% 16.52/11.05 (last(s9)),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5374, 5373])).
% 16.52/11.05 tff(5376,plain,
% 16.52/11.05 (((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s9)) | (~xuntil2p30(s9)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s9)) | (~xuntil2p30(s9)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5377,plain,
% 16.52/11.05 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s9)) | (~xuntil2p30(s9)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5378,plain,
% 16.52/11.05 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s9)) | (~xuntil2p30(s9))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5377, 5376])).
% 16.52/11.05 tff(5379,plain,
% 16.52/11.05 (~xuntil2p30(s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5378, 5375, 5372])).
% 16.52/11.05 tff(5380,plain,
% 16.52/11.05 (^[X: $i] : refl((node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 16.52/11.05 inference(bind,[status(th)],[])).
% 16.52/11.05 tff(5381,plain,
% 16.52/11.05 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 16.52/11.05 inference(quant_intro,[status(thm)],[5380])).
% 16.52/11.05 tff(5382,plain,
% 16.52/11.05 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5383,plain,
% 16.52/11.05 (^[X: $i] : rewrite(((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 16.52/11.05 inference(bind,[status(th)],[])).
% 16.52/11.05 tff(5384,plain,
% 16.52/11.05 (![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 16.52/11.05 inference(quant_intro,[status(thm)],[5383])).
% 16.52/11.05 tff(5385,axiom,(![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty12')).
% 16.52/11.05 tff(5386,plain,
% 16.52/11.05 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5385, 5384])).
% 16.52/11.05 tff(5387,plain,
% 16.52/11.05 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5386, 5382])).
% 16.52/11.05 tff(5388,plain,(
% 16.52/11.05 ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 16.52/11.05 inference(skolemize,[status(sab)],[5387])).
% 16.52/11.05 tff(5389,plain,
% 16.52/11.05 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5388, 5381])).
% 16.52/11.05 tff(5390,plain,
% 16.52/11.05 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5391,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5392,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5391, 5390])).
% 16.52/11.05 tff(5393,plain,
% 16.52/11.05 (node26(s9) | (~until2p29(s9))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5392, 5389, 5379])).
% 16.52/11.05 tff(5394,plain,
% 16.52/11.05 (~until2p29(s9)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5393, 5355])).
% 16.52/11.05 tff(5395,plain,
% 16.52/11.05 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 16.52/11.05 inference(bind,[status(th)],[])).
% 16.52/11.05 tff(5396,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(quant_intro,[status(thm)],[5395])).
% 16.52/11.05 tff(5397,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5398,plain,
% 16.52/11.05 (^[Y: $i, X: $i] : rewrite(((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 16.52/11.05 inference(bind,[status(th)],[])).
% 16.52/11.05 tff(5399,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(quant_intro,[status(thm)],[5398])).
% 16.52/11.05 tff(5400,axiom,(![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty13')).
% 16.52/11.05 tff(5401,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5400, 5399])).
% 16.52/11.05 tff(5402,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5401, 5397])).
% 16.52/11.05 tff(5403,plain,(
% 16.52/11.05 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(skolemize,[status(sab)],[5402])).
% 16.52/11.05 tff(5404,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5403, 5396])).
% 16.52/11.05 tff(5405,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5406,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5407,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5406, 5405])).
% 16.52/11.05 tff(5408,plain,
% 16.52/11.05 (until2p29(s9) | (~xuntil2p30(s8))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5407, 4840, 5404])).
% 16.52/11.05 tff(5409,plain,
% 16.52/11.05 (~xuntil2p30(s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5408, 5394])).
% 16.52/11.05 tff(5410,plain,
% 16.52/11.05 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5411,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5412,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5411, 5410])).
% 16.52/11.05 tff(5413,plain,
% 16.52/11.05 (xuntil2p30(s8) | (~until2p29(s8))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5412, 5389, 5356])).
% 16.52/11.05 tff(5414,plain,
% 16.52/11.05 (~until2p29(s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5413, 5409])).
% 16.52/11.05 tff(5415,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5416,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5417,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5416, 5415])).
% 16.52/11.05 tff(5418,plain,
% 16.52/11.05 (until2p29(s8) | (~xuntil2p30(s7))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5417, 3928, 5404])).
% 16.52/11.05 tff(5419,plain,
% 16.52/11.05 (~xuntil2p30(s7)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5418, 5414])).
% 16.52/11.05 tff(5420,plain,
% 16.52/11.05 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5421,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5422,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5421, 5420])).
% 16.52/11.05 tff(5423,plain,
% 16.52/11.05 (xuntil2p30(s7) | (~until2p29(s7))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5422, 5389, 5322])).
% 16.52/11.05 tff(5424,plain,
% 16.52/11.05 (~until2p29(s7)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5423, 5419])).
% 16.52/11.05 tff(5425,plain,
% 16.52/11.05 (^[Y: $i, X: $i] : refl(((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)))),
% 16.52/11.05 inference(bind,[status(th)],[])).
% 16.52/11.05 tff(5426,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 16.52/11.05 inference(quant_intro,[status(thm)],[5425])).
% 16.52/11.05 tff(5427,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5428,plain,
% 16.52/11.05 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((until2p29(Y) | (~trans(X, Y))) | (~last(X))) <=> ((~last(X)) | (~trans(X, Y)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> (((~last(X)) | (~trans(X, Y)) | until2p29(Y)) | (~xuntil28(X))))), rewrite((((~last(X)) | (~trans(X, Y)) | until2p29(Y)) | (~xuntil28(X))) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))))),
% 16.52/11.05 inference(bind,[status(th)],[])).
% 16.52/11.05 tff(5429,plain,
% 16.52/11.05 (![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 16.52/11.05 inference(quant_intro,[status(thm)],[5428])).
% 16.52/11.05 tff(5430,axiom,(![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty11')).
% 16.52/11.05 tff(5431,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5430, 5429])).
% 16.52/11.05 tff(5432,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5431, 5427])).
% 16.52/11.05 tff(5433,plain,(
% 16.52/11.05 ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 16.52/11.05 inference(skolemize,[status(sab)],[5432])).
% 16.52/11.05 tff(5434,plain,
% 16.52/11.05 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5433, 5426])).
% 16.52/11.05 tff(5435,assumption,(xuntil28(s9)), introduced(assumption)).
% 16.52/11.05 tff(5436,assumption,(~until2p29(s8)), introduced(assumption)).
% 16.52/11.05 tff(5437,assumption,(trans(s9, s8)), introduced(assumption)).
% 16.52/11.05 tff(5438,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5439,plain,
% 16.52/11.05 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8)) <=> (until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5440,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8))))),
% 16.52/11.05 inference(monotonicity,[status(thm)],[5439])).
% 16.52/11.05 tff(5441,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)))),
% 16.52/11.05 inference(transitivity,[status(thm)],[5440, 5438])).
% 16.52/11.05 tff(5442,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8)) | until2p29(s8))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5443,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s8))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5442, 5441])).
% 16.52/11.05 tff(5444,plain,
% 16.52/11.05 ($false),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5443, 5375, 5437, 5434, 5436, 5435])).
% 16.52/11.05 tff(5445,plain,((~trans(s9, s8)) | until2p29(s8) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.52/11.05 tff(5446,plain,
% 16.52/11.05 (~trans(s9, s8)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5445, 5414, 5365])).
% 16.52/11.05 tff(5447,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5448,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5449,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5448, 5447])).
% 16.52/11.05 tff(5450,plain,
% 16.52/11.05 (until2p29(s7) | (~xuntil2p30(s6))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5449, 1839, 5404])).
% 16.52/11.05 tff(5451,plain,
% 16.52/11.05 (~xuntil2p30(s6)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5450, 5424])).
% 16.52/11.05 tff(5452,plain,
% 16.52/11.05 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5453,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5454,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5453, 5452])).
% 16.52/11.05 tff(5455,plain,
% 16.52/11.05 (xuntil2p30(s6) | (~until2p29(s6))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5454, 5389, 5320])).
% 16.52/11.05 tff(5456,plain,
% 16.52/11.05 (~until2p29(s6)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5455, 5451])).
% 16.52/11.05 tff(5457,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5458,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5459,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5458, 5457])).
% 16.52/11.05 tff(5460,plain,
% 16.52/11.05 (until2p29(s6) | (~xuntil2p30(s5))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5459, 1597, 5404])).
% 16.52/11.05 tff(5461,plain,
% 16.52/11.05 (~xuntil2p30(s5)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5460, 5456])).
% 16.52/11.05 tff(5462,plain,
% 16.52/11.05 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5463,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.05 tff(5464,plain,
% 16.52/11.05 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5))),
% 16.52/11.05 inference(modus_ponens,[status(thm)],[5463, 5462])).
% 16.52/11.05 tff(5465,plain,
% 16.52/11.05 (xuntil2p30(s5) | (~until2p29(s5))),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5464, 5389, 5323])).
% 16.52/11.05 tff(5466,plain,
% 16.52/11.05 (~until2p29(s5)),
% 16.52/11.05 inference(unit_resolution,[status(thm)],[5465, 5461])).
% 16.52/11.05 tff(5467,plain,
% 16.52/11.05 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 16.52/11.05 inference(rewrite,[status(thm)],[])).
% 16.52/11.05 tff(5468,plain,
% 16.52/11.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 16.52/11.05 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5469,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5468, 5467])).
% 16.52/11.06 tff(5470,plain,
% 16.52/11.06 (until2p29(s5) | (~xuntil2p30(s4))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5469, 1516, 5404])).
% 16.52/11.06 tff(5471,plain,
% 16.52/11.06 (~xuntil2p30(s4)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5470, 5466])).
% 16.52/11.06 tff(5472,assumption,(~node26(s4)), introduced(assumption)).
% 16.52/11.06 tff(5473,plain,
% 16.52/11.06 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5474,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5475,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5474, 5473])).
% 16.52/11.06 tff(5476,plain,
% 16.52/11.06 (xuntil2p30(s4) | (~until2p29(s4))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5475, 5389, 5472])).
% 16.52/11.06 tff(5477,plain,
% 16.52/11.06 (~until2p29(s4)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5476, 5471])).
% 16.52/11.06 tff(5478,assumption,(~until2p29(s4)), introduced(assumption)).
% 16.52/11.06 tff(5479,assumption,(trans(s9, s4)), introduced(assumption)).
% 16.52/11.06 tff(5480,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5481,plain,
% 16.52/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4)) <=> (until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5482,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4))))),
% 16.52/11.06 inference(monotonicity,[status(thm)],[5481])).
% 16.52/11.06 tff(5483,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)))),
% 16.52/11.06 inference(transitivity,[status(thm)],[5482, 5480])).
% 16.52/11.06 tff(5484,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4)) | until2p29(s4))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5485,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s4))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5484, 5483])).
% 16.52/11.06 tff(5486,plain,
% 16.52/11.06 ($false),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5485, 5375, 5479, 5434, 5478, 5435])).
% 16.52/11.06 tff(5487,plain,((~trans(s9, s4)) | until2p29(s4) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.52/11.06 tff(5488,plain,
% 16.52/11.06 (~trans(s9, s4)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5487, 5477, 5365])).
% 16.52/11.06 tff(5489,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5490,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5491,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5490, 5489])).
% 16.52/11.06 tff(5492,plain,
% 16.52/11.06 (until2p29(s4) | (~xuntil2p30(s3))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5491, 1009, 5404])).
% 16.52/11.06 tff(5493,plain,
% 16.52/11.06 (~xuntil2p30(s3)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5492, 5477])).
% 16.52/11.06 tff(5494,assumption,(~node26(s3)), introduced(assumption)).
% 16.52/11.06 tff(5495,plain,
% 16.52/11.06 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5496,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5497,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5496, 5495])).
% 16.52/11.06 tff(5498,plain,
% 16.52/11.06 (xuntil2p30(s3) | (~until2p29(s3))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5497, 5389, 5494])).
% 16.52/11.06 tff(5499,plain,
% 16.52/11.06 (~until2p29(s3)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5498, 5493])).
% 16.52/11.06 tff(5500,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5501,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5502,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5501, 5500])).
% 16.52/11.06 tff(5503,plain,
% 16.52/11.06 (until2p29(s3) | (~xuntil2p30(s2))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5502, 587, 5404])).
% 16.52/11.06 tff(5504,plain,
% 16.52/11.06 (~xuntil2p30(s2)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5503, 5499])).
% 16.52/11.06 tff(5505,assumption,(~node26(s2)), introduced(assumption)).
% 16.52/11.06 tff(5506,plain,
% 16.52/11.06 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5507,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5508,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5507, 5506])).
% 16.52/11.06 tff(5509,plain,
% 16.52/11.06 (xuntil2p30(s2) | (~until2p29(s2))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5508, 5389, 5505])).
% 16.52/11.06 tff(5510,plain,
% 16.52/11.06 (~until2p29(s2)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5509, 5504])).
% 16.52/11.06 tff(5511,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5512,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5513,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5512, 5511])).
% 16.52/11.06 tff(5514,plain,
% 16.52/11.06 (until2p29(s2) | (~xuntil2p30(s1))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5513, 344, 5404])).
% 16.52/11.06 tff(5515,plain,
% 16.52/11.06 (~xuntil2p30(s1)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5514, 5510])).
% 16.52/11.06 tff(5516,plain,
% 16.52/11.06 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5517,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5518,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5517, 5516])).
% 16.52/11.06 tff(5519,plain,
% 16.52/11.06 (xuntil2p30(s1) | (~until2p29(s1))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5518, 5389, 3701])).
% 16.52/11.06 tff(5520,plain,
% 16.52/11.06 (~until2p29(s1)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5519, 5515])).
% 16.52/11.06 tff(5521,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5522,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5523,plain,
% 16.52/11.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5522, 5521])).
% 16.52/11.06 tff(5524,plain,
% 16.52/11.06 (until2p29(s1) | (~xuntil2p30(s0))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5523, 98, 5404])).
% 16.52/11.06 tff(5525,plain,
% 16.52/11.06 (~xuntil2p30(s0)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5524, 5520])).
% 16.52/11.06 tff(5526,plain,
% 16.52/11.06 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5527,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 16.52/11.06 inference(quant_inst,[status(thm)],[])).
% 16.52/11.06 tff(5528,plain,
% 16.52/11.06 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0))),
% 16.52/11.06 inference(modus_ponens,[status(thm)],[5527, 5526])).
% 16.52/11.06 tff(5529,plain,
% 16.52/11.06 (xuntil2p30(s0) | (~until2p29(s0))),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5528, 5389, 3738])).
% 16.52/11.06 tff(5530,plain,
% 16.52/11.06 (~until2p29(s0)),
% 16.52/11.06 inference(unit_resolution,[status(thm)],[5529, 5525])).
% 16.52/11.06 tff(5531,assumption,(~until2p29(s0)), introduced(assumption)).
% 16.52/11.06 tff(5532,assumption,(trans(s9, s0)), introduced(assumption)).
% 16.52/11.06 tff(5533,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5534,plain,
% 16.52/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0)) <=> ((~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))),
% 16.52/11.06 inference(rewrite,[status(thm)],[])).
% 16.52/11.06 tff(5535,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0))))),
% 16.52/11.06 inference(monotonicity,[status(thm)],[5534])).
% 16.52/11.06 tff(5536,plain,
% 16.52/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0)))),
% 16.60/11.06 inference(transitivity,[status(thm)],[5535, 5533])).
% 16.60/11.06 tff(5537,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s0)) | until2p29(s0))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5538,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s9)) | (~xuntil28(s9)) | until2p29(s0) | (~trans(s9, s0))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5537, 5536])).
% 16.60/11.06 tff(5539,plain,
% 16.60/11.06 ($false),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5538, 5375, 5532, 5434, 5435, 5531])).
% 16.60/11.06 tff(5540,plain,((~trans(s9, s0)) | (~xuntil28(s9)) | until2p29(s0)), inference(lemma,lemma(discharge,[]))).
% 16.60/11.06 tff(5541,plain,
% 16.60/11.06 (~trans(s9, s0)),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5540, 5365, 5530])).
% 16.60/11.06 tff(5542,assumption,(~until2p29(s5)), introduced(assumption)).
% 16.60/11.06 tff(5543,assumption,(trans(s9, s5)), introduced(assumption)).
% 16.60/11.06 tff(5544,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5545,plain,
% 16.60/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5)) <=> (until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5546,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5))))),
% 16.60/11.06 inference(monotonicity,[status(thm)],[5545])).
% 16.60/11.06 tff(5547,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)))),
% 16.60/11.06 inference(transitivity,[status(thm)],[5546, 5544])).
% 16.60/11.06 tff(5548,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5)) | until2p29(s5))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5549,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s5))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5548, 5547])).
% 16.60/11.06 tff(5550,plain,
% 16.60/11.06 ($false),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5549, 5375, 5543, 5434, 5542, 5435])).
% 16.60/11.06 tff(5551,plain,((~trans(s9, s5)) | until2p29(s5) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.06 tff(5552,plain,
% 16.60/11.06 (~trans(s9, s5)),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5551, 5466, 5365])).
% 16.60/11.06 tff(5553,assumption,(~until2p29(s1)), introduced(assumption)).
% 16.60/11.06 tff(5554,assumption,(trans(s9, s1)), introduced(assumption)).
% 16.60/11.06 tff(5555,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5556,plain,
% 16.60/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1)) <=> (until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5557,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1))))),
% 16.60/11.06 inference(monotonicity,[status(thm)],[5556])).
% 16.60/11.06 tff(5558,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)))),
% 16.60/11.06 inference(transitivity,[status(thm)],[5557, 5555])).
% 16.60/11.06 tff(5559,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1)) | until2p29(s1))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5560,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s1))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5559, 5558])).
% 16.60/11.06 tff(5561,plain,
% 16.60/11.06 ($false),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5560, 5375, 5554, 5434, 5553, 5435])).
% 16.60/11.06 tff(5562,plain,((~trans(s9, s1)) | until2p29(s1) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.06 tff(5563,plain,
% 16.60/11.06 (~trans(s9, s1)),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5562, 5520, 5365])).
% 16.60/11.06 tff(5564,assumption,(~until2p29(s3)), introduced(assumption)).
% 16.60/11.06 tff(5565,assumption,(trans(s9, s3)), introduced(assumption)).
% 16.60/11.06 tff(5566,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5567,plain,
% 16.60/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3)) <=> (until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5568,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3))))),
% 16.60/11.06 inference(monotonicity,[status(thm)],[5567])).
% 16.60/11.06 tff(5569,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)))),
% 16.60/11.06 inference(transitivity,[status(thm)],[5568, 5566])).
% 16.60/11.06 tff(5570,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3)) | until2p29(s3))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5571,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s3))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5570, 5569])).
% 16.60/11.06 tff(5572,plain,
% 16.60/11.06 ($false),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5571, 5375, 5565, 5434, 5564, 5435])).
% 16.60/11.06 tff(5573,plain,((~trans(s9, s3)) | until2p29(s3) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.06 tff(5574,plain,
% 16.60/11.06 (~trans(s9, s3)),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5573, 5499, 5365])).
% 16.60/11.06 tff(5575,assumption,(~until2p29(s6)), introduced(assumption)).
% 16.60/11.06 tff(5576,assumption,(trans(s9, s6)), introduced(assumption)).
% 16.60/11.06 tff(5577,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5578,plain,
% 16.60/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6)) <=> (until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5579,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6))))),
% 16.60/11.06 inference(monotonicity,[status(thm)],[5578])).
% 16.60/11.06 tff(5580,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)))),
% 16.60/11.06 inference(transitivity,[status(thm)],[5579, 5577])).
% 16.60/11.06 tff(5581,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6)) | until2p29(s6))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5582,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s6))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5581, 5580])).
% 16.60/11.06 tff(5583,plain,
% 16.60/11.06 ($false),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5582, 5375, 5576, 5434, 5575, 5435])).
% 16.60/11.06 tff(5584,plain,((~trans(s9, s6)) | until2p29(s6) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.06 tff(5585,plain,
% 16.60/11.06 (~trans(s9, s6)),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5584, 5456, 5365])).
% 16.60/11.06 tff(5586,assumption,(~until2p29(s2)), introduced(assumption)).
% 16.60/11.06 tff(5587,assumption,(trans(s9, s2)), introduced(assumption)).
% 16.60/11.06 tff(5588,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5589,plain,
% 16.60/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2)) <=> (until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5590,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2))))),
% 16.60/11.06 inference(monotonicity,[status(thm)],[5589])).
% 16.60/11.06 tff(5591,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)))),
% 16.60/11.06 inference(transitivity,[status(thm)],[5590, 5588])).
% 16.60/11.06 tff(5592,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2)) | until2p29(s2))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5593,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s2))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5592, 5591])).
% 16.60/11.06 tff(5594,plain,
% 16.60/11.06 ($false),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5593, 5375, 5587, 5434, 5586, 5435])).
% 16.60/11.06 tff(5595,plain,((~trans(s9, s2)) | until2p29(s2) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.06 tff(5596,plain,
% 16.60/11.06 (~trans(s9, s2)),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5595, 5510, 5365])).
% 16.60/11.06 tff(5597,plain,
% 16.60/11.06 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 16.60/11.06 inference(bind,[status(th)],[])).
% 16.60/11.06 tff(5598,plain,
% 16.60/11.06 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 16.60/11.06 inference(quant_intro,[status(thm)],[5597])).
% 16.60/11.06 tff(5599,plain,
% 16.60/11.06 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5600,plain,
% 16.60/11.06 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 16.60/11.06 inference(bind,[status(th)],[])).
% 16.60/11.06 tff(5601,plain,
% 16.60/11.06 (![X: $i] : ((loop | (~last(X))) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 16.60/11.06 inference(quant_intro,[status(thm)],[5600])).
% 16.60/11.06 tff(5602,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty10')).
% 16.60/11.06 tff(5603,plain,
% 16.60/11.06 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5602, 5601])).
% 16.60/11.06 tff(5604,plain,
% 16.60/11.06 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5603, 5599])).
% 16.60/11.06 tff(5605,plain,(
% 16.60/11.06 ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 16.60/11.06 inference(skolemize,[status(sab)],[5604])).
% 16.60/11.06 tff(5606,plain,
% 16.60/11.06 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5605, 5598])).
% 16.60/11.06 tff(5607,plain,
% 16.60/11.06 (((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s9)) | (~xuntil28(s9)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s9)) | (~xuntil28(s9)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5608,plain,
% 16.60/11.06 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s9)) | (~xuntil28(s9)))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5609,plain,
% 16.60/11.06 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s9)) | (~xuntil28(s9))),
% 16.60/11.06 inference(modus_ponens,[status(thm)],[5608, 5607])).
% 16.60/11.06 tff(5610,plain,
% 16.60/11.06 (loop | (~xuntil28(s9))),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5609, 5375, 5606])).
% 16.60/11.06 tff(5611,plain,
% 16.60/11.06 (loop),
% 16.60/11.06 inference(unit_resolution,[status(thm)],[5610, 5365])).
% 16.60/11.06 tff(5612,assumption,(~until2p29(s9)), introduced(assumption)).
% 16.60/11.06 tff(5613,assumption,(trans(s9, s9)), introduced(assumption)).
% 16.60/11.06 tff(5614,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5615,plain,
% 16.60/11.06 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9)) <=> (until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))),
% 16.60/11.06 inference(rewrite,[status(thm)],[])).
% 16.60/11.06 tff(5616,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9))))),
% 16.60/11.06 inference(monotonicity,[status(thm)],[5615])).
% 16.60/11.06 tff(5617,plain,
% 16.60/11.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)))),
% 16.60/11.06 inference(transitivity,[status(thm)],[5616, 5614])).
% 16.60/11.06 tff(5618,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9)) | until2p29(s9))),
% 16.60/11.06 inference(quant_inst,[status(thm)],[])).
% 16.60/11.06 tff(5619,plain,
% 16.60/11.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s9))),
% 16.60/11.07 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 16.60/11.07 tff(5620,plain,
% 16.60/11.07 ($false),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5619, 5375, 5613, 5434, 5612, 5435])).
% 16.60/11.07 tff(5621,plain,((~trans(s9, s9)) | until2p29(s9) | (~xuntil28(s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.07 tff(5622,plain,
% 16.60/11.07 (~trans(s9, s9)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5621, 5394, 5365])).
% 16.60/11.07 tff(5623,plain,
% 16.60/11.07 (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5624,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8)) | trans(s9, s9)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5625,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7)) | trans(s9, s8)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5626,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6)) | trans(s9, s7)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5627,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5)) | trans(s9, s6)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5628,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4)) | trans(s9, s5)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5629,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3)) | trans(s9, s4)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5630,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2)) | trans(s9, s3)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5631,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0) | trans(s9, s1)) | trans(s9, s2)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5632,plain,
% 16.60/11.07 ((((~loop) | trans(s9, s0)) | trans(s9, s1)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5633,plain,
% 16.60/11.07 (((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1)) | trans(s9, s2))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5632])).
% 16.60/11.07 tff(5634,plain,
% 16.60/11.07 (((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5633, 5631])).
% 16.60/11.07 tff(5635,plain,
% 16.60/11.07 ((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2)) | trans(s9, s3))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5634])).
% 16.60/11.07 tff(5636,plain,
% 16.60/11.07 ((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5635, 5630])).
% 16.60/11.07 tff(5637,plain,
% 16.60/11.07 (((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3)) | trans(s9, s4))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5636])).
% 16.60/11.07 tff(5638,plain,
% 16.60/11.07 (((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5637, 5629])).
% 16.60/11.07 tff(5639,plain,
% 16.60/11.07 ((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4)) | trans(s9, s5))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5638])).
% 16.60/11.07 tff(5640,plain,
% 16.60/11.07 ((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5639, 5628])).
% 16.60/11.07 tff(5641,plain,
% 16.60/11.07 (((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5)) | trans(s9, s6))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5640])).
% 16.60/11.07 tff(5642,plain,
% 16.60/11.07 (((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5641, 5627])).
% 16.60/11.07 tff(5643,plain,
% 16.60/11.07 ((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6)) | trans(s9, s7))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5642])).
% 16.60/11.07 tff(5644,plain,
% 16.60/11.07 ((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5643, 5626])).
% 16.60/11.07 tff(5645,plain,
% 16.60/11.07 (((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7)) | trans(s9, s8))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5644])).
% 16.60/11.07 tff(5646,plain,
% 16.60/11.07 (((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5645, 5625])).
% 16.60/11.07 tff(5647,plain,
% 16.60/11.07 ((((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) | trans(s9, s9)) <=> (((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8)) | trans(s9, s9))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5646])).
% 16.60/11.07 tff(5648,plain,
% 16.60/11.07 ((((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) | trans(s9, s9)) <=> ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5647, 5624])).
% 16.60/11.07 tff(5649,axiom,(((((((((((~loop) | trans(s9, s0)) | trans(s9, s1)) | trans(s9, s2)) | trans(s9, s3)) | trans(s9, s4)) | trans(s9, s5)) | trans(s9, s6)) | trans(s9, s7)) | trans(s9, s8)) | trans(s9, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound12')).
% 16.60/11.07 tff(5650,plain,
% 16.60/11.07 ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9)),
% 16.60/11.07 inference(modus_ponens,[status(thm)],[5649, 5648])).
% 16.60/11.07 tff(5651,plain,
% 16.60/11.07 ((~loop) | trans(s9, s0) | trans(s9, s1) | trans(s9, s2) | trans(s9, s3) | trans(s9, s4) | trans(s9, s5) | trans(s9, s6) | trans(s9, s7) | trans(s9, s8) | trans(s9, s9)),
% 16.60/11.07 inference(modus_ponens,[status(thm)],[5650, 5623])).
% 16.60/11.07 tff(5652,plain,
% 16.60/11.07 (trans(s9, s7)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5651, 5622, 5611, 5596, 5585, 5574, 5563, 5552, 5541, 5488, 5446])).
% 16.60/11.07 tff(5653,plain,
% 16.60/11.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5654,plain,
% 16.60/11.07 (((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7)) <=> (until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5655,plain,
% 16.60/11.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7))))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5654])).
% 16.60/11.07 tff(5656,plain,
% 16.60/11.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5655, 5653])).
% 16.60/11.07 tff(5657,plain,
% 16.60/11.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7)) | until2p29(s7))),
% 16.60/11.07 inference(quant_inst,[status(thm)],[])).
% 16.60/11.07 tff(5658,plain,
% 16.60/11.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s9)) | (~xuntil28(s9)) | (~trans(s9, s7))),
% 16.60/11.07 inference(modus_ponens,[status(thm)],[5657, 5656])).
% 16.60/11.07 tff(5659,plain,
% 16.60/11.07 ($false),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5658, 5375, 5652, 5434, 5424, 5365])).
% 16.60/11.07 tff(5660,plain,(node26(s9) | node26(s2) | node26(s3) | node26(s4) | node26(s5) | node26(s6) | node26(s7) | node26(s8) | (~until27(s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.07 tff(5661,plain,
% 16.60/11.07 (node26(s9) | node26(s3) | node26(s4) | node26(s5) | node26(s6) | node26(s7) | node26(s8) | (~until27(s9))),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5660, 3670])).
% 16.60/11.07 tff(5662,plain,
% 16.60/11.07 (node26(s9) | node26(s4) | node26(s5) | node26(s6) | node26(s7) | node26(s8) | (~until27(s9))),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5661, 3642])).
% 16.60/11.07 tff(5663,plain,
% 16.60/11.07 (node26(s9) | node26(s5) | node26(s6) | node26(s7) | node26(s8) | (~until27(s9))),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5662, 3314])).
% 16.60/11.07 tff(5664,plain,
% 16.60/11.07 (~until27(s9)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5663, 5356, 5323, 5355, 5322, 5320])).
% 16.60/11.07 tff(5665,plain,
% 16.60/11.07 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5666,plain,
% 16.60/11.07 (((~until27(s8)) | node26(s8) | xuntil28(s8)) <=> (xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5667,plain,
% 16.60/11.07 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s8)) | node26(s8) | xuntil28(s8))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8))))),
% 16.60/11.07 inference(monotonicity,[status(thm)],[5666])).
% 16.60/11.07 tff(5668,plain,
% 16.60/11.07 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s8)) | node26(s8) | xuntil28(s8))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 16.60/11.07 inference(transitivity,[status(thm)],[5667, 5665])).
% 16.60/11.07 tff(5669,plain,
% 16.60/11.07 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s8)) | node26(s8) | xuntil28(s8))),
% 16.60/11.07 inference(quant_inst,[status(thm)],[])).
% 16.60/11.07 tff(5670,plain,
% 16.60/11.07 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8))),
% 16.60/11.07 inference(modus_ponens,[status(thm)],[5669, 5668])).
% 16.60/11.07 tff(5671,plain,
% 16.60/11.07 (xuntil28(s8) | node26(s8)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5670, 3751, 5321])).
% 16.60/11.07 tff(5672,plain,
% 16.60/11.07 (xuntil28(s8)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5671, 5356])).
% 16.60/11.07 tff(5673,plain,
% 16.60/11.07 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5674,plain,
% 16.60/11.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 16.60/11.07 inference(quant_inst,[status(thm)],[])).
% 16.60/11.07 tff(5675,plain,
% 16.60/11.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9)),
% 16.60/11.07 inference(modus_ponens,[status(thm)],[5674, 5673])).
% 16.60/11.07 tff(5676,plain,
% 16.60/11.07 ((~xuntil28(s8)) | until27(s9)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5675, 4840, 3769])).
% 16.60/11.07 tff(5677,plain,
% 16.60/11.07 ($false),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5676, 5672, 5664])).
% 16.60/11.07 tff(5678,plain,(node26(s8) | (~until27(s8)) | node26(s5) | node26(s9) | node26(s7) | node26(s6)), inference(lemma,lemma(discharge,[]))).
% 16.60/11.07 tff(5679,plain,
% 16.60/11.07 ($false),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5678, 5354, 5341, 5323, 5322, 5321, 5320])).
% 16.60/11.07 tff(5680,plain,(m_and_h_gate_v_out(c_e_h_1, c_r, s8) | node26(s5) | node26(s7) | (~until27(s8)) | node26(s6) | node25(s9) | node23(s9) | node25(s8) | node23(s8) | node20(c_e_h_1, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 16.60/11.07 tff(5681,plain,
% 16.60/11.07 (m_and_h_gate_v_out(c_e_h_1, c_r, s8) | node26(s7) | (~until27(s8)) | node25(s9) | node23(s9) | node25(s8) | node23(s8) | node20(c_e_h_1, c_r, s8)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5680, 5319, 3271])).
% 16.60/11.07 tff(5682,plain,
% 16.60/11.07 (m_and_h_gate_v_out(c_e_h_1, c_r, s8) | node26(s7) | (~until27(s8)) | node25(s9) | node23(s9) | node20(c_e_h_1, c_r, s8)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5681, 5316, 5312])).
% 16.60/11.07 tff(5683,plain,
% 16.60/11.07 (node25(s9)),
% 16.60/11.07 inference(unit_resolution,[status(thm)],[5682, 4870, 4827, 4792, 3945, 3933])).
% 16.60/11.07 tff(5684,plain,
% 16.60/11.07 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s9) | (~node25(s9)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s9) | (~node25(s9)))),
% 16.60/11.07 inference(rewrite,[status(thm)],[])).
% 16.60/11.07 tff(5685,plain,
% 16.60/11.07 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s9) | (~node25(s9)))),
% 16.60/11.07 inference(quant_inst,[status(thm)],[])).
% 16.60/11.07 tff(5686,plain,
% 16.60/11.07 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s9) | (~node25(s9))),
% 16.60/11.07 inference(modus_ponens,[status(thm)],[5685, 5684])).
% 16.60/11.08 tff(5687,plain,
% 16.60/11.08 (m_user_v_ack(c_e_h_2, c_u, s9)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5686, 3213, 5683])).
% 16.60/11.08 tff(5688,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s9)), introduced(assumption)).
% 16.60/11.08 tff(5689,assumption,(m_user_v_ack(c_e_h_2, c_u, s9)), introduced(assumption)).
% 16.60/11.08 tff(5690,plain,
% 16.60/11.08 (((~![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_2, c_u, s9)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_u, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5691,plain,
% 16.60/11.08 ((~![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_2, c_u, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9))),
% 16.60/11.08 inference(quant_inst,[status(thm)],[])).
% 16.60/11.08 tff(5692,plain,
% 16.60/11.08 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9)),
% 16.60/11.08 inference(modus_ponens,[status(thm)],[5691, 5690])).
% 16.60/11.08 tff(5693,plain,
% 16.60/11.08 ($false),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5692, 1864, 5689, 5688])).
% 16.60/11.08 tff(5694,plain,((~m_user_v_ack(c_e_h_2, c_u, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 16.60/11.08 tff(5695,plain,
% 16.60/11.08 (m_and_h_gate_v_out(c_e_h_2, c_r, s9)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5694, 5687])).
% 16.60/11.08 tff(5696,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s9)), introduced(assumption)).
% 16.60/11.08 tff(5697,assumption,(~node20(c_e_h_2, c_r, s8)), introduced(assumption)).
% 16.60/11.08 tff(5698,assumption,(node22(c_e_h_2, c_r, s8, s9)), introduced(assumption)).
% 16.60/11.08 tff(5699,plain,
% 16.60/11.08 (((~![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_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, 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_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5700,plain,
% 16.60/11.08 ((~![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_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8))),
% 16.60/11.08 inference(quant_inst,[status(thm)],[])).
% 16.60/11.08 tff(5701,plain,
% 16.60/11.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)),
% 16.60/11.08 inference(modus_ponens,[status(thm)],[5700, 5699])).
% 16.60/11.08 tff(5702,plain,
% 16.60/11.08 ($false),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5701, 127, 5698, 5301, 5696])).
% 16.60/11.08 tff(5703,plain,((~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9))), inference(lemma,lemma(discharge,[]))).
% 16.60/11.08 tff(5704,plain,
% 16.60/11.08 (~node22(c_e_h_2, c_r, s8, s9)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5703, 5696, 5301])).
% 16.60/11.08 tff(5705,plain,
% 16.60/11.08 (((~![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_r, s8, s9) | node22(c_e_h_2, 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_2, c_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5706,plain,
% 16.60/11.08 ((~![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_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9))),
% 16.60/11.08 inference(quant_inst,[status(thm)],[])).
% 16.60/11.08 tff(5707,plain,
% 16.60/11.08 ((~![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_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9)),
% 16.60/11.08 inference(modus_ponens,[status(thm)],[5706, 5705])).
% 16.60/11.08 tff(5708,plain,
% 16.60/11.08 (node21(c_e_h_2, c_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5707, 112, 4844])).
% 16.60/11.08 tff(5709,plain,
% 16.60/11.08 (node21(c_e_h_2, c_r, s8, s9)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5708, 5704])).
% 16.60/11.08 tff(5710,plain,
% 16.60/11.08 (((~![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_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, 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_2, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, c_r, s8, s9)))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5711,plain,
% 16.60/11.08 ((~![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_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, c_r, s8, s9)))),
% 16.60/11.08 inference(quant_inst,[status(thm)],[])).
% 16.60/11.08 tff(5712,plain,
% 16.60/11.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, c_r, s8, s9))),
% 16.60/11.08 inference(modus_ponens,[status(thm)],[5711, 5710])).
% 16.60/11.08 tff(5713,plain,
% 16.60/11.08 ($false),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5712, 82, 5709, 5697, 5696])).
% 16.60/11.08 tff(5714,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | node20(c_e_h_2, c_r, s8) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 16.60/11.08 tff(5715,plain,
% 16.60/11.08 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | node20(c_e_h_2, c_r, s8)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5714, 5300])).
% 16.60/11.08 tff(5716,plain,
% 16.60/11.08 (node20(c_e_h_2, c_r, s8)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5715, 5695])).
% 16.60/11.08 tff(5717,plain,
% 16.60/11.08 (((~![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_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, 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_2, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s8))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5718,plain,
% 16.60/11.08 ((~![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_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s8))),
% 16.60/11.08 inference(quant_inst,[status(thm)],[])).
% 16.60/11.08 tff(5719,plain,
% 16.60/11.08 ((~![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_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s8)),
% 16.60/11.08 inference(modus_ponens,[status(thm)],[5718, 5717])).
% 16.60/11.08 tff(5720,plain,
% 16.60/11.08 (m_and_h_gate_v_in2(c_e_h_2, c_r, s8)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5719, 68, 5716])).
% 16.60/11.08 tff(5721,plain,
% 16.60/11.08 (((~![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_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, 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_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5722,plain,
% 16.60/11.08 ((~![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_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 16.60/11.08 inference(quant_inst,[status(thm)],[])).
% 16.60/11.08 tff(5723,plain,
% 16.60/11.08 ((~![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_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 16.60/11.08 inference(modus_ponens,[status(thm)],[5722, 5721])).
% 16.60/11.08 tff(5724,plain,
% 16.60/11.08 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5723, 1625, 5720])).
% 16.60/11.08 tff(5725,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)), introduced(assumption)).
% 16.60/11.08 tff(5726,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), introduced(assumption)).
% 16.60/11.08 tff(5727,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)), introduced(assumption)).
% 16.60/11.08 tff(5728,plain,
% 16.60/11.08 (((~![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_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, 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_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5729,plain,
% 16.60/11.08 ((~![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_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 16.60/11.08 inference(quant_inst,[status(thm)],[])).
% 16.60/11.08 tff(5730,plain,
% 16.60/11.08 ((~![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_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 16.60/11.08 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 16.60/11.08 tff(5731,plain,
% 16.60/11.08 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5730, 1145])).
% 16.60/11.08 tff(5732,plain,
% 16.60/11.08 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)),
% 16.60/11.08 inference(unit_resolution,[status(thm)],[5731, 4873])).
% 16.60/11.08 tff(5733,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)), introduced(assumption)).
% 16.60/11.08 tff(5734,assumption,(node11(c_e_h_2, c_n, s6, s7)), introduced(assumption)).
% 16.60/11.08 tff(5735,plain,
% 16.60/11.08 (((~![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_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, 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_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7)))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5736,plain,
% 16.60/11.08 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7)))),
% 16.60/11.08 inference(rewrite,[status(thm)],[])).
% 16.60/11.08 tff(5737,plain,
% 16.60/11.08 (((~![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_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, 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_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7))))),
% 16.60/11.08 inference(monotonicity,[status(thm)],[5736])).
% 16.60/11.08 tff(5738,plain,
% 16.60/11.08 (((~![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_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, 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_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7)))),
% 16.60/11.08 inference(transitivity,[status(thm)],[5737, 5735])).
% 16.60/11.08 tff(5739,plain,
% 16.60/11.08 ((~![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_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))),
% 16.62/11.08 inference(quant_inst,[status(thm)],[])).
% 16.62/11.08 tff(5740,plain,
% 16.62/11.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7))),
% 16.62/11.08 inference(modus_ponens,[status(thm)],[5739, 5738])).
% 16.62/11.08 tff(5741,plain,
% 16.62/11.08 ($false),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5740, 1223, 5733, 5726, 5734])).
% 16.62/11.08 tff(5742,plain,((~node11(c_e_h_2, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.08 tff(5743,plain,
% 16.62/11.08 (~node11(c_e_h_2, c_n, s6, s7)),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5742, 5733, 5726])).
% 16.62/11.08 tff(5744,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)), introduced(assumption)).
% 16.62/11.08 tff(5745,assumption,(node10(c_e_h_2, c_n, s6, s7)), introduced(assumption)).
% 16.62/11.08 tff(5746,plain,
% 16.62/11.08 (((~![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_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, 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_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7)))),
% 16.62/11.08 inference(rewrite,[status(thm)],[])).
% 16.62/11.08 tff(5747,plain,
% 16.62/11.08 (((~node10(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7)))),
% 16.62/11.08 inference(rewrite,[status(thm)],[])).
% 16.62/11.08 tff(5748,plain,
% 16.62/11.08 (((~![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_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, 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_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7))))),
% 16.62/11.08 inference(monotonicity,[status(thm)],[5747])).
% 16.62/11.08 tff(5749,plain,
% 16.62/11.08 (((~![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_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, 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_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7)))),
% 16.62/11.08 inference(transitivity,[status(thm)],[5748, 5746])).
% 16.62/11.08 tff(5750,plain,
% 16.62/11.08 ((~![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_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))),
% 16.62/11.08 inference(quant_inst,[status(thm)],[])).
% 16.62/11.08 tff(5751,plain,
% 16.62/11.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7))),
% 16.62/11.08 inference(modus_ponens,[status(thm)],[5750, 5749])).
% 16.62/11.08 tff(5752,plain,
% 16.62/11.08 ($false),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5751, 1160, 5727, 5744, 5733, 5745])).
% 16.62/11.08 tff(5753,plain,((~node10(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.08 tff(5754,plain,
% 16.62/11.08 (~node10(c_e_h_2, c_n, s6, s7)),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5753, 5733, 5727, 5744])).
% 16.62/11.08 tff(5755,plain,
% 16.62/11.08 (((~![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_2, c_n, s6, s7) | node11(c_e_h_2, 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_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7))),
% 16.62/11.08 inference(rewrite,[status(thm)],[])).
% 16.62/11.08 tff(5756,plain,
% 16.62/11.08 ((~![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_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7))),
% 16.62/11.08 inference(quant_inst,[status(thm)],[])).
% 16.62/11.08 tff(5757,plain,
% 16.62/11.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7)),
% 16.62/11.08 inference(modus_ponens,[status(thm)],[5756, 5755])).
% 16.62/11.08 tff(5758,plain,
% 16.62/11.08 (node10(c_e_h_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7)),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5757, 1179, 1843])).
% 16.62/11.08 tff(5759,plain,
% 16.62/11.08 ($false),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5758, 5754, 5743])).
% 16.62/11.08 tff(5760,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.08 tff(5761,plain,
% 16.62/11.08 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5760, 5732, 5727, 5726])).
% 16.62/11.08 tff(5762,plain,
% 16.62/11.08 (((~![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, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, 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_2, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))),
% 16.62/11.08 inference(rewrite,[status(thm)],[])).
% 16.62/11.08 tff(5763,plain,
% 16.62/11.08 ((~![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, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))),
% 16.62/11.08 inference(quant_inst,[status(thm)],[])).
% 16.62/11.08 tff(5764,plain,
% 16.62/11.08 ((~![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, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))),
% 16.62/11.08 inference(modus_ponens,[status(thm)],[5763, 5762])).
% 16.62/11.08 tff(5765,plain,
% 16.62/11.08 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5764, 1276, 5761])).
% 16.62/11.08 tff(5766,plain,
% 16.62/11.08 (((~![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, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, 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_2, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7))),
% 16.62/11.08 inference(rewrite,[status(thm)],[])).
% 16.62/11.08 tff(5767,plain,
% 16.62/11.08 ((~![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, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7))),
% 16.62/11.08 inference(quant_inst,[status(thm)],[])).
% 16.62/11.08 tff(5768,plain,
% 16.62/11.08 ((~![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, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)),
% 16.62/11.08 inference(modus_ponens,[status(thm)],[5767, 5766])).
% 16.62/11.08 tff(5769,plain,
% 16.62/11.08 (~node9(c_e_h_2, c_m, s7)),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5768, 1290, 5765])).
% 16.62/11.08 tff(5770,assumption,(~node9(c_e_h_2, c_m, s7)), introduced(assumption)).
% 16.62/11.08 tff(5771,assumption,(node10(c_e_h_2, c_m, s7, s8)), introduced(assumption)).
% 16.62/11.08 tff(5772,plain,
% 16.62/11.08 (((~![Y: $i, I0: $i, 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, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, 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_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 16.62/11.08 inference(rewrite,[status(thm)],[])).
% 16.62/11.08 tff(5773,plain,
% 16.62/11.08 ((node9(c_e_h_2, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, c_m, s7, s8))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 16.62/11.08 inference(rewrite,[status(thm)],[])).
% 16.62/11.08 tff(5774,plain,
% 16.62/11.08 (((~![Y: $i, I0: $i, 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, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, 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_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8))))),
% 16.62/11.08 inference(monotonicity,[status(thm)],[5773])).
% 16.62/11.08 tff(5775,plain,
% 16.62/11.08 (((~![Y: $i, I0: $i, 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, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, 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_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 16.62/11.08 inference(transitivity,[status(thm)],[5774, 5772])).
% 16.62/11.08 tff(5776,plain,
% 16.62/11.08 ((~![Y: $i, I0: $i, 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, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 16.62/11.08 inference(quant_inst,[status(thm)],[])).
% 16.62/11.08 tff(5777,plain,
% 16.62/11.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8))),
% 16.62/11.08 inference(modus_ponens,[status(thm)],[5776, 5775])).
% 16.62/11.08 tff(5778,plain,
% 16.62/11.08 ($false),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5777, 1304, 5725, 5771, 5770])).
% 16.62/11.08 tff(5779,plain,((~node10(c_e_h_2, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.08 tff(5780,plain,
% 16.62/11.08 (~node10(c_e_h_2, c_m, s7, s8)),
% 16.62/11.08 inference(unit_resolution,[status(thm)],[5779, 5769, 5725])).
% 16.62/11.09 tff(5781,plain,
% 16.62/11.09 (((~![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_2, c_m, s7, s8) | node11(c_e_h_2, 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_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5782,plain,
% 16.62/11.09 ((~![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_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5783,plain,
% 16.62/11.09 ((~![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_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8)),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5782, 5781])).
% 16.62/11.09 tff(5784,plain,
% 16.62/11.09 (node10(c_e_h_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5783, 1179, 4760])).
% 16.62/11.09 tff(5785,plain,
% 16.62/11.09 (node11(c_e_h_2, c_m, s7, s8)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5784, 5780])).
% 16.62/11.09 tff(5786,assumption,(node11(c_e_h_2, c_m, s7, s8)), introduced(assumption)).
% 16.62/11.09 tff(5787,plain,
% 16.62/11.09 (((~![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_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, 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_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5788,plain,
% 16.62/11.09 ((~![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_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5789,plain,
% 16.62/11.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5788, 5787])).
% 16.62/11.09 tff(5790,plain,
% 16.62/11.09 ($false),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5789, 1258, 5725, 5265, 5786])).
% 16.62/11.09 tff(5791,plain,((~node11(c_e_h_2, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.09 tff(5792,plain,
% 16.62/11.09 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5791, 5785, 5725])).
% 16.62/11.09 tff(5793,plain,
% 16.62/11.09 (~node11(c_e_h_2, c_m, s6, s7)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[4878, 5792, 4873])).
% 16.62/11.09 tff(5794,plain,
% 16.62/11.09 (~node10(c_e_h_2, c_m, s6, s7)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5255, 5792, 5246])).
% 16.62/11.09 tff(5795,plain,
% 16.62/11.09 ($false),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5261, 5794, 5793])).
% 16.62/11.09 tff(5796,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6) | node9(c_e_h_2, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.09 tff(5797,plain,
% 16.62/11.09 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6))),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5796, 5237, 5245, 2975])).
% 16.62/11.09 tff(5798,plain,
% 16.62/11.09 (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5797, 5724])).
% 16.62/11.09 tff(5799,plain,
% 16.62/11.09 (((~![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_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, 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_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5800,plain,
% 16.62/11.09 ((~![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_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5801,plain,
% 16.62/11.09 ((~![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_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6)),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5800, 5799])).
% 16.62/11.09 tff(5802,plain,
% 16.62/11.09 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5801, 1099])).
% 16.62/11.09 tff(5803,plain,
% 16.62/11.09 (m_c_h_element_v_out(c_e_h_2, c_e, s6)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5802, 5798])).
% 16.62/11.09 tff(5804,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s6)), introduced(assumption)).
% 16.62/11.09 tff(5805,plain,
% 16.62/11.09 (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5134, 5129])).
% 16.62/11.09 tff(5806,plain,
% 16.62/11.09 (~m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5197, 5805, 5138])).
% 16.62/11.09 tff(5807,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s5)), introduced(assumption)).
% 16.62/11.09 tff(5808,assumption,(node15(c_e_h_2, c_e, s5, s6)), introduced(assumption)).
% 16.62/11.09 tff(5809,plain,
% 16.62/11.09 (((~![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, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, 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_2, c_e, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5810,plain,
% 16.62/11.09 ((~![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, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5811,plain,
% 16.62/11.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 16.62/11.09 tff(5812,plain,
% 16.62/11.09 ($false),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5811, 178, 5807, 5804, 5808])).
% 16.62/11.09 tff(5813,plain,((~node15(c_e_h_2, c_e, s5, s6)) | 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, s6))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.09 tff(5814,plain,
% 16.62/11.09 (~node15(c_e_h_2, c_e, s5, s6)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5813, 5804, 5807])).
% 16.62/11.09 tff(5815,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s5)), introduced(assumption)).
% 16.62/11.09 tff(5816,assumption,(node14(c_e_h_2, c_e, s5, s6)), introduced(assumption)).
% 16.62/11.09 tff(5817,plain,
% 16.62/11.09 (((~![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_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node14(c_e_h_2, 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_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node14(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5818,plain,
% 16.62/11.09 (((~node14(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node14(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5819,plain,
% 16.62/11.09 (((~![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_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, 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_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node14(c_e_h_2, c_e, s5, s6))))),
% 16.62/11.09 inference(monotonicity,[status(thm)],[5818])).
% 16.62/11.09 tff(5820,plain,
% 16.62/11.09 (((~![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_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, 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_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node14(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(transitivity,[status(thm)],[5819, 5817])).
% 16.62/11.09 tff(5821,plain,
% 16.62/11.09 ((~![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_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5822,plain,
% 16.62/11.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node14(c_e_h_2, c_e, s5, s6))),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5821, 5820])).
% 16.62/11.09 tff(5823,plain,
% 16.62/11.09 ($false),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5822, 254, 5804, 5816, 5815])).
% 16.62/11.09 tff(5824,plain,((~node14(c_e_h_2, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.09 tff(5825,plain,
% 16.62/11.09 (~node14(c_e_h_2, c_e, s5, s6)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5824, 5804, 5815])).
% 16.62/11.09 tff(5826,plain,
% 16.62/11.09 (((~![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_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_2, c_e, s5, s6))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5827,plain,
% 16.62/11.09 ((~![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_e, s5, s6))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5828,plain,
% 16.62/11.09 ((~![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_e, s5, s6)),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5827, 5826])).
% 16.62/11.09 tff(5829,plain,
% 16.62/11.09 (node19(c_e_h_2, c_e, s5, s6)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5828, 221, 1601])).
% 16.62/11.09 tff(5830,plain,
% 16.62/11.09 (((~![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)))) | ((~node19(c_e_h_2, c_e, s5, s6)) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | node16(c_e_h_2, 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_2, c_e, s5, s6)) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | node16(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5831,plain,
% 16.62/11.09 ((node16(c_e_h_2, c_e, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6))) <=> ((~node19(c_e_h_2, c_e, s5, s6)) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | node16(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5832,plain,
% 16.62/11.09 (((~![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, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, 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_2, c_e, s5, s6)) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | node16(c_e_h_2, c_e, s5)))),
% 16.62/11.09 inference(monotonicity,[status(thm)],[5831])).
% 16.62/11.09 tff(5833,plain,
% 16.62/11.09 (((~![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, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, 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_2, c_e, s5, s6)) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | node16(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(transitivity,[status(thm)],[5832, 5830])).
% 16.62/11.09 tff(5834,plain,
% 16.62/11.09 ((~![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, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5835,plain,
% 16.62/11.09 ((~![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)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | node16(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5834, 5833])).
% 16.62/11.09 tff(5836,plain,
% 16.62/11.09 (node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | node16(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5835, 235, 5829])).
% 16.62/11.09 tff(5837,plain,
% 16.62/11.09 (node16(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5836, 5825, 5814])).
% 16.62/11.09 tff(5838,assumption,(node18(c_e_h_2, c_e, s5, s6)), introduced(assumption)).
% 16.62/11.09 tff(5839,plain,
% 16.62/11.09 (((~![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_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node18(c_e_h_2, 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_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node18(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5840,plain,
% 16.62/11.09 (((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, c_e, s5, s6))) <=> (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, s6)) | (~node18(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5841,plain,
% 16.62/11.09 (((~![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_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, 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_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node18(c_e_h_2, c_e, s5, s6))))),
% 16.62/11.09 inference(monotonicity,[status(thm)],[5840])).
% 16.62/11.09 tff(5842,plain,
% 16.62/11.09 (((~![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_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, 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_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node18(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(transitivity,[status(thm)],[5841, 5839])).
% 16.62/11.09 tff(5843,plain,
% 16.62/11.09 ((~![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_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5844,plain,
% 16.62/11.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node18(c_e_h_2, c_e, s5, s6))),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5843, 5842])).
% 16.62/11.09 tff(5845,plain,
% 16.62/11.09 ($false),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5844, 560, 5807, 5804, 5838])).
% 16.62/11.09 tff(5846,plain,((~node18(c_e_h_2, c_e, s5, s6)) | 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, s6))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.09 tff(5847,plain,
% 16.62/11.09 (~node18(c_e_h_2, c_e, s5, s6)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5846, 5804, 5807])).
% 16.62/11.09 tff(5848,plain,
% 16.62/11.09 (((~![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_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, 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_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5849,plain,
% 16.62/11.09 ((node17(c_e_h_2, c_e, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6))) <=> ((~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(rewrite,[status(thm)],[])).
% 16.62/11.09 tff(5850,plain,
% 16.62/11.09 (((~![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, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, 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)))) | ((~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5)))),
% 16.62/11.09 inference(monotonicity,[status(thm)],[5849])).
% 16.62/11.09 tff(5851,plain,
% 16.62/11.09 (((~![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, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, 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)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5))),
% 16.62/11.09 inference(transitivity,[status(thm)],[5850, 5848])).
% 16.62/11.09 tff(5852,plain,
% 16.62/11.09 ((~![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, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))),
% 16.62/11.09 inference(quant_inst,[status(thm)],[])).
% 16.62/11.09 tff(5853,plain,
% 16.62/11.09 ((~![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_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(modus_ponens,[status(thm)],[5852, 5851])).
% 16.62/11.09 tff(5854,plain,
% 16.62/11.09 (node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5853, 542, 5829])).
% 16.62/11.09 tff(5855,plain,
% 16.62/11.09 (node17(c_e_h_2, c_e, s5)),
% 16.62/11.09 inference(unit_resolution,[status(thm)],[5854, 5847])).
% 16.62/11.09 tff(5856,plain,
% 16.62/11.09 (((~![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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, 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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5857,plain,
% 16.62/11.10 ((m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5858,plain,
% 16.62/11.10 (((~![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, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, 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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5))))),
% 16.62/11.10 inference(monotonicity,[status(thm)],[5857])).
% 16.62/11.10 tff(5859,plain,
% 16.62/11.10 (((~![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, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, 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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(transitivity,[status(thm)],[5858, 5856])).
% 16.62/11.10 tff(5860,plain,
% 16.62/11.10 ((~![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, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5861,plain,
% 16.62/11.10 ((~![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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5))),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5860, 5859])).
% 16.62/11.10 tff(5862,plain,
% 16.62/11.10 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5))),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5861, 767, 5815])).
% 16.62/11.10 tff(5863,plain,
% 16.62/11.10 (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5862, 5855])).
% 16.62/11.10 tff(5864,plain,
% 16.62/11.10 (((~![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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, 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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s5))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5865,plain,
% 16.62/11.10 ((~![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_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s5))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5866,plain,
% 16.62/11.10 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5865, 5864])).
% 16.62/11.10 tff(5867,plain,
% 16.62/11.10 ((~node16(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5866, 209, 5815])).
% 16.62/11.10 tff(5868,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5867, 5863, 5837])).
% 16.62/11.10 tff(5869,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.10 tff(5870,plain,
% 16.62/11.10 (m_c_h_element_v_in1(c_e_h_2, c_e, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5869, 5807, 5804])).
% 16.62/11.10 tff(5871,plain,
% 16.62/11.10 (~node18(c_e_h_2, c_e, s5, s6)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5846, 5807, 5804])).
% 16.62/11.10 tff(5872,plain,
% 16.62/11.10 (node17(c_e_h_2, c_e, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5854, 5871])).
% 16.62/11.10 tff(5873,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s5)), introduced(assumption)).
% 16.62/11.10 tff(5874,plain,
% 16.62/11.10 (((~![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_2, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, 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_2, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5875,plain,
% 16.62/11.10 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5876,plain,
% 16.62/11.10 (((~![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, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, 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_2, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5))))),
% 16.62/11.10 inference(monotonicity,[status(thm)],[5875])).
% 16.62/11.10 tff(5877,plain,
% 16.62/11.10 (((~![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, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, 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_2, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(transitivity,[status(thm)],[5876, 5874])).
% 16.62/11.10 tff(5878,plain,
% 16.62/11.10 ((~![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, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5879,plain,
% 16.62/11.10 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5))),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5878, 5877])).
% 16.62/11.10 tff(5880,plain,
% 16.62/11.10 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5))),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5879, 524, 5873])).
% 16.62/11.10 tff(5881,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5880, 5872, 5870])).
% 16.62/11.10 tff(5882,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, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.10 tff(5883,plain,
% 16.62/11.10 (m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5882, 5806, 5804])).
% 16.62/11.10 tff(5884,assumption,(~node20(c_e_h_2, c_i, s4)), introduced(assumption)).
% 16.62/11.10 tff(5885,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s5)), introduced(assumption)).
% 16.62/11.10 tff(5886,assumption,(node21(c_e_h_2, c_i, s4, s5)), introduced(assumption)).
% 16.62/11.10 tff(5887,plain,
% 16.62/11.10 (((~![Y: $i, I0: $i, X: $i, 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) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5)))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5888,plain,
% 16.62/11.10 ((~![Y: $i, I0: $i, X: $i, 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)))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5889,plain,
% 16.62/11.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5))),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5888, 5887])).
% 16.62/11.10 tff(5890,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5889, 82, 5886, 5885, 5884])).
% 16.62/11.10 tff(5891,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,[]))).
% 16.62/11.10 tff(5892,plain,
% 16.62/11.10 (~node21(c_e_h_2, c_i, s4, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5891, 5885, 5884])).
% 16.62/11.10 tff(5893,plain,
% 16.62/11.10 (((~![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))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5894,plain,
% 16.62/11.10 ((~![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))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5895,plain,
% 16.62/11.10 ((~![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)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5894, 5893])).
% 16.62/11.10 tff(5896,plain,
% 16.62/11.10 (node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5895, 112, 1520])).
% 16.62/11.10 tff(5897,plain,
% 16.62/11.10 (node22(c_e_h_2, c_i, s4, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5896, 5892])).
% 16.62/11.10 tff(5898,plain,
% 16.62/11.10 (((~![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, 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))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5899,plain,
% 16.62/11.10 ((~![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, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5900,plain,
% 16.62/11.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5899, 5898])).
% 16.62/11.10 tff(5901,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5900, 127, 5129, 5897, 5885])).
% 16.62/11.10 tff(5902,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,[]))).
% 16.62/11.10 tff(5903,plain,
% 16.62/11.10 (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5902, 5129, 5884])).
% 16.62/11.10 tff(5904,plain,
% 16.62/11.10 (((~![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_2, c_e, 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_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5905,plain,
% 16.62/11.10 ((~![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_2, c_e, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5906,plain,
% 16.62/11.10 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5905, 5904])).
% 16.62/11.10 tff(5907,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5906, 612, 5903, 5883])).
% 16.62/11.10 tff(5908,plain,(m_and_h_gate_v_out(c_e_h_2, c_i, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | node20(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.10 tff(5909,plain,
% 16.62/11.10 ((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | node20(c_e_h_2, c_i, s4)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5908, 5127, 2593])).
% 16.62/11.10 tff(5910,plain,
% 16.62/11.10 (node20(c_e_h_2, c_i, s4)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5909, 5803])).
% 16.62/11.10 tff(5911,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)), introduced(assumption)).
% 16.62/11.10 tff(5912,assumption,(node20(c_e_h_2, c_i, s4)), introduced(assumption)).
% 16.62/11.10 tff(5913,plain,
% 16.62/11.10 (((~![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, 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))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5914,plain,
% 16.62/11.10 ((~![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, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5915,plain,
% 16.62/11.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5914, 5913])).
% 16.62/11.10 tff(5916,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5915, 283, 5912, 5911])).
% 16.62/11.10 tff(5917,plain,(m_and_h_gate_v_in1(c_e_h_2, c_i, s4) | (~node20(c_e_h_2, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.10 tff(5918,plain,
% 16.62/11.10 (m_and_h_gate_v_in1(c_e_h_2, c_i, s4)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5917, 5910])).
% 16.62/11.10 tff(5919,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_i, s4)), introduced(assumption)).
% 16.62/11.10 tff(5920,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s4)), introduced(assumption)).
% 16.62/11.10 tff(5921,plain,
% 16.62/11.10 (((~![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, 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))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5922,plain,
% 16.62/11.10 ((~![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, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5923,plain,
% 16.62/11.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5922, 5921])).
% 16.62/11.10 tff(5924,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5923, 269, 5920, 5919])).
% 16.62/11.10 tff(5925,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 16.62/11.10 tff(5926,plain,
% 16.62/11.10 (m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5925, 5918])).
% 16.62/11.10 tff(5927,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s3)), introduced(assumption)).
% 16.62/11.10 tff(5928,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s4)), introduced(assumption)).
% 16.62/11.10 tff(5929,assumption,(node15(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 16.62/11.10 tff(5930,plain,
% 16.62/11.10 (((~![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_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))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5931,plain,
% 16.62/11.10 ((~![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_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5932,plain,
% 16.62/11.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5931, 5930])).
% 16.62/11.10 tff(5933,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5932, 178, 5928, 5927, 5929])).
% 16.62/11.10 tff(5934,plain,((~node15(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_out(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.10 tff(5935,plain,
% 16.62/11.10 (~node15(c_e_h_2, c_h, s3, s4)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5934, 5928, 5927])).
% 16.62/11.10 tff(5936,assumption,(node18(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 16.62/11.10 tff(5937,plain,
% 16.62/11.10 (((~![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)))) | ((~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)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $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, 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)))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5938,plain,
% 16.62/11.10 (((~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))) <=> ((~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)))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5939,plain,
% 16.62/11.10 (((~![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_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)))) | ((~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))))),
% 16.62/11.10 inference(monotonicity,[status(thm)],[5938])).
% 16.62/11.10 tff(5940,plain,
% 16.62/11.10 (((~![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_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)))) | (~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)))),
% 16.62/11.10 inference(transitivity,[status(thm)],[5939, 5937])).
% 16.62/11.10 tff(5941,plain,
% 16.62/11.10 ((~![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_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)))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5942,plain,
% 16.62/11.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5941, 5940])).
% 16.62/11.10 tff(5943,plain,
% 16.62/11.10 ($false),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5942, 560, 5928, 5927, 5936])).
% 16.62/11.10 tff(5944,plain,((~node18(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_out(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.10 tff(5945,plain,
% 16.62/11.10 (~node18(c_e_h_2, c_h, s3, s4)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5944, 5928, 5927])).
% 16.62/11.10 tff(5946,plain,
% 16.62/11.10 (((~![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))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5947,plain,
% 16.62/11.10 ((~![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))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5948,plain,
% 16.62/11.10 ((~![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)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5947, 5946])).
% 16.62/11.10 tff(5949,plain,
% 16.62/11.10 (node19(c_e_h_2, c_h, s3, s4)),
% 16.62/11.10 inference(unit_resolution,[status(thm)],[5948, 221, 1013])).
% 16.62/11.10 tff(5950,plain,
% 16.62/11.10 (((~![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_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, 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_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5951,plain,
% 16.62/11.10 ((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))) <=> (node18(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))),
% 16.62/11.10 inference(rewrite,[status(thm)],[])).
% 16.62/11.10 tff(5952,plain,
% 16.62/11.10 (((~![Y: $i, 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)))) | (node18(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)))),
% 16.62/11.10 inference(monotonicity,[status(thm)],[5951])).
% 16.62/11.10 tff(5953,plain,
% 16.62/11.10 (((~![Y: $i, 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)))) | node18(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))),
% 16.62/11.10 inference(transitivity,[status(thm)],[5952, 5950])).
% 16.62/11.10 tff(5954,plain,
% 16.62/11.10 ((~![Y: $i, 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)))),
% 16.62/11.10 inference(quant_inst,[status(thm)],[])).
% 16.62/11.10 tff(5955,plain,
% 16.62/11.10 ((~![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_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3)),
% 16.62/11.10 inference(modus_ponens,[status(thm)],[5954, 5953])).
% 16.62/11.11 tff(5956,plain,
% 16.62/11.11 (node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5955, 542, 5949])).
% 16.62/11.11 tff(5957,plain,
% 16.62/11.11 (node17(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5956, 5945])).
% 16.62/11.11 tff(5958,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s3)), introduced(assumption)).
% 16.62/11.11 tff(5959,plain,
% 16.62/11.11 (((~![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_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)))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5960,plain,
% 16.62/11.11 ((~![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_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)))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(5961,plain,
% 16.62/11.11 ((~![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_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))),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[5960, 5959])).
% 16.62/11.11 tff(5962,plain,
% 16.62/11.11 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3))),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5961, 524, 5958])).
% 16.62/11.11 tff(5963,plain,
% 16.62/11.11 (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5962, 5957])).
% 16.62/11.11 tff(5964,plain,
% 16.62/11.11 (((~![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_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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5965,plain,
% 16.62/11.11 ((~![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_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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(5966,plain,
% 16.62/11.11 ((~![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_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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 16.62/11.11 tff(5967,plain,
% 16.62/11.11 ((~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5966, 209, 5958])).
% 16.62/11.11 tff(5968,plain,
% 16.62/11.11 (~node16(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5967, 5963])).
% 16.62/11.11 tff(5969,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s3)), introduced(assumption)).
% 16.62/11.11 tff(5970,assumption,(node14(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 16.62/11.11 tff(5971,plain,
% 16.62/11.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_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, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, 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_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4)))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5972,plain,
% 16.62/11.11 (((~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))) <=> ((~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) | (~node14(c_e_h_2, c_h, s3, s4)))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5973,plain,
% 16.62/11.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))) | ((~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) | (~node14(c_e_h_2, c_h, s3, s4))))),
% 16.62/11.11 inference(monotonicity,[status(thm)],[5972])).
% 16.62/11.11 tff(5974,plain,
% 16.62/11.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))) | (~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) | (~node14(c_e_h_2, c_h, s3, s4)))),
% 16.62/11.11 inference(transitivity,[status(thm)],[5973, 5971])).
% 16.62/11.11 tff(5975,plain,
% 16.62/11.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, 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)))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(5976,plain,
% 16.62/11.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4))),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[5975, 5974])).
% 16.62/11.11 tff(5977,plain,
% 16.62/11.11 ($false),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5976, 254, 5928, 5970, 5969])).
% 16.62/11.11 tff(5978,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.11 tff(5979,plain,
% 16.62/11.11 (~node14(c_e_h_2, c_h, s3, s4)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5978, 5963, 5928])).
% 16.62/11.11 tff(5980,plain,
% 16.62/11.11 (((~![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)))) | (node15(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))) <=> ((~![Y: $i, I0: $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, 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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5981,plain,
% 16.62/11.11 ((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))) <=> (node15(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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5982,plain,
% 16.62/11.11 (((~![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_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)))) | (node15(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)))),
% 16.62/11.11 inference(monotonicity,[status(thm)],[5981])).
% 16.62/11.11 tff(5983,plain,
% 16.62/11.11 (((~![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_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)))) | node15(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))),
% 16.62/11.11 inference(transitivity,[status(thm)],[5982, 5980])).
% 16.62/11.11 tff(5984,plain,
% 16.62/11.11 ((~![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_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)))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(5985,plain,
% 16.62/11.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_h, s3, s4) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node16(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[5984, 5983])).
% 16.62/11.11 tff(5986,plain,
% 16.62/11.11 (node15(c_e_h_2, c_h, s3, s4) | node14(c_e_h_2, c_h, s3, s4) | node16(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5985, 235, 5949])).
% 16.62/11.11 tff(5987,plain,
% 16.62/11.11 ($false),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5986, 5979, 5968, 5935])).
% 16.62/11.11 tff(5988,plain,((~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, s3) | m_c_h_element_v_out(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.11 tff(5989,plain,
% 16.62/11.11 ((~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, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5988, 5096])).
% 16.62/11.11 tff(5990,plain,
% 16.62/11.11 (m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5989, 5926])).
% 16.62/11.11 tff(5991,plain,
% 16.62/11.11 (((~![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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5992,plain,
% 16.62/11.11 ((~![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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(5993,plain,
% 16.62/11.11 ((~![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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[5992, 5991])).
% 16.62/11.11 tff(5994,plain,
% 16.62/11.11 (m_or_h_gate_v_out(c_e_h_2, c_j, s3)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5993, 195, 5990])).
% 16.62/11.11 tff(5995,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s2)), introduced(assumption)).
% 16.62/11.11 tff(5996,plain,
% 16.62/11.11 (((~![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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(5997,plain,
% 16.62/11.11 ((~![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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(5998,plain,
% 16.62/11.11 ((~![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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[5997, 5996])).
% 16.62/11.11 tff(5999,plain,
% 16.62/11.11 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[5998, 420, 132])).
% 16.62/11.11 tff(6000,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s0)), introduced(assumption)).
% 16.62/11.11 tff(6001,plain,
% 16.62/11.11 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6002,plain,
% 16.62/11.11 ($false),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6001, 165, 6000])).
% 16.62/11.11 tff(6003,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.11 tff(6004,plain,
% 16.62/11.11 (((~![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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6005,plain,
% 16.62/11.11 ((~![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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6006,plain,
% 16.62/11.11 ((~![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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6005, 6004])).
% 16.62/11.11 tff(6007,plain,
% 16.62/11.11 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6006, 3971, 6003])).
% 16.62/11.11 tff(6008,plain,
% 16.62/11.11 (((~![I0: $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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6009,plain,
% 16.62/11.11 ((~![I0: $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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6010,plain,
% 16.62/11.11 ((~![I0: $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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6009, 6008])).
% 16.62/11.11 tff(6011,plain,
% 16.62/11.11 (~node20(c_e_h_1, c_q, s0)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6010, 283, 6007])).
% 16.62/11.11 tff(6012,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s1)), introduced(assumption)).
% 16.62/11.11 tff(6013,assumption,(node22(c_e_h_1, c_q, s0, s1)), introduced(assumption)).
% 16.62/11.11 tff(6014,plain,
% 16.62/11.11 (((~![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_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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6015,plain,
% 16.62/11.11 ((~![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_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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6016,plain,
% 16.62/11.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6015, 6014])).
% 16.62/11.11 tff(6017,plain,
% 16.62/11.11 ($false),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6016, 127, 1895, 6012, 6013])).
% 16.62/11.11 tff(6018,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,[]))).
% 16.62/11.11 tff(6019,plain,
% 16.62/11.11 (~node22(c_e_h_1, c_q, s0, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6018, 6012])).
% 16.62/11.11 tff(6020,plain,
% 16.62/11.11 (((~![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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6021,plain,
% 16.62/11.11 ((~![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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6022,plain,
% 16.62/11.11 ((~![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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6021, 6020])).
% 16.62/11.11 tff(6023,plain,
% 16.62/11.11 (node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6022, 112, 102])).
% 16.62/11.11 tff(6024,plain,
% 16.62/11.11 (node21(c_e_h_1, c_q, s0, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6023, 6019])).
% 16.62/11.11 tff(6025,plain,
% 16.62/11.11 (((~![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_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)))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6026,plain,
% 16.62/11.11 ((~![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_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)))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6027,plain,
% 16.62/11.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1))),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6026, 6025])).
% 16.62/11.11 tff(6028,plain,
% 16.62/11.11 ($false),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6027, 82, 6012, 6024, 6011])).
% 16.62/11.11 tff(6029,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 16.62/11.11 tff(6030,plain,
% 16.62/11.11 (((~![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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6031,plain,
% 16.62/11.11 ((~![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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6032,plain,
% 16.62/11.11 ((~![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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6031, 6030])).
% 16.62/11.11 tff(6033,plain,
% 16.62/11.11 (node3(c_e_h_1, c_e_h_2, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6032, 1898, 376])).
% 16.62/11.11 tff(6034,plain,
% 16.62/11.11 (((~![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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6035,plain,
% 16.62/11.11 ((~![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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6036,plain,
% 16.62/11.11 ((~![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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6035, 6034])).
% 16.62/11.11 tff(6037,plain,
% 16.62/11.11 ((~m_cell_v_ack(c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6036, 393, 6033])).
% 16.62/11.11 tff(6038,plain,
% 16.62/11.11 (~m_cell_v_ack(c_e_h_2, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6037, 6029])).
% 16.62/11.11 tff(6039,plain,
% 16.62/11.11 (((~![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))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6040,plain,
% 16.62/11.11 ((~![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))),
% 16.62/11.11 inference(quant_inst,[status(thm)],[])).
% 16.62/11.11 tff(6041,plain,
% 16.62/11.11 ((~![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)),
% 16.62/11.11 inference(modus_ponens,[status(thm)],[6040, 6039])).
% 16.62/11.11 tff(6042,plain,
% 16.62/11.11 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)),
% 16.62/11.11 inference(unit_resolution,[status(thm)],[6041, 405, 6038])).
% 16.62/11.11 tff(6043,assumption,(node5(c_e_h_2, c_j, s1, s2)), introduced(assumption)).
% 16.62/11.11 tff(6044,plain,
% 16.62/11.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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, 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) | (~node5(c_e_h_2, 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_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) | (~node5(c_e_h_2, c_j, s1, s2)))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6045,plain,
% 16.62/11.11 ((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_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) | (~node5(c_e_h_2, c_j, s1, s2)))),
% 16.62/11.11 inference(rewrite,[status(thm)],[])).
% 16.62/11.11 tff(6046,plain,
% 16.62/11.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_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) | (~node5(c_e_h_2, c_j, s1, s2))))),
% 16.62/11.11 inference(monotonicity,[status(thm)],[6045])).
% 16.62/11.11 tff(6047,plain,
% 16.62/11.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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_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) | (~node5(c_e_h_2, c_j, s1, s2)))),
% 16.62/11.11 inference(transitivity,[status(thm)],[6046, 6044])).
% 16.62/11.11 tff(6048,plain,
% 16.62/11.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_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)))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6049,plain,
% 16.66/11.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2))),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6048, 6047])).
% 16.66/11.12 tff(6050,plain,
% 16.66/11.12 ($false),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6049, 473, 5995, 6043, 6042, 5999])).
% 16.66/11.12 tff(6051,plain,((~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2))), inference(lemma,lemma(discharge,[]))).
% 16.66/11.12 tff(6052,plain,
% 16.66/11.12 (~node5(c_e_h_2, c_j, s1, s2)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6051, 5995])).
% 16.66/11.12 tff(6053,plain,
% 16.66/11.12 (((~![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_j, s1, s2) | node6(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)) | node5(c_e_h_2, c_j, s1, s2) | node6(c_e_h_2, c_j, s1, s2))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6054,plain,
% 16.66/11.12 ((node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node5(c_e_h_2, c_j, s1, s2) | node6(c_e_h_2, c_j, s1, s2))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6055,plain,
% 16.66/11.12 (((~![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)) | node5(c_e_h_2, c_j, s1, s2) | node6(c_e_h_2, c_j, s1, s2)))),
% 16.66/11.12 inference(monotonicity,[status(thm)],[6054])).
% 16.66/11.12 tff(6056,plain,
% 16.66/11.12 (((~![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)) | node5(c_e_h_2, c_j, s1, s2) | node6(c_e_h_2, c_j, s1, s2))),
% 16.66/11.12 inference(transitivity,[status(thm)],[6055, 6053])).
% 16.66/11.12 tff(6057,plain,
% 16.66/11.12 ((~![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)))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6058,plain,
% 16.66/11.12 ((~![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_j, s1, s2) | node6(c_e_h_2, c_j, s1, s2)),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 16.66/11.12 tff(6059,plain,
% 16.66/11.12 (node5(c_e_h_2, c_j, s1, s2) | node6(c_e_h_2, c_j, s1, s2)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6058, 455, 348])).
% 16.66/11.12 tff(6060,plain,
% 16.66/11.12 (node6(c_e_h_2, c_j, s1, s2)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6059, 6052])).
% 16.66/11.12 tff(6061,plain,
% 16.66/11.12 (((~![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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6062,plain,
% 16.66/11.12 (((~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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6063,plain,
% 16.66/11.12 (((~![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, 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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~node6(c_e_h_2, c_j, s1, s2))))),
% 16.66/11.12 inference(monotonicity,[status(thm)],[6062])).
% 16.66/11.12 tff(6064,plain,
% 16.66/11.12 (((~![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, 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, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 16.66/11.12 inference(transitivity,[status(thm)],[6063, 6061])).
% 16.66/11.12 tff(6065,plain,
% 16.66/11.12 ((~![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, 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))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6066,plain,
% 16.66/11.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~node6(c_e_h_2, c_j, s1, s2))),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6065, 6064])).
% 16.66/11.12 tff(6067,plain,
% 16.66/11.12 ($false),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6066, 436, 5995, 1944, 6060])).
% 16.66/11.12 tff(6068,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 16.66/11.12 tff(6069,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s3)), introduced(assumption)).
% 16.66/11.12 tff(6070,assumption,(node6(c_e_h_2, c_j, s2, s3)), introduced(assumption)).
% 16.66/11.12 tff(6071,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s2)), introduced(assumption)).
% 16.66/11.12 tff(6072,plain,
% 16.66/11.12 (((~![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, s2) | (~node6(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] : ((~node6(I0, I1, X, Y)) | (~m_or_h_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, s2) | (~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6073,plain,
% 16.66/11.12 (((~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, s2) | (~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6074,plain,
% 16.66/11.12 (((~![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, 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, s2) | (~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3))))),
% 16.66/11.12 inference(monotonicity,[status(thm)],[6073])).
% 16.66/11.12 tff(6075,plain,
% 16.66/11.12 (((~![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, 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, s2) | (~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))),
% 16.66/11.12 inference(transitivity,[status(thm)],[6074, 6072])).
% 16.66/11.12 tff(6076,plain,
% 16.66/11.12 ((~![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, 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))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6077,plain,
% 16.66/11.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6076, 6075])).
% 16.66/11.12 tff(6078,plain,
% 16.66/11.12 ($false),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6077, 436, 6071, 6070, 6069])).
% 16.66/11.12 tff(6079,plain,((~node6(c_e_h_2, c_j, s2, 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))), inference(lemma,lemma(discharge,[]))).
% 16.66/11.12 tff(6080,plain,
% 16.66/11.12 ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6079, 6068])).
% 16.66/11.12 tff(6081,plain,
% 16.66/11.12 (~node6(c_e_h_2, c_j, s2, s3)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6080, 5994])).
% 16.66/11.12 tff(6082,plain,
% 16.66/11.12 (((~![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_2, c_j, s2, s3) | node6(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)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6083,plain,
% 16.66/11.12 ((node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6084,plain,
% 16.66/11.12 (((~![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)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3)))),
% 16.66/11.12 inference(monotonicity,[status(thm)],[6083])).
% 16.66/11.12 tff(6085,plain,
% 16.66/11.12 (((~![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)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3))),
% 16.66/11.12 inference(transitivity,[status(thm)],[6084, 6082])).
% 16.66/11.12 tff(6086,plain,
% 16.66/11.12 ((~![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)))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6087,plain,
% 16.66/11.12 ((~![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_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3)),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6086, 6085])).
% 16.66/11.12 tff(6088,plain,
% 16.66/11.12 (node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6087, 455, 591])).
% 16.66/11.12 tff(6089,plain,
% 16.66/11.12 (node5(c_e_h_2, c_j, s2, s3)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6088, 6081])).
% 16.66/11.12 tff(6090,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)), introduced(assumption)).
% 16.66/11.12 tff(6091,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s2)), introduced(assumption)).
% 16.66/11.12 tff(6092,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s1)), introduced(assumption)).
% 16.66/11.12 tff(6093,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s0)), introduced(assumption)).
% 16.66/11.12 tff(6094,plain,
% 16.66/11.12 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6095,plain,
% 16.66/11.12 ($false),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6094, 9, 6093])).
% 16.66/11.12 tff(6096,plain,(~m_and_h_gate_v_out(c_e_h_1, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 16.66/11.12 tff(6097,plain,
% 16.66/11.12 (((~![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))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6098,plain,
% 16.66/11.12 ((~![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))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6099,plain,
% 16.66/11.12 ((~![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)),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6098, 6097])).
% 16.66/11.12 tff(6100,plain,
% 16.66/11.12 (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6099, 4285, 6096])).
% 16.66/11.12 tff(6101,assumption,(node14(c_e_h_1, c_f, s0, s1)), introduced(assumption)).
% 16.66/11.12 tff(6102,plain,
% 16.66/11.12 (((~![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_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, 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_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6103,plain,
% 16.66/11.12 (((~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)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6104,plain,
% 16.66/11.12 (((~![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_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)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1))))),
% 16.66/11.12 inference(monotonicity,[status(thm)],[6103])).
% 16.66/11.12 tff(6105,plain,
% 16.66/11.12 (((~![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_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)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)))),
% 16.66/11.12 inference(transitivity,[status(thm)],[6104, 6102])).
% 16.66/11.12 tff(6106,plain,
% 16.66/11.12 ((~![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_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)))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6107,plain,
% 16.66/11.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1))),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6106, 6105])).
% 16.66/11.12 tff(6108,plain,
% 16.66/11.12 ($false),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6107, 254, 6092, 6101, 6100])).
% 16.66/11.12 tff(6109,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,[]))).
% 16.66/11.12 tff(6110,plain,
% 16.66/11.12 (~node14(c_e_h_1, c_f, s0, s1)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6109, 6092])).
% 16.66/11.12 tff(6111,plain,
% 16.66/11.12 (^[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)))),
% 16.66/11.12 inference(bind,[status(th)],[])).
% 16.66/11.12 tff(6112,plain,
% 16.66/11.12 (![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))),
% 16.66/11.12 inference(quant_intro,[status(thm)],[6111])).
% 16.66/11.12 tff(6113,plain,
% 16.66/11.12 (![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))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6114,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')).
% 16.66/11.12 tff(6115,plain,
% 16.66/11.12 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 16.66/11.12 tff(6116,plain,(
% 16.66/11.12 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 16.66/11.12 inference(skolemize,[status(sab)],[6115])).
% 16.66/11.12 tff(6117,plain,
% 16.66/11.12 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6116, 6112])).
% 16.66/11.12 tff(6118,plain,
% 16.66/11.12 (((~![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))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6119,plain,
% 16.66/11.12 ((~![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))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6120,plain,
% 16.66/11.12 ((~![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)),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6119, 6118])).
% 16.66/11.12 tff(6121,plain,
% 16.66/11.12 (~m_c_h_element_v_in2(c_e_h_1, c_f, s0)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6120, 6117, 305])).
% 16.66/11.12 tff(6122,plain,
% 16.66/11.12 (((~![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_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))),
% 16.66/11.12 inference(rewrite,[status(thm)],[])).
% 16.66/11.12 tff(6123,plain,
% 16.66/11.12 ((~![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_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))),
% 16.66/11.12 inference(quant_inst,[status(thm)],[])).
% 16.66/11.12 tff(6124,plain,
% 16.66/11.12 ((~![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_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)),
% 16.66/11.12 inference(modus_ponens,[status(thm)],[6123, 6122])).
% 16.66/11.12 tff(6125,plain,
% 16.66/11.12 ((~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 16.66/11.12 inference(unit_resolution,[status(thm)],[6124, 209, 6121])).
% 16.66/11.13 tff(6126,plain,
% 16.66/11.13 (~node16(c_e_h_1, c_f, s0)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6125, 6100])).
% 16.66/11.13 tff(6127,plain,
% 16.66/11.13 (((~![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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6128,plain,
% 16.66/11.13 ((~![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))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6129,plain,
% 16.66/11.13 ((~![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)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6128, 6127])).
% 16.66/11.13 tff(6130,plain,
% 16.66/11.13 (node19(c_e_h_1, c_f, s0, s1)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6129, 221, 102])).
% 16.66/11.13 tff(6131,plain,
% 16.66/11.13 (((~![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_f, s0) | node14(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))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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) | (~node19(c_e_h_1, c_f, s0, s1)) | node15(c_e_h_1, c_f, s0, s1))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6132,plain,
% 16.66/11.13 ((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))) <=> (node16(c_e_h_1, c_f, s0) | node14(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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6133,plain,
% 16.66/11.13 (((~![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_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)))) | (node16(c_e_h_1, c_f, s0) | node14(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)))),
% 16.66/11.13 inference(monotonicity,[status(thm)],[6132])).
% 16.66/11.13 tff(6134,plain,
% 16.66/11.13 (((~![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_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)))) | node16(c_e_h_1, c_f, s0) | node14(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))),
% 16.66/11.13 inference(transitivity,[status(thm)],[6133, 6131])).
% 16.66/11.13 tff(6135,plain,
% 16.66/11.13 ((~![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_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)))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6136,plain,
% 16.66/11.13 ((~![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_f, s0) | node14(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)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6135, 6134])).
% 16.66/11.13 tff(6137,plain,
% 16.66/11.13 (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)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6136, 235, 6130])).
% 16.66/11.13 tff(6138,plain,
% 16.66/11.13 (node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6137, 6126])).
% 16.66/11.13 tff(6139,plain,
% 16.66/11.13 (node15(c_e_h_1, c_f, s0, s1)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6138, 6110])).
% 16.66/11.13 tff(6140,plain,
% 16.66/11.13 (((~![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_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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6141,plain,
% 16.66/11.13 ((~![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_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6142,plain,
% 16.66/11.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6141, 6140])).
% 16.66/11.13 tff(6143,plain,
% 16.66/11.13 ($false),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6142, 178, 6092, 6003, 6139])).
% 16.66/11.13 tff(6144,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 16.66/11.13 tff(6145,plain,
% 16.66/11.13 (((~![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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6146,plain,
% 16.66/11.13 ((~![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))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6147,plain,
% 16.66/11.13 ((~![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)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6146, 6145])).
% 16.66/11.13 tff(6148,plain,
% 16.66/11.13 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6147, 3971, 6144])).
% 16.66/11.13 tff(6149,plain,
% 16.66/11.13 (((~![I0: $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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6150,plain,
% 16.66/11.13 ((~![I0: $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))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6151,plain,
% 16.66/11.13 ((~![I0: $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)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6150, 6149])).
% 16.66/11.13 tff(6152,plain,
% 16.66/11.13 (~node20(c_e_h_1, c_q, s1)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6151, 283, 6148])).
% 16.66/11.13 tff(6153,assumption,(node21(c_e_h_1, c_q, s1, s2)), introduced(assumption)).
% 16.66/11.13 tff(6154,plain,
% 16.66/11.13 (((~![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)))) | ((~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)))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6155,plain,
% 16.66/11.13 ((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)))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6156,plain,
% 16.66/11.13 (((~![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_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))))),
% 16.66/11.13 inference(monotonicity,[status(thm)],[6155])).
% 16.66/11.13 tff(6157,plain,
% 16.66/11.13 (((~![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_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)))),
% 16.66/11.13 inference(transitivity,[status(thm)],[6156, 6154])).
% 16.66/11.13 tff(6158,plain,
% 16.66/11.13 ((~![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_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6159,plain,
% 16.66/11.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2))),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6158, 6157])).
% 16.66/11.13 tff(6160,plain,
% 16.66/11.13 ($false),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6159, 82, 6091, 6153, 6152])).
% 16.66/11.13 tff(6161,plain,((~node21(c_e_h_1, c_q, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 16.66/11.13 tff(6162,plain,
% 16.66/11.13 (~node21(c_e_h_1, c_q, s1, s2)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6161, 6091])).
% 16.66/11.13 tff(6163,plain,
% 16.66/11.13 (((~![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_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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6164,plain,
% 16.66/11.13 ((~![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_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6165,plain,
% 16.66/11.13 ((~![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_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6164, 6163])).
% 16.66/11.13 tff(6166,plain,
% 16.66/11.13 (node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6165, 112, 348])).
% 16.66/11.13 tff(6167,plain,
% 16.66/11.13 (node22(c_e_h_1, c_q, s1, s2)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6166, 6162])).
% 16.66/11.13 tff(6168,plain,
% 16.66/11.13 (((~![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_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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6169,plain,
% 16.66/11.13 ((~![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_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6170,plain,
% 16.66/11.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6169, 6168])).
% 16.66/11.13 tff(6171,plain,
% 16.66/11.13 ($false),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6170, 127, 6091, 6029, 6167])).
% 16.66/11.13 tff(6172,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 16.66/11.13 tff(6173,plain,
% 16.66/11.13 (((~![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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6174,plain,
% 16.66/11.13 ((~![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))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6175,plain,
% 16.66/11.13 ((~![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)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6174, 6173])).
% 16.66/11.13 tff(6176,plain,
% 16.66/11.13 (node3(c_e_h_1, c_e_h_2, s2)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6175, 1898, 376])).
% 16.66/11.13 tff(6177,plain,
% 16.66/11.13 (((~![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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6178,plain,
% 16.66/11.13 ((~![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))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6179,plain,
% 16.66/11.13 ((~![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)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6178, 6177])).
% 16.66/11.13 tff(6180,plain,
% 16.66/11.13 ((~m_cell_v_ack(c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6179, 393, 6176])).
% 16.66/11.13 tff(6181,plain,
% 16.66/11.13 (~m_cell_v_ack(c_e_h_2, s2)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6180, 6172])).
% 16.66/11.13 tff(6182,plain,
% 16.66/11.13 (((~![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_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))),
% 16.66/11.13 inference(rewrite,[status(thm)],[])).
% 16.66/11.13 tff(6183,plain,
% 16.66/11.13 ((~![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_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2))),
% 16.66/11.13 inference(quant_inst,[status(thm)],[])).
% 16.66/11.13 tff(6184,plain,
% 16.66/11.13 ((~![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_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2)),
% 16.66/11.13 inference(modus_ponens,[status(thm)],[6183, 6182])).
% 16.66/11.13 tff(6185,plain,
% 16.66/11.13 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)),
% 16.66/11.13 inference(unit_resolution,[status(thm)],[6184, 405, 6181])).
% 16.66/11.13 tff(6186,assumption,(node5(c_e_h_2, c_j, s2, s3)), introduced(assumption)).
% 16.66/11.13 tff(6187,plain,
% 16.66/11.13 (((~![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, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, 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_in2(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_in1(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)))),
% 16.67/11.13 inference(rewrite,[status(thm)],[])).
% 16.67/11.13 tff(6188,plain,
% 16.67/11.13 ((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_in2(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_in1(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)))),
% 16.67/11.13 inference(rewrite,[status(thm)],[])).
% 16.67/11.13 tff(6189,plain,
% 16.67/11.13 (((~![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, 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_in2(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_in1(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3))))),
% 16.67/11.13 inference(monotonicity,[status(thm)],[6188])).
% 16.67/11.13 tff(6190,plain,
% 16.67/11.13 (((~![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, 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_in2(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_in1(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)))),
% 16.67/11.13 inference(transitivity,[status(thm)],[6189, 6187])).
% 16.67/11.13 tff(6191,plain,
% 16.67/11.13 ((~![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, 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)))),
% 16.67/11.13 inference(quant_inst,[status(thm)],[])).
% 16.67/11.13 tff(6192,plain,
% 16.67/11.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3))),
% 16.67/11.13 inference(modus_ponens,[status(thm)],[6191, 6190])).
% 16.67/11.13 tff(6193,plain,
% 16.67/11.13 ($false),
% 16.67/11.13 inference(unit_resolution,[status(thm)],[6192, 473, 6186, 6069, 6185, 6090])).
% 16.67/11.13 tff(6194,plain,((~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_in1(c_e_h_2, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 16.67/11.13 tff(6195,plain,
% 16.67/11.13 (m_or_h_gate_v_in1(c_e_h_2, c_j, s2)),
% 16.67/11.13 inference(unit_resolution,[status(thm)],[6194, 6089, 5994])).
% 16.67/11.13 tff(6196,plain,
% 16.67/11.13 (((~![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, 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))),
% 16.67/11.13 inference(rewrite,[status(thm)],[])).
% 16.67/11.13 tff(6197,plain,
% 16.67/11.13 ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 16.67/11.13 inference(quant_inst,[status(thm)],[])).
% 16.67/11.13 tff(6198,plain,
% 16.67/11.13 ((~![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, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2)),
% 16.67/11.13 inference(modus_ponens,[status(thm)],[6197, 6196])).
% 16.67/11.13 tff(6199,plain,
% 16.67/11.13 (m_and_h_gate_v_out(c_e_h_2, c_l, s2)),
% 16.67/11.13 inference(unit_resolution,[status(thm)],[6198, 420, 6195])).
% 16.67/11.13 tff(6200,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s2)), introduced(assumption)).
% 16.67/11.13 tff(6201,assumption,(node21(c_e_h_2, c_l, s1, s2)), introduced(assumption)).
% 16.67/11.13 tff(6202,plain,
% 16.67/11.13 (((~![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))),
% 16.67/11.13 inference(rewrite,[status(thm)],[])).
% 16.67/11.13 tff(6203,plain,
% 16.67/11.13 ((~![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))),
% 16.67/11.13 inference(quant_inst,[status(thm)],[])).
% 16.67/11.13 tff(6204,plain,
% 16.67/11.13 ((~![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)),
% 16.67/11.13 inference(modus_ponens,[status(thm)],[6203, 6202])).
% 16.67/11.13 tff(6205,plain,
% 16.67/11.13 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)),
% 16.67/11.13 inference(unit_resolution,[status(thm)],[6204, 53, 2695])).
% 16.67/11.13 tff(6206,plain,
% 16.67/11.13 (((~![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))),
% 16.67/11.13 inference(rewrite,[status(thm)],[])).
% 16.67/11.13 tff(6207,plain,
% 16.67/11.13 ((~![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))),
% 16.67/11.13 inference(quant_inst,[status(thm)],[])).
% 16.67/11.13 tff(6208,plain,
% 16.67/11.13 ((~![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)),
% 16.67/11.13 inference(modus_ponens,[status(thm)],[6207, 6206])).
% 16.67/11.13 tff(6209,plain,
% 16.67/11.13 (~node20(c_e_h_2, c_l, s1)),
% 16.67/11.13 inference(unit_resolution,[status(thm)],[6208, 68, 6205])).
% 16.67/11.13 tff(6210,plain,
% 16.67/11.13 (((~![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_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)))),
% 16.67/11.13 inference(rewrite,[status(thm)],[])).
% 16.67/11.13 tff(6211,plain,
% 16.67/11.13 ((~![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_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2)))),
% 16.67/11.13 inference(quant_inst,[status(thm)],[])).
% 16.67/11.13 tff(6212,plain,
% 16.67/11.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2))),
% 16.67/11.13 inference(modus_ponens,[status(thm)],[6211, 6210])).
% 16.67/11.13 tff(6213,plain,
% 16.67/11.13 ($false),
% 16.67/11.13 inference(unit_resolution,[status(thm)],[6212, 82, 6209, 6201, 6200])).
% 16.67/11.13 tff(6214,plain,((~node21(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,[]))).
% 16.67/11.13 tff(6215,plain,
% 16.67/11.13 (~node21(c_e_h_2, c_l, s1, s2)),
% 16.67/11.15 inference(unit_resolution,[status(thm)],[6214, 6199])).
% 16.67/11.15 tff(6216,plain,
% 16.67/11.15 (((~![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))),
% 16.67/11.15 inference(rewrite,[status(thm)],[])).
% 16.67/11.15 tff(6217,plain,
% 16.67/11.15 ((~![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))),
% 16.67/11.15 inference(quant_inst,[status(thm)],[])).
% 16.67/11.15 tff(6218,plain,
% 16.67/11.15 ((~![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)),
% 16.67/11.15 inference(modus_ponens,[status(thm)],[6217, 6216])).
% 16.67/11.15 tff(6219,plain,
% 16.67/11.15 (node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2)),
% 16.67/11.15 inference(unit_resolution,[status(thm)],[6218, 112, 348])).
% 16.67/11.15 tff(6220,plain,
% 16.67/11.15 (node22(c_e_h_2, c_l, s1, s2)),
% 16.67/11.15 inference(unit_resolution,[status(thm)],[6219, 6215])).
% 16.67/11.15 tff(6221,plain,
% 16.67/11.15 (((~![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_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))),
% 16.67/11.15 inference(rewrite,[status(thm)],[])).
% 16.67/11.15 tff(6222,plain,
% 16.67/11.15 ((~![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_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 16.67/11.15 inference(quant_inst,[status(thm)],[])).
% 16.67/11.15 tff(6223,plain,
% 16.67/11.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1)),
% 16.67/11.15 inference(modus_ponens,[status(thm)],[6222, 6221])).
% 16.67/11.15 tff(6224,plain,
% 16.67/11.15 ($false),
% 16.67/11.15 inference(unit_resolution,[status(thm)],[6223, 127, 6220, 6199, 132])).
% 16.67/11.15 % SZS output end Proof
%------------------------------------------------------------------------------