TSTP Solution File: SWV419-1.005 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV419-1.005 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 15:11:45 EDT 2022
% Result : Unsatisfiable 3.12s 2.24s
% Output : Proof 3.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV419-1.005 : TPTP v8.1.0. Released v3.5.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.35 % Computer : n001.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun Sep 4 03:21:27 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 3.12/2.24 % SZS status Unsatisfiable
% 3.12/2.24 % SZS output start Proof
% 3.12/2.24 tff(m_and_h_gate_v_in1_type, type, (
% 3.12/2.24 m_and_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(s2_type, type, (
% 3.12/2.24 s2: $i)).
% 3.12/2.24 tff(c_r_type, type, (
% 3.12/2.24 c_r: $i)).
% 3.12/2.24 tff(c_e_h_3_type, type, (
% 3.12/2.24 c_e_h_3: $i)).
% 3.12/2.24 tff(m_c_h_element_v_out_type, type, (
% 3.12/2.24 m_c_h_element_v_out: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(c_e_type, type, (
% 3.12/2.24 c_e: $i)).
% 3.12/2.24 tff(node17_type, type, (
% 3.12/2.24 node17: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(s1_type, type, (
% 3.12/2.24 s1: $i)).
% 3.12/2.24 tff(node18_type, type, (
% 3.12/2.24 node18: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node16_type, type, (
% 3.12/2.24 node16: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(s0_type, type, (
% 3.12/2.24 s0: $i)).
% 3.12/2.24 tff(m_c_h_element_v_in2_type, type, (
% 3.12/2.24 m_c_h_element_v_in2: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(m_and_h_gate_v_out_type, type, (
% 3.12/2.24 m_and_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(c_i_type, type, (
% 3.12/2.24 c_i: $i)).
% 3.12/2.24 tff(m_c_h_element_v_in1_type, type, (
% 3.12/2.24 m_c_h_element_v_in1: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(c_c_type, type, (
% 3.12/2.24 c_c: $i)).
% 3.12/2.24 tff(node15_type, type, (
% 3.12/2.24 node15: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node14_type, type, (
% 3.12/2.24 node14: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node19_type, type, (
% 3.12/2.24 node19: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(trans_type, type, (
% 3.12/2.24 trans: ( $i * $i ) > $o)).
% 3.12/2.24 tff(succ_type, type, (
% 3.12/2.24 succ: ( $i * $i ) > $o)).
% 3.12/2.24 tff(node22_type, type, (
% 3.12/2.24 node22: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node21_type, type, (
% 3.12/2.24 node21: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node20_type, type, (
% 3.12/2.24 node20: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(m_mutex_h_half_v_out_type, type, (
% 3.12/2.24 m_mutex_h_half_v_out: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(c_a_type, type, (
% 3.12/2.24 c_a: $i)).
% 3.12/2.24 tff(s3_type, type, (
% 3.12/2.24 s3: $i)).
% 3.12/2.24 tff(m_mutex_h_half_v_inp_type, type, (
% 3.12/2.24 m_mutex_h_half_v_inp: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(m_user_v_req_type, type, (
% 3.12/2.24 m_user_v_req: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(c_u_type, type, (
% 3.12/2.24 c_u: $i)).
% 3.12/2.24 tff(node12_type, type, (
% 3.12/2.24 node12: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node13_type, type, (
% 3.12/2.24 node13: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(s4_type, type, (
% 3.12/2.24 s4: $i)).
% 3.12/2.24 tff(m_user_v_ack_type, type, (
% 3.12/2.24 m_user_v_ack: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node25_type, type, (
% 3.12/2.24 node25: $i > $o)).
% 3.12/2.24 tff(node26_type, type, (
% 3.12/2.24 node26: $i > $o)).
% 3.12/2.24 tff(node23_type, type, (
% 3.12/2.24 node23: $i > $o)).
% 3.12/2.24 tff(c_e_h_1_type, type, (
% 3.12/2.24 c_e_h_1: $i)).
% 3.12/2.24 tff(m_and_h_gate_v_in2_type, type, (
% 3.12/2.24 m_and_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(m_and_h_gate_h_init_v_out_type, type, (
% 3.12/2.24 m_and_h_gate_h_init_v_out: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(c_m_type, type, (
% 3.12/2.24 c_m: $i)).
% 3.12/2.24 tff(m_and_h_gate_h_init_v_in2_type, type, (
% 3.12/2.24 m_and_h_gate_h_init_v_in2: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(c_n_type, type, (
% 3.12/2.24 c_n: $i)).
% 3.12/2.24 tff(m_and_h_gate_h_init_v_init_h_out_type, type, (
% 3.12/2.24 m_and_h_gate_h_init_v_init_h_out: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(m_cell_v_token_type, type, (
% 3.12/2.24 m_cell_v_token: ( $i * $i ) > $o)).
% 3.12/2.24 tff(node11_type, type, (
% 3.12/2.24 node11: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node10_type, type, (
% 3.12/2.24 node10: ( $i * $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node9_type, type, (
% 3.12/2.24 node9: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(m_and_h_gate_h_init_v_in1_type, type, (
% 3.12/2.24 m_and_h_gate_h_init_v_in1: ( $i * $i * $i ) > $o)).
% 3.12/2.24 tff(node24_type, type, (
% 3.12/2.24 node24: $i > $o)).
% 3.12/2.24 tff(xuntil28_type, type, (
% 3.12/2.24 xuntil28: $i > $o)).
% 3.12/2.24 tff(until27_type, type, (
% 3.12/2.24 until27: $i > $o)).
% 3.12/2.24 tff(c_e_h_2_type, type, (
% 3.12/2.24 c_e_h_2: $i)).
% 3.12/2.24 tff(until2p29_type, type, (
% 3.12/2.24 until2p29: $i > $o)).
% 3.12/2.24 tff(xuntil2p30_type, type, (
% 3.12/2.24 xuntil2p30: $i > $o)).
% 3.12/2.24 tff(last_type, type, (
% 3.12/2.24 last: $i > $o)).
% 3.12/2.24 tff(loop_type, type, (
% 3.12/2.24 loop: $o)).
% 3.12/2.24 tff(1,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 3.12/2.24 tff(2,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 3.12/2.24 tff(3,plain,
% 3.12/2.24 (^[I0: $i, I1: $i] : refl((~m_and_h_gate_v_out(I0, I1, s0)) <=> (~m_and_h_gate_v_out(I0, I1, s0)))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(4,plain,
% 3.12/2.24 (![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))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[3])).
% 3.12/2.24 tff(5,plain,
% 3.12/2.24 (![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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 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')).
% 3.12/2.24 tff(7,plain,
% 3.12/2.24 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[6, 5])).
% 3.12/2.24 tff(8,plain,(
% 3.12/2.24 ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 3.12/2.24 inference(skolemize,[status(sab)],[7])).
% 3.12/2.24 tff(9,plain,
% 3.12/2.24 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[8, 4])).
% 3.12/2.24 tff(10,plain,
% 3.12/2.24 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(11,plain,
% 3.12/2.24 ($false),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 3.12/2.24 tff(12,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.24 tff(13,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 3.12/2.24 tff(14,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s0)), introduced(assumption)).
% 3.12/2.24 tff(15,plain,
% 3.12/2.24 (^[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)))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(16,plain,
% 3.12/2.24 (![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))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[15])).
% 3.12/2.24 tff(17,plain,
% 3.12/2.24 (![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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(18,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')).
% 3.12/2.24 tff(19,plain,
% 3.12/2.24 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[18, 17])).
% 3.12/2.24 tff(20,plain,(
% 3.12/2.24 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 3.12/2.24 inference(skolemize,[status(sab)],[19])).
% 3.12/2.24 tff(21,plain,
% 3.12/2.24 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[20, 16])).
% 3.12/2.24 tff(22,plain,
% 3.12/2.24 (((~![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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(23,plain,
% 3.12/2.24 ((~![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))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(24,plain,
% 3.12/2.24 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[23, 22])).
% 3.12/2.24 tff(25,plain,
% 3.12/2.24 ($false),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[24, 21, 14, 13])).
% 3.12/2.24 tff(26,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.24 tff(27,plain,
% 3.12/2.24 (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[26, 12])).
% 3.12/2.24 tff(28,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s0)), introduced(assumption)).
% 3.12/2.24 tff(29,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s0)), introduced(assumption)).
% 3.12/2.24 tff(30,plain,
% 3.12/2.24 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(31,plain,
% 3.12/2.24 ($false),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[30, 9, 29])).
% 3.12/2.24 tff(32,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.24 tff(33,plain,
% 3.12/2.24 (^[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)))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(34,plain,
% 3.12/2.24 (![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))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[33])).
% 3.12/2.24 tff(35,plain,
% 3.12/2.24 (![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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(36,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')).
% 3.12/2.24 tff(37,plain,
% 3.12/2.24 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[36, 35])).
% 3.12/2.24 tff(38,plain,(
% 3.12/2.24 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 3.12/2.24 inference(skolemize,[status(sab)],[37])).
% 3.12/2.24 tff(39,plain,
% 3.12/2.24 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[38, 34])).
% 3.12/2.24 tff(40,plain,
% 3.12/2.24 (((~![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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(41,plain,
% 3.12/2.24 ((~![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))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(42,plain,
% 3.12/2.24 ((~![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)),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[41, 40])).
% 3.12/2.24 tff(43,plain,
% 3.12/2.24 (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[42, 39, 32])).
% 3.12/2.24 tff(44,assumption,(node16(c_e_h_3, c_e, s0)), introduced(assumption)).
% 3.12/2.24 tff(45,plain,
% 3.12/2.24 (^[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)))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(46,plain,
% 3.12/2.24 (![I0: $i, X: $i, 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))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[45])).
% 3.12/2.24 tff(47,plain,
% 3.12/2.24 (![I0: $i, X: $i, 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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(48,plain,
% 3.12/2.24 (^[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)))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(49,plain,
% 3.12/2.24 (![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~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))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[48])).
% 3.12/2.24 tff(50,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')).
% 3.12/2.24 tff(51,plain,
% 3.12/2.24 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[50, 49])).
% 3.12/2.24 tff(52,plain,
% 3.12/2.24 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[51, 47])).
% 3.12/2.24 tff(53,plain,(
% 3.12/2.24 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 3.12/2.24 inference(skolemize,[status(sab)],[52])).
% 3.12/2.24 tff(54,plain,
% 3.12/2.24 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[53, 46])).
% 3.12/2.24 tff(55,plain,
% 3.12/2.24 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(56,plain,
% 3.12/2.24 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, 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))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(57,plain,
% 3.12/2.24 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.12/2.24 tff(58,plain,
% 3.12/2.24 ($false),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[57, 54, 44, 43, 28])).
% 3.12/2.24 tff(59,plain,((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.24 tff(60,plain,
% 3.12/2.24 (~node16(c_e_h_3, c_e, s0)),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[59, 27])).
% 3.12/2.24 tff(61,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 3.12/2.24 tff(62,assumption,(~node16(c_e_h_3, c_e, s0)), introduced(assumption)).
% 3.12/2.24 tff(63,assumption,(node14(c_e_h_3, c_e, s0, s1)), introduced(assumption)).
% 3.12/2.24 tff(64,plain,
% 3.12/2.24 (^[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))))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(65,plain,
% 3.12/2.24 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[64])).
% 3.12/2.24 tff(66,plain,
% 3.12/2.24 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(67,plain,
% 3.12/2.24 (^[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))))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(68,plain,
% 3.12/2.24 (![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)))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[67])).
% 3.12/2.24 tff(69,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')).
% 3.12/2.24 tff(70,plain,
% 3.12/2.24 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[69, 68])).
% 3.12/2.24 tff(71,plain,
% 3.12/2.24 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[70, 66])).
% 3.12/2.24 tff(72,plain,(
% 3.12/2.24 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 3.12/2.24 inference(skolemize,[status(sab)],[71])).
% 3.12/2.24 tff(73,plain,
% 3.12/2.24 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[72, 65])).
% 3.12/2.24 tff(74,plain,
% 3.12/2.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(75,plain,
% 3.12/2.24 (((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(76,plain,
% 3.12/2.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1))))),
% 3.12/2.24 inference(monotonicity,[status(thm)],[75])).
% 3.12/2.24 tff(77,plain,
% 3.12/2.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 3.12/2.24 inference(transitivity,[status(thm)],[76, 74])).
% 3.12/2.24 tff(78,plain,
% 3.12/2.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_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)))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(79,plain,
% 3.12/2.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[78, 77])).
% 3.12/2.24 tff(80,plain,
% 3.12/2.24 ($false),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[79, 73, 63, 43, 61])).
% 3.12/2.24 tff(81,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,[]))).
% 3.12/2.24 tff(82,plain,
% 3.12/2.24 (~node14(c_e_h_3, c_e, s0, s1)),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[81, 61])).
% 3.12/2.24 tff(83,plain,
% 3.12/2.24 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 3.12/2.24 inference(bind,[status(th)],[])).
% 3.12/2.24 tff(84,plain,
% 3.12/2.24 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 3.12/2.24 inference(quant_intro,[status(thm)],[83])).
% 3.12/2.24 tff(85,plain,
% 3.12/2.24 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(86,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 3.12/2.24 tff(87,plain,
% 3.12/2.24 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[86, 85])).
% 3.12/2.24 tff(88,plain,(
% 3.12/2.24 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 3.12/2.24 inference(skolemize,[status(sab)],[87])).
% 3.12/2.24 tff(89,plain,
% 3.12/2.24 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[88, 84])).
% 3.12/2.24 tff(90,plain,
% 3.12/2.24 (succ(s0, s1) <=> succ(s0, s1)),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(91,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 3.12/2.24 tff(92,plain,
% 3.12/2.24 (succ(s0, s1)),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[91, 90])).
% 3.12/2.24 tff(93,plain,
% 3.12/2.24 (((~![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))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(94,plain,
% 3.12/2.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(95,plain,
% 3.12/2.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[94, 93])).
% 3.12/2.24 tff(96,plain,
% 3.12/2.24 (trans(s0, s1)),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[95, 92, 89])).
% 3.12/2.24 tff(97,plain,
% 3.12/2.24 (^[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)))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(98,plain,
% 3.12/2.25 (![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))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[97])).
% 3.12/2.25 tff(99,plain,
% 3.12/2.25 (![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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(100,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')).
% 3.12/2.25 tff(101,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[100, 99])).
% 3.12/2.25 tff(102,plain,(
% 3.12/2.25 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 3.12/2.25 inference(skolemize,[status(sab)],[101])).
% 3.12/2.25 tff(103,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[102, 98])).
% 3.12/2.25 tff(104,plain,
% 3.12/2.25 (((~![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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(105,plain,
% 3.12/2.25 ((~![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))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(106,plain,
% 3.12/2.25 ((~![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)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[105, 104])).
% 3.12/2.25 tff(107,plain,
% 3.12/2.25 (node19(c_e_h_3, c_e, s0, s1)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[106, 103, 96])).
% 3.12/2.25 tff(108,plain,
% 3.12/2.25 (^[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))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(109,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[108])).
% 3.12/2.25 tff(110,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(111,plain,
% 3.12/2.25 (^[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)))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(112,plain,
% 3.12/2.25 (![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)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[111])).
% 3.12/2.25 tff(113,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')).
% 3.12/2.25 tff(114,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[113, 112])).
% 3.12/2.25 tff(115,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[114, 110])).
% 3.12/2.25 tff(116,plain,(
% 3.12/2.25 ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(skolemize,[status(sab)],[115])).
% 3.12/2.25 tff(117,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[116, 109])).
% 3.12/2.25 tff(118,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s0, s1) | node14(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node16(c_e_h_3, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s0, s1) | node14(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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(119,plain,
% 3.12/2.25 ((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))) <=> (node15(c_e_h_3, c_e, s0, s1) | node14(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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(120,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))) | (node15(c_e_h_3, c_e, s0, s1) | node14(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)))),
% 3.12/2.25 inference(monotonicity,[status(thm)],[119])).
% 3.12/2.25 tff(121,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))) | node15(c_e_h_3, c_e, s0, s1) | node14(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))),
% 3.12/2.25 inference(transitivity,[status(thm)],[120, 118])).
% 3.12/2.25 tff(122,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(123,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s0, s1) | node14(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)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[122, 121])).
% 3.12/2.25 tff(124,plain,
% 3.12/2.25 (node15(c_e_h_3, c_e, s0, s1) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[123, 117, 107])).
% 3.12/2.25 tff(125,plain,
% 3.12/2.25 (node15(c_e_h_3, c_e, s0, s1)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[124, 82, 62])).
% 3.12/2.25 tff(126,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s0)), introduced(assumption)).
% 3.12/2.25 tff(127,plain,
% 3.12/2.25 (^[I0: $i, I1: $i] : refl((~m_c_h_element_v_out(I0, I1, s0)) <=> (~m_c_h_element_v_out(I0, I1, s0)))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(128,plain,
% 3.12/2.25 (![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))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[127])).
% 3.12/2.25 tff(129,plain,
% 3.12/2.25 (![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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(130,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')).
% 3.12/2.25 tff(131,plain,
% 3.12/2.25 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[130, 129])).
% 3.12/2.25 tff(132,plain,(
% 3.12/2.25 ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 3.12/2.25 inference(skolemize,[status(sab)],[131])).
% 3.12/2.25 tff(133,plain,
% 3.12/2.25 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[132, 128])).
% 3.12/2.25 tff(134,plain,
% 3.12/2.25 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(135,plain,
% 3.12/2.25 ($false),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[134, 133, 126])).
% 3.12/2.25 tff(136,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.25 tff(137,plain,
% 3.12/2.25 (^[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)))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(138,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[137])).
% 3.12/2.25 tff(139,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(140,plain,
% 3.12/2.25 (^[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)))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(141,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~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))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[140])).
% 3.12/2.25 tff(142,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')).
% 3.12/2.25 tff(143,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[142, 141])).
% 3.12/2.25 tff(144,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[143, 139])).
% 3.12/2.25 tff(145,plain,(
% 3.12/2.25 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 3.12/2.25 inference(skolemize,[status(sab)],[144])).
% 3.12/2.25 tff(146,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[145, 138])).
% 3.12/2.25 tff(147,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(148,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_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))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(149,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[148, 147])).
% 3.12/2.25 tff(150,plain,
% 3.12/2.25 ($false),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[149, 146, 136, 125, 61])).
% 3.12/2.25 tff(151,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | node16(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.25 tff(152,plain,
% 3.12/2.25 (~m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[151, 60])).
% 3.12/2.25 tff(153,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 3.12/2.25 tff(154,assumption,(node18(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 3.12/2.25 tff(155,plain,
% 3.12/2.25 (^[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))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(156,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[155])).
% 3.12/2.25 tff(157,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(158,plain,
% 3.12/2.25 (^[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))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(159,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[158])).
% 3.12/2.25 tff(160,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')).
% 3.12/2.25 tff(161,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[160, 159])).
% 3.12/2.25 tff(162,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[161, 157])).
% 3.12/2.25 tff(163,plain,(
% 3.12/2.25 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 3.12/2.25 inference(skolemize,[status(sab)],[162])).
% 3.12/2.25 tff(164,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[163, 156])).
% 3.12/2.25 tff(165,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node18(c_e_h_3, 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_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node18(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(166,plain,
% 3.12/2.25 (((~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) | (~node18(c_e_h_3, c_e, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node18(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(167,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, 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_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node18(c_e_h_3, c_e, s1, s2))))),
% 3.12/2.25 inference(monotonicity,[status(thm)],[166])).
% 3.12/2.25 tff(168,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, 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_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node18(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.25 inference(transitivity,[status(thm)],[167, 165])).
% 3.12/2.25 tff(169,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(170,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node18(c_e_h_3, c_e, s1, s2))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[169, 168])).
% 3.12/2.25 tff(171,plain,
% 3.12/2.25 ($false),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[170, 164, 154, 153, 1])).
% 3.12/2.25 tff(172,plain,((~node18(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.25 tff(173,plain,
% 3.12/2.25 ((~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[172, 152])).
% 3.12/2.25 tff(174,plain,
% 3.12/2.25 (~node18(c_e_h_3, c_e, s1, s2)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[173, 1])).
% 3.12/2.25 tff(175,plain,
% 3.12/2.25 (succ(s1, s2) <=> succ(s1, s2)),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(176,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 3.12/2.25 tff(177,plain,
% 3.12/2.25 (succ(s1, s2)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[176, 175])).
% 3.12/2.25 tff(178,plain,
% 3.12/2.25 (((~![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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(179,plain,
% 3.12/2.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(180,plain,
% 3.12/2.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[179, 178])).
% 3.12/2.25 tff(181,plain,
% 3.12/2.25 (trans(s1, s2)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[180, 177, 89])).
% 3.12/2.25 tff(182,plain,
% 3.12/2.25 (((~![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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(183,plain,
% 3.12/2.25 ((~![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))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(184,plain,
% 3.12/2.25 ((~![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)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[183, 182])).
% 3.12/2.25 tff(185,plain,
% 3.12/2.25 (node19(c_e_h_3, c_e, s1, s2)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[184, 103, 181])).
% 3.12/2.25 tff(186,plain,
% 3.12/2.25 (^[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))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(187,plain,
% 3.12/2.25 (![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)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[186])).
% 3.12/2.25 tff(188,plain,
% 3.12/2.25 (![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)))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(189,plain,
% 3.12/2.25 (^[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))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(190,plain,
% 3.12/2.25 (![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)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[189])).
% 3.12/2.25 tff(191,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')).
% 3.12/2.25 tff(192,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[191, 190])).
% 3.12/2.25 tff(193,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[192, 188])).
% 3.12/2.25 tff(194,plain,(
% 3.12/2.25 ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(skolemize,[status(sab)],[193])).
% 3.12/2.25 tff(195,plain,
% 3.12/2.25 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[194, 187])).
% 3.12/2.25 tff(196,plain,
% 3.12/2.25 (((~![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_e, s1, s2)) | node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, 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_3, c_e, s1, s2)) | node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(197,plain,
% 3.12/2.25 ((node17(c_e_h_3, c_e, s1) | node18(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)) | node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(198,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | node18(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] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s1, s2)) | node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.25 inference(monotonicity,[status(thm)],[197])).
% 3.12/2.25 tff(199,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | node18(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] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s1, s2)) | node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2))),
% 3.12/2.25 inference(transitivity,[status(thm)],[198, 196])).
% 3.12/2.25 tff(200,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(201,plain,
% 3.12/2.25 ((~![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_e, s1, s2)) | node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[200, 199])).
% 3.12/2.25 tff(202,plain,
% 3.12/2.25 (node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[201, 195, 185])).
% 3.12/2.25 tff(203,plain,
% 3.12/2.25 (node17(c_e_h_3, c_e, s1)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[202, 174])).
% 3.12/2.25 tff(204,assumption,(node15(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 3.12/2.25 tff(205,plain,
% 3.12/2.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_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))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(206,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_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))),
% 3.12/2.25 inference(quant_inst,[status(thm)],[])).
% 3.12/2.25 tff(207,plain,
% 3.12/2.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[206, 205])).
% 3.12/2.25 tff(208,plain,
% 3.12/2.25 ($false),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[207, 146, 204, 153, 1])).
% 3.12/2.25 tff(209,plain,((~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.25 tff(210,plain,
% 3.12/2.25 ((~node15(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[209, 152])).
% 3.12/2.25 tff(211,plain,
% 3.12/2.25 (~node15(c_e_h_3, c_e, s1, s2)),
% 3.12/2.25 inference(unit_resolution,[status(thm)],[210, 1])).
% 3.12/2.25 tff(212,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s1)), introduced(assumption)).
% 3.12/2.25 tff(213,assumption,(node17(c_e_h_3, c_e, s1)), introduced(assumption)).
% 3.12/2.25 tff(214,plain,
% 3.12/2.25 (^[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))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(215,plain,
% 3.12/2.25 (![I0: $i, X: $i, 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)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[214])).
% 3.12/2.25 tff(216,plain,
% 3.12/2.25 (![I0: $i, X: $i, 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)))),
% 3.12/2.25 inference(rewrite,[status(thm)],[])).
% 3.12/2.25 tff(217,plain,
% 3.12/2.25 (^[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))))),
% 3.12/2.25 inference(bind,[status(th)],[])).
% 3.12/2.25 tff(218,plain,
% 3.12/2.25 (![I0: $i, X: $i, 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)))),
% 3.12/2.25 inference(quant_intro,[status(thm)],[217])).
% 3.12/2.25 tff(219,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')).
% 3.12/2.25 tff(220,plain,
% 3.12/2.25 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.12/2.25 tff(221,plain,
% 3.12/2.25 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 3.12/2.25 inference(modus_ponens,[status(thm)],[220, 216])).
% 3.12/2.25 tff(222,plain,(
% 3.12/2.25 ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 3.12/2.25 inference(skolemize,[status(sab)],[221])).
% 3.12/2.25 tff(223,plain,
% 3.12/2.25 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[222, 215])).
% 3.12/2.26 tff(224,plain,
% 3.12/2.26 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(225,plain,
% 3.12/2.26 (((~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) | (~node17(c_e_h_3, c_e, s1))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(226,plain,
% 3.12/2.26 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1))))),
% 3.12/2.26 inference(monotonicity,[status(thm)],[225])).
% 3.12/2.26 tff(227,plain,
% 3.12/2.26 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))),
% 3.12/2.26 inference(transitivity,[status(thm)],[226, 224])).
% 3.12/2.26 tff(228,plain,
% 3.12/2.26 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(229,plain,
% 3.12/2.26 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[228, 227])).
% 3.12/2.26 tff(230,plain,
% 3.12/2.26 (m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1))),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[229, 223, 213])).
% 3.12/2.26 tff(231,plain,
% 3.12/2.26 (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[230, 212])).
% 3.12/2.26 tff(232,assumption,(~node15(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 3.12/2.26 tff(233,plain,
% 3.12/2.26 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(234,plain,
% 3.12/2.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_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))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(235,plain,
% 3.12/2.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_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)),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[234, 233])).
% 3.12/2.26 tff(236,plain,
% 3.12/2.26 (~node16(c_e_h_3, c_e, s1)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[235, 54, 231, 212])).
% 3.12/2.26 tff(237,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(238,plain,
% 3.12/2.26 ((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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(239,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))),
% 3.12/2.26 inference(monotonicity,[status(thm)],[238])).
% 3.12/2.26 tff(240,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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))),
% 3.12/2.26 inference(transitivity,[status(thm)],[239, 237])).
% 3.12/2.26 tff(241,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(242,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~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)),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[241, 240])).
% 3.12/2.26 tff(243,plain,
% 3.12/2.26 (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)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[242, 117, 185])).
% 3.12/2.26 tff(244,plain,
% 3.12/2.26 (node14(c_e_h_3, c_e, s1, s2)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[243, 236, 232])).
% 3.12/2.26 tff(245,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(246,plain,
% 3.12/2.26 (((~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_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(247,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_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_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2))))),
% 3.12/2.26 inference(monotonicity,[status(thm)],[246])).
% 3.12/2.26 tff(248,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_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_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 3.12/2.26 inference(transitivity,[status(thm)],[247, 245])).
% 3.12/2.26 tff(249,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_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)))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(250,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[249, 248])).
% 3.12/2.26 tff(251,plain,
% 3.12/2.26 ($false),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[250, 73, 244, 1, 231])).
% 3.12/2.26 tff(252,plain,(m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | node15(c_e_h_3, c_e, s1, s2) | (~node17(c_e_h_3, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.26 tff(253,plain,
% 3.12/2.26 (m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[252, 203, 211, 1])).
% 3.12/2.26 tff(254,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 3.12/2.26 tff(255,assumption,(node21(c_e_h_3, c_c, s0, s1)), introduced(assumption)).
% 3.12/2.26 tff(256,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), introduced(assumption)).
% 3.12/2.26 tff(257,plain,
% 3.12/2.26 (^[I0: $i, I1: $i] : refl((~m_mutex_h_half_v_out(I0, I1, s0)) <=> (~m_mutex_h_half_v_out(I0, I1, s0)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(258,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[257])).
% 3.12/2.26 tff(259,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(260,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')).
% 3.12/2.26 tff(261,plain,
% 3.12/2.26 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[260, 259])).
% 3.12/2.26 tff(262,plain,(
% 3.12/2.26 ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 3.12/2.26 inference(skolemize,[status(sab)],[261])).
% 3.12/2.26 tff(263,plain,
% 3.12/2.26 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[262, 258])).
% 3.12/2.26 tff(264,plain,
% 3.12/2.26 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(265,plain,
% 3.12/2.26 ($false),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[264, 263, 256])).
% 3.12/2.26 tff(266,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.26 tff(267,plain,
% 3.12/2.26 (^[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)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(268,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[267])).
% 3.12/2.26 tff(269,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(270,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')).
% 3.12/2.26 tff(271,plain,
% 3.12/2.26 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[270, 269])).
% 3.12/2.26 tff(272,plain,(
% 3.12/2.26 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 3.12/2.26 inference(skolemize,[status(sab)],[271])).
% 3.12/2.26 tff(273,plain,
% 3.12/2.26 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[272, 268])).
% 3.12/2.26 tff(274,plain,
% 3.12/2.26 (((~![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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(275,plain,
% 3.12/2.26 ((~![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))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(276,plain,
% 3.12/2.26 ((~![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)),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[275, 274])).
% 3.12/2.26 tff(277,plain,
% 3.12/2.26 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[276, 273, 266])).
% 3.12/2.26 tff(278,plain,
% 3.12/2.26 (^[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)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(279,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[278])).
% 3.12/2.26 tff(280,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(281,plain,
% 3.12/2.26 (^[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)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(282,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[281])).
% 3.12/2.26 tff(283,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')).
% 3.12/2.26 tff(284,plain,
% 3.12/2.26 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[283, 282])).
% 3.12/2.26 tff(285,plain,
% 3.12/2.26 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[284, 280])).
% 3.12/2.26 tff(286,plain,(
% 3.12/2.26 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 3.12/2.26 inference(skolemize,[status(sab)],[285])).
% 3.12/2.26 tff(287,plain,
% 3.12/2.26 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[286, 279])).
% 3.12/2.26 tff(288,plain,
% 3.12/2.26 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(289,plain,
% 3.12/2.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(290,plain,
% 3.12/2.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[289, 288])).
% 3.12/2.26 tff(291,plain,
% 3.12/2.26 (~node20(c_e_h_3, c_c, s0)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[290, 287, 277])).
% 3.12/2.26 tff(292,plain,
% 3.12/2.26 (^[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))))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(293,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[292])).
% 3.12/2.26 tff(294,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(295,plain,
% 3.12/2.26 (^[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))))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(296,plain,
% 3.12/2.26 (![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)))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[295])).
% 3.12/2.26 tff(297,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')).
% 3.12/2.26 tff(298,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[297, 296])).
% 3.12/2.26 tff(299,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[298, 294])).
% 3.12/2.26 tff(300,plain,(
% 3.12/2.26 ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 3.12/2.26 inference(skolemize,[status(sab)],[299])).
% 3.12/2.26 tff(301,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[300, 293])).
% 3.12/2.26 tff(302,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_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)))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(303,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(304,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[303, 302])).
% 3.12/2.26 tff(305,plain,
% 3.12/2.26 ($false),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[304, 301, 291, 254, 255])).
% 3.12/2.26 tff(306,plain,((~node21(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,[]))).
% 3.12/2.26 tff(307,plain,
% 3.12/2.26 (~node21(c_e_h_3, c_c, s0, s1)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[306, 254])).
% 3.12/2.26 tff(308,plain,
% 3.12/2.26 (^[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)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(309,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[308])).
% 3.12/2.26 tff(310,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(311,plain,
% 3.12/2.26 (^[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)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(312,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[311])).
% 3.12/2.26 tff(313,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')).
% 3.12/2.26 tff(314,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[313, 312])).
% 3.12/2.26 tff(315,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[314, 310])).
% 3.12/2.26 tff(316,plain,(
% 3.12/2.26 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 3.12/2.26 inference(skolemize,[status(sab)],[315])).
% 3.12/2.26 tff(317,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[316, 309])).
% 3.12/2.26 tff(318,plain,
% 3.12/2.26 (((~![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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(319,plain,
% 3.12/2.26 ((~![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))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(320,plain,
% 3.12/2.26 ((~![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)),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[319, 318])).
% 3.12/2.26 tff(321,plain,
% 3.12/2.26 (node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[320, 317, 96])).
% 3.12/2.26 tff(322,plain,
% 3.12/2.26 (node22(c_e_h_3, c_c, s0, s1)),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[321, 307])).
% 3.12/2.26 tff(323,plain,
% 3.12/2.26 (^[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)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(324,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[323])).
% 3.12/2.26 tff(325,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(326,plain,
% 3.12/2.26 (^[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)))),
% 3.12/2.26 inference(bind,[status(th)],[])).
% 3.12/2.26 tff(327,plain,
% 3.12/2.26 (![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))),
% 3.12/2.26 inference(quant_intro,[status(thm)],[326])).
% 3.12/2.26 tff(328,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')).
% 3.12/2.26 tff(329,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[328, 327])).
% 3.12/2.26 tff(330,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[329, 325])).
% 3.12/2.26 tff(331,plain,(
% 3.12/2.26 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 3.12/2.26 inference(skolemize,[status(sab)],[330])).
% 3.12/2.26 tff(332,plain,
% 3.12/2.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[331, 324])).
% 3.12/2.26 tff(333,plain,
% 3.12/2.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_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))),
% 3.12/2.26 inference(rewrite,[status(thm)],[])).
% 3.12/2.26 tff(334,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 3.12/2.26 inference(quant_inst,[status(thm)],[])).
% 3.12/2.26 tff(335,plain,
% 3.12/2.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 3.12/2.26 inference(modus_ponens,[status(thm)],[334, 333])).
% 3.12/2.26 tff(336,plain,
% 3.12/2.26 ($false),
% 3.12/2.26 inference(unit_resolution,[status(thm)],[335, 332, 32, 254, 322])).
% 3.12/2.26 tff(337,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.26 tff(338,plain,
% 3.12/2.26 (((~![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))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(339,plain,
% 3.12/2.27 ((~![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))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(340,plain,
% 3.12/2.27 ((~![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)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[339, 338])).
% 3.12/2.27 tff(341,plain,
% 3.12/2.27 (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[340, 39, 337])).
% 3.12/2.27 tff(342,plain,
% 3.12/2.27 (^[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))))),
% 3.12/2.27 inference(bind,[status(th)],[])).
% 3.12/2.27 tff(343,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 3.12/2.27 inference(quant_intro,[status(thm)],[342])).
% 3.12/2.27 tff(344,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(345,plain,
% 3.12/2.27 (^[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)))))),
% 3.12/2.27 inference(bind,[status(th)],[])).
% 3.12/2.27 tff(346,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 3.12/2.27 inference(quant_intro,[status(thm)],[345])).
% 3.12/2.27 tff(347,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')).
% 3.12/2.27 tff(348,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[347, 346])).
% 3.12/2.27 tff(349,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[348, 344])).
% 3.12/2.27 tff(350,plain,(
% 3.12/2.27 ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 3.12/2.27 inference(skolemize,[status(sab)],[349])).
% 3.12/2.27 tff(351,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[350, 343])).
% 3.12/2.27 tff(352,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | (~node17(c_e_h_3, 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_3, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | (~node17(c_e_h_3, c_e, s1)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(353,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | (~node17(c_e_h_3, c_e, s1)))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(354,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | (~node17(c_e_h_3, c_e, s1))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[353, 352])).
% 3.12/2.27 tff(355,plain,
% 3.12/2.27 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | (~node17(c_e_h_3, c_e, s1))),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[354, 351, 341])).
% 3.12/2.27 tff(356,plain,
% 3.12/2.27 ($false),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[355, 253, 203])).
% 3.12/2.27 tff(357,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.27 tff(358,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s2)), introduced(assumption)).
% 3.12/2.27 tff(359,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 3.12/2.27 tff(360,plain,
% 3.12/2.27 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)))),
% 3.12/2.27 inference(bind,[status(th)],[])).
% 3.12/2.27 tff(361,plain,
% 3.12/2.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 3.12/2.27 inference(quant_intro,[status(thm)],[360])).
% 3.12/2.27 tff(362,plain,
% 3.12/2.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(363,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')).
% 3.12/2.27 tff(364,plain,
% 3.12/2.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[363, 362])).
% 3.12/2.27 tff(365,plain,(
% 3.12/2.27 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 3.12/2.27 inference(skolemize,[status(sab)],[364])).
% 3.12/2.27 tff(366,plain,
% 3.12/2.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[365, 361])).
% 3.12/2.27 tff(367,plain,
% 3.12/2.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, 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))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(368,plain,
% 3.12/2.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(369,plain,
% 3.12/2.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[368, 367])).
% 3.12/2.27 tff(370,plain,
% 3.12/2.27 ($false),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[369, 366, 359, 358])).
% 3.12/2.27 tff(371,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.27 tff(372,plain,
% 3.12/2.27 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[371, 357])).
% 3.12/2.27 tff(373,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 3.12/2.27 tff(374,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 3.12/2.27 tff(375,assumption,(node18(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 3.12/2.27 tff(376,plain,
% 3.12/2.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(377,plain,
% 3.12/2.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(378,plain,
% 3.12/2.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[377, 376])).
% 3.12/2.27 tff(379,plain,
% 3.12/2.27 ($false),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[378, 164, 375, 374, 359])).
% 3.12/2.27 tff(380,plain,((~node18(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.27 tff(381,plain,
% 3.12/2.27 (~node18(c_e_h_3, c_e, s2, s3)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[380, 359, 374])).
% 3.12/2.27 tff(382,plain,
% 3.12/2.27 (succ(s2, s3) <=> succ(s2, s3)),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(383,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 3.12/2.27 tff(384,plain,
% 3.12/2.27 (succ(s2, s3)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[383, 382])).
% 3.12/2.27 tff(385,plain,
% 3.12/2.27 (((~![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))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(386,plain,
% 3.12/2.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(387,plain,
% 3.12/2.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[386, 385])).
% 3.12/2.27 tff(388,plain,
% 3.12/2.27 (trans(s2, s3)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[387, 384, 89])).
% 3.12/2.27 tff(389,plain,
% 3.12/2.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(390,plain,
% 3.12/2.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(391,plain,
% 3.12/2.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[390, 389])).
% 3.12/2.27 tff(392,plain,
% 3.12/2.27 (node19(c_e_h_3, c_e, s2, s3)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[391, 103, 388])).
% 3.12/2.27 tff(393,plain,
% 3.12/2.27 (((~![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_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3) | node17(c_e_h_3, 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_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3) | node17(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(394,plain,
% 3.12/2.27 ((node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))) <=> ((~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3) | node17(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(395,plain,
% 3.12/2.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3) | node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(monotonicity,[status(thm)],[394])).
% 3.12/2.27 tff(396,plain,
% 3.12/2.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3) | node17(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(transitivity,[status(thm)],[395, 393])).
% 3.12/2.27 tff(397,plain,
% 3.12/2.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(398,plain,
% 3.12/2.27 ((~![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_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3) | node17(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[397, 396])).
% 3.12/2.27 tff(399,plain,
% 3.12/2.27 (node18(c_e_h_3, c_e, s2, s3) | node17(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[398, 195, 392])).
% 3.12/2.27 tff(400,plain,
% 3.12/2.27 (node17(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[399, 381])).
% 3.12/2.27 tff(401,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s2)), introduced(assumption)).
% 3.12/2.27 tff(402,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(403,plain,
% 3.12/2.27 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(404,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))))),
% 3.12/2.27 inference(monotonicity,[status(thm)],[403])).
% 3.12/2.27 tff(405,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(transitivity,[status(thm)],[404, 402])).
% 3.12/2.27 tff(406,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(407,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[406, 405])).
% 3.12/2.27 tff(408,plain,
% 3.12/2.27 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[407, 223, 401])).
% 3.12/2.27 tff(409,plain,
% 3.12/2.27 (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[408, 400])).
% 3.12/2.27 tff(410,assumption,(node15(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 3.12/2.27 tff(411,plain,
% 3.12/2.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(412,plain,
% 3.12/2.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(413,plain,
% 3.12/2.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[412, 411])).
% 3.12/2.27 tff(414,plain,
% 3.12/2.27 ($false),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[413, 146, 410, 374, 359])).
% 3.12/2.27 tff(415,plain,((~node15(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.27 tff(416,plain,
% 3.12/2.27 (~node15(c_e_h_3, c_e, s2, s3)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[415, 359, 374])).
% 3.12/2.27 tff(417,assumption,(node17(c_e_h_3, c_e, s2)), introduced(assumption)).
% 3.12/2.27 tff(418,assumption,(node16(c_e_h_3, c_e, s2)), introduced(assumption)).
% 3.12/2.27 tff(419,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s2)), introduced(assumption)).
% 3.12/2.27 tff(420,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(421,plain,
% 3.12/2.27 ((m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(422,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2))))),
% 3.12/2.27 inference(monotonicity,[status(thm)],[421])).
% 3.12/2.27 tff(423,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(transitivity,[status(thm)],[422, 420])).
% 3.12/2.27 tff(424,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(425,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[424, 423])).
% 3.12/2.27 tff(426,plain,
% 3.12/2.27 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[425, 351, 417])).
% 3.12/2.27 tff(427,plain,
% 3.12/2.27 (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[426, 419])).
% 3.12/2.27 tff(428,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(429,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(quant_inst,[status(thm)],[])).
% 3.12/2.27 tff(430,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[429, 428])).
% 3.12/2.27 tff(431,plain,
% 3.12/2.27 (m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[430, 54, 418])).
% 3.12/2.27 tff(432,plain,
% 3.12/2.27 ($false),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[431, 427, 419])).
% 3.12/2.27 tff(433,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node16(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.27 tff(434,plain,
% 3.12/2.27 (m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[433, 418, 417])).
% 3.12/2.27 tff(435,plain,
% 3.12/2.27 (m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[407, 223, 417])).
% 3.12/2.27 tff(436,plain,
% 3.12/2.27 (m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 3.12/2.27 inference(unit_resolution,[status(thm)],[435, 434])).
% 3.12/2.27 tff(437,plain,
% 3.12/2.27 (^[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))))),
% 3.12/2.27 inference(bind,[status(th)],[])).
% 3.12/2.27 tff(438,plain,
% 3.12/2.27 (![I0: $i, X: $i, 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)))),
% 3.12/2.27 inference(quant_intro,[status(thm)],[437])).
% 3.12/2.27 tff(439,plain,
% 3.12/2.27 (![I0: $i, X: $i, 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)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(440,plain,
% 3.12/2.27 (^[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))))),
% 3.12/2.27 inference(bind,[status(th)],[])).
% 3.12/2.27 tff(441,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~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)))),
% 3.12/2.27 inference(quant_intro,[status(thm)],[440])).
% 3.12/2.27 tff(442,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')).
% 3.12/2.27 tff(443,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[442, 441])).
% 3.12/2.27 tff(444,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[443, 439])).
% 3.12/2.27 tff(445,plain,(
% 3.12/2.27 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 3.12/2.27 inference(skolemize,[status(sab)],[444])).
% 3.12/2.27 tff(446,plain,
% 3.12/2.27 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 3.12/2.27 inference(modus_ponens,[status(thm)],[445, 438])).
% 3.12/2.27 tff(447,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(448,plain,
% 3.12/2.27 (((~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(rewrite,[status(thm)],[])).
% 3.12/2.27 tff(449,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2))))),
% 3.12/2.27 inference(monotonicity,[status(thm)],[448])).
% 3.12/2.27 tff(450,plain,
% 3.12/2.27 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2)))),
% 3.12/2.27 inference(transitivity,[status(thm)],[449, 447])).
% 3.12/2.27 tff(451,plain,
% 3.12/2.27 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(452,plain,
% 3.12/2.28 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | (~node16(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[451, 450])).
% 3.12/2.28 tff(453,plain,
% 3.12/2.28 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[452, 446, 418])).
% 3.12/2.28 tff(454,plain,
% 3.12/2.28 ($false),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[453, 436, 434])).
% 3.12/2.28 tff(455,plain,((~node16(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.28 tff(456,plain,
% 3.12/2.28 (~node16(c_e_h_3, c_e, s2)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[455, 400])).
% 3.12/2.28 tff(457,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, 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)))) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(458,plain,
% 3.12/2.28 ((node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))) <=> (node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(459,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2)))),
% 3.12/2.28 inference(monotonicity,[status(thm)],[458])).
% 3.12/2.28 tff(460,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(transitivity,[status(thm)],[459, 457])).
% 3.12/2.28 tff(461,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(462,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[461, 460])).
% 3.12/2.28 tff(463,plain,
% 3.12/2.28 (node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[462, 117, 392])).
% 3.12/2.28 tff(464,plain,
% 3.12/2.28 (node14(c_e_h_3, c_e, s2, s3)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[463, 456, 416])).
% 3.12/2.28 tff(465,assumption,(node14(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 3.12/2.28 tff(466,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(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, s3)) | (~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(467,plain,
% 3.12/2.28 (((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(468,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)))),
% 3.12/2.28 inference(monotonicity,[status(thm)],[467])).
% 3.12/2.28 tff(469,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 3.12/2.28 inference(transitivity,[status(thm)],[468, 466])).
% 3.12/2.28 tff(470,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(471,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[470, 469])).
% 3.12/2.28 tff(472,plain,
% 3.12/2.28 ($false),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[471, 73, 465, 419, 374])).
% 3.12/2.28 tff(473,plain,((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.28 tff(474,plain,
% 3.12/2.28 ($false),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[473, 464, 409, 374])).
% 3.12/2.28 tff(475,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, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.28 tff(476,plain,
% 3.12/2.28 (m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[475, 359, 374])).
% 3.12/2.28 tff(477,assumption,(m_user_v_req(c_e_h_3, c_u, s0)), introduced(assumption)).
% 3.12/2.28 tff(478,plain,
% 3.12/2.28 (^[I0: $i, I1: $i] : refl((~m_user_v_req(I0, I1, s0)) <=> (~m_user_v_req(I0, I1, s0)))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(479,plain,
% 3.12/2.28 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[478])).
% 3.12/2.28 tff(480,plain,
% 3.12/2.28 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(481,axiom,(![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_user_1')).
% 3.12/2.28 tff(482,plain,
% 3.12/2.28 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[481, 480])).
% 3.12/2.28 tff(483,plain,(
% 3.12/2.28 ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 3.12/2.28 inference(skolemize,[status(sab)],[482])).
% 3.12/2.28 tff(484,plain,
% 3.12/2.28 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[483, 479])).
% 3.12/2.28 tff(485,plain,
% 3.12/2.28 ((~![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))) | (~m_user_v_req(c_e_h_3, c_u, s0))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(486,plain,
% 3.12/2.28 ($false),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[485, 484, 477])).
% 3.12/2.28 tff(487,plain,(~m_user_v_req(c_e_h_3, c_u, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.28 tff(488,plain,
% 3.12/2.28 (^[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)))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(489,plain,
% 3.12/2.28 (![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))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[488])).
% 3.12/2.28 tff(490,plain,
% 3.12/2.28 (![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))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(491,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')).
% 3.12/2.28 tff(492,plain,
% 3.12/2.28 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[491, 490])).
% 3.12/2.28 tff(493,plain,(
% 3.12/2.28 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 3.12/2.28 inference(skolemize,[status(sab)],[492])).
% 3.12/2.28 tff(494,plain,
% 3.12/2.28 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[493, 489])).
% 3.12/2.28 tff(495,plain,
% 3.12/2.28 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(496,plain,
% 3.12/2.28 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(497,plain,
% 3.12/2.28 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[496, 495])).
% 3.12/2.28 tff(498,plain,
% 3.12/2.28 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[497, 494, 487])).
% 3.12/2.28 tff(499,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s1)), introduced(assumption)).
% 3.12/2.28 tff(500,assumption,(node13(c_e_h_3, c_a, s0, s1)), introduced(assumption)).
% 3.12/2.28 tff(501,plain,
% 3.12/2.28 (^[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)))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(502,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $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))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[501])).
% 3.12/2.28 tff(503,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $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))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(504,plain,
% 3.12/2.28 (^[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)))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(505,plain,
% 3.12/2.28 (![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))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[504])).
% 3.12/2.28 tff(506,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')).
% 3.12/2.28 tff(507,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[506, 505])).
% 3.12/2.28 tff(508,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[507, 503])).
% 3.12/2.28 tff(509,plain,(
% 3.12/2.28 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 3.12/2.28 inference(skolemize,[status(sab)],[508])).
% 3.12/2.28 tff(510,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[509, 502])).
% 3.12/2.28 tff(511,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(512,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(513,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[512, 511])).
% 3.12/2.28 tff(514,plain,
% 3.12/2.28 ($false),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[513, 510, 500, 266, 499])).
% 3.12/2.28 tff(515,plain,((~node13(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.28 tff(516,plain,
% 3.12/2.28 (~node13(c_e_h_3, c_a, s0, s1)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[515, 499])).
% 3.12/2.28 tff(517,plain,
% 3.12/2.28 (^[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)))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(518,plain,
% 3.12/2.28 (![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))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[517])).
% 3.12/2.28 tff(519,plain,
% 3.12/2.28 (![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))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(520,plain,
% 3.12/2.28 (^[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)))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(521,plain,
% 3.12/2.28 (![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))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[520])).
% 3.12/2.28 tff(522,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')).
% 3.12/2.28 tff(523,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[522, 521])).
% 3.12/2.28 tff(524,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[523, 519])).
% 3.12/2.28 tff(525,plain,(
% 3.12/2.28 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 3.12/2.28 inference(skolemize,[status(sab)],[524])).
% 3.12/2.28 tff(526,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[525, 518])).
% 3.12/2.28 tff(527,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(528,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(529,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[528, 527])).
% 3.12/2.28 tff(530,plain,
% 3.12/2.28 (node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[529, 526, 96])).
% 3.12/2.28 tff(531,plain,
% 3.12/2.28 (node12(c_e_h_3, c_a, s0, s1)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[530, 516])).
% 3.12/2.28 tff(532,plain,
% 3.12/2.28 (^[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))))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(533,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[532])).
% 3.12/2.28 tff(534,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $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)))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(535,plain,
% 3.12/2.28 (^[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))))),
% 3.12/2.28 inference(bind,[status(th)],[])).
% 3.12/2.28 tff(536,plain,
% 3.12/2.28 (![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)))),
% 3.12/2.28 inference(quant_intro,[status(thm)],[535])).
% 3.12/2.28 tff(537,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')).
% 3.12/2.28 tff(538,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[537, 536])).
% 3.12/2.28 tff(539,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[538, 534])).
% 3.12/2.28 tff(540,plain,(
% 3.12/2.28 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 3.12/2.28 inference(skolemize,[status(sab)],[539])).
% 3.12/2.28 tff(541,plain,
% 3.12/2.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[540, 533])).
% 3.12/2.28 tff(542,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_3, 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_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(543,plain,
% 3.12/2.28 (((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> ((~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(544,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)))),
% 3.12/2.28 inference(monotonicity,[status(thm)],[543])).
% 3.12/2.28 tff(545,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0))),
% 3.12/2.28 inference(transitivity,[status(thm)],[544, 542])).
% 3.12/2.28 tff(546,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(547,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[546, 545])).
% 3.12/2.28 tff(548,plain,
% 3.12/2.28 ($false),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[547, 541, 531, 499, 498])).
% 3.12/2.28 tff(549,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.28 tff(550,plain,
% 3.12/2.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(551,plain,
% 3.12/2.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(552,plain,
% 3.12/2.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[551, 550])).
% 3.12/2.28 tff(553,plain,
% 3.12/2.28 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[552, 273, 549])).
% 3.12/2.28 tff(554,plain,
% 3.12/2.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(555,plain,
% 3.12/2.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(556,plain,
% 3.12/2.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1)),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[555, 554])).
% 3.12/2.28 tff(557,plain,
% 3.12/2.28 (~node20(c_e_h_3, c_c, s1)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[556, 287, 553])).
% 3.12/2.28 tff(558,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s2)), introduced(assumption)).
% 3.12/2.28 tff(559,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 3.12/2.28 tff(560,assumption,(~node20(c_e_h_3, c_c, s1)), introduced(assumption)).
% 3.12/2.28 tff(561,assumption,(node21(c_e_h_3, c_c, s1, s2)), introduced(assumption)).
% 3.12/2.28 tff(562,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))),
% 3.12/2.28 inference(rewrite,[status(thm)],[])).
% 3.12/2.28 tff(563,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))),
% 3.12/2.28 inference(quant_inst,[status(thm)],[])).
% 3.12/2.28 tff(564,plain,
% 3.12/2.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2))),
% 3.12/2.28 inference(modus_ponens,[status(thm)],[563, 562])).
% 3.12/2.28 tff(565,plain,
% 3.12/2.28 ($false),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[564, 301, 561, 560, 558])).
% 3.12/2.28 tff(566,plain,((~node21(c_e_h_3, c_c, s1, s2)) | node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.28 tff(567,plain,
% 3.12/2.28 (~node21(c_e_h_3, c_c, s1, s2)),
% 3.12/2.28 inference(unit_resolution,[status(thm)],[566, 558, 560])).
% 3.12/2.28 tff(568,plain,
% 3.12/2.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(569,plain,
% 3.12/2.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(570,plain,
% 3.12/2.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[569, 568])).
% 3.12/2.29 tff(571,plain,
% 3.12/2.29 (node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[570, 317, 181])).
% 3.12/2.29 tff(572,plain,
% 3.12/2.29 (node22(c_e_h_3, c_c, s1, s2)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[571, 567])).
% 3.12/2.29 tff(573,plain,
% 3.12/2.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(574,plain,
% 3.12/2.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(575,plain,
% 3.12/2.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[574, 573])).
% 3.12/2.29 tff(576,plain,
% 3.12/2.29 ($false),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[575, 332, 572, 559, 558])).
% 3.12/2.29 tff(577,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1) | node20(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.29 tff(578,plain,
% 3.12/2.29 (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[577, 337, 557])).
% 3.12/2.29 tff(579,assumption,(m_c_h_element_v_in1(c_e_h_3, c_e, s2)), introduced(assumption)).
% 3.12/2.29 tff(580,plain,
% 3.12/2.29 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, 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_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(581,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(582,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[581, 580])).
% 3.12/2.29 tff(583,plain,
% 3.12/2.29 ($false),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[582, 39, 579, 578])).
% 3.12/2.29 tff(584,plain,(~m_c_h_element_v_in1(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.29 tff(585,plain,
% 3.12/2.29 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | (~node17(c_e_h_3, c_e, s2))),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[425, 351, 584])).
% 3.12/2.29 tff(586,plain,
% 3.12/2.29 ($false),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[585, 400, 476])).
% 3.12/2.29 tff(587,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, s3))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.29 tff(588,plain,
% 3.12/2.29 (~m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[587, 357])).
% 3.12/2.29 tff(589,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s3)), introduced(assumption)).
% 3.12/2.29 tff(590,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 3.12/2.29 tff(591,plain,
% 3.12/2.29 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(592,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(593,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[592, 591])).
% 3.12/2.29 tff(594,plain,
% 3.12/2.29 ($false),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[593, 366, 590, 589])).
% 3.12/2.29 tff(595,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.29 tff(596,plain,
% 3.12/2.29 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[595, 588])).
% 3.12/2.29 tff(597,plain,
% 3.12/2.29 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(598,plain,
% 3.12/2.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(599,plain,
% 3.12/2.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[598, 597])).
% 3.12/2.29 tff(600,plain,
% 3.12/2.29 (~node20(c_e_h_3, c_r, s3)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[599, 287, 596])).
% 3.12/2.29 tff(601,assumption,(m_user_v_ack(c_e_h_3, c_u, s3)), introduced(assumption)).
% 3.12/2.29 tff(602,plain,
% 3.12/2.29 (^[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)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(603,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[602])).
% 3.12/2.29 tff(604,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(605,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')).
% 3.12/2.29 tff(606,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[605, 604])).
% 3.12/2.29 tff(607,plain,(
% 3.12/2.29 ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 3.12/2.29 inference(skolemize,[status(sab)],[606])).
% 3.12/2.29 tff(608,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[607, 603])).
% 3.12/2.29 tff(609,plain,
% 3.12/2.29 (((~![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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(610,plain,
% 3.12/2.29 ((~![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))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(611,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[610, 609])).
% 3.12/2.29 tff(612,plain,
% 3.12/2.29 ($false),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[611, 608, 601, 373])).
% 3.12/2.29 tff(613,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,[]))).
% 3.12/2.29 tff(614,plain,
% 3.12/2.29 (~m_user_v_ack(c_e_h_3, c_u, s3)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[613, 373])).
% 3.12/2.29 tff(615,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 3.12/2.29 tff(616,assumption,(node21(c_e_h_1, c_r, s2, s3)), introduced(assumption)).
% 3.12/2.29 tff(617,assumption,(m_cell_v_token(c_e_h_1, s0)), introduced(assumption)).
% 3.12/2.29 tff(618,plain,
% 3.12/2.29 (^[X: $i] : refl((~m_cell_v_token(c_e_h_1, X)) <=> (~m_cell_v_token(c_e_h_1, X)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(619,plain,
% 3.12/2.29 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[618])).
% 3.12/2.29 tff(620,plain,
% 3.12/2.29 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(621,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_1, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_3')).
% 3.12/2.29 tff(622,plain,
% 3.12/2.29 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[621, 620])).
% 3.12/2.29 tff(623,plain,(
% 3.12/2.29 ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 3.12/2.29 inference(skolemize,[status(sab)],[622])).
% 3.12/2.29 tff(624,plain,
% 3.12/2.29 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[623, 619])).
% 3.12/2.29 tff(625,plain,
% 3.12/2.29 ((~![X: $i] : (~m_cell_v_token(c_e_h_1, X))) | (~m_cell_v_token(c_e_h_1, s0))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(626,plain,
% 3.12/2.29 ($false),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[625, 624, 617])).
% 3.12/2.29 tff(627,plain,(~m_cell_v_token(c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.29 tff(628,plain,
% 3.12/2.29 (^[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)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(629,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[628])).
% 3.12/2.29 tff(630,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(631,plain,
% 3.12/2.29 (^[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)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(632,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[631])).
% 3.12/2.29 tff(633,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')).
% 3.12/2.29 tff(634,plain,
% 3.12/2.29 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[633, 632])).
% 3.12/2.29 tff(635,plain,
% 3.12/2.29 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[634, 630])).
% 3.12/2.29 tff(636,plain,(
% 3.12/2.29 ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 3.12/2.29 inference(skolemize,[status(sab)],[635])).
% 3.12/2.29 tff(637,plain,
% 3.12/2.29 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[636, 629])).
% 3.12/2.29 tff(638,plain,
% 3.12/2.29 (((~![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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(639,plain,
% 3.12/2.29 ((~![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))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(640,plain,
% 3.12/2.29 ((~![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)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[639, 638])).
% 3.12/2.29 tff(641,plain,
% 3.12/2.29 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[640, 637, 627])).
% 3.12/2.29 tff(642,plain,
% 3.12/2.29 (^[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)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(643,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[642])).
% 3.12/2.29 tff(644,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(645,plain,
% 3.12/2.29 (^[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)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(646,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[645])).
% 3.12/2.29 tff(647,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')).
% 3.12/2.29 tff(648,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[647, 646])).
% 3.12/2.29 tff(649,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[648, 644])).
% 3.12/2.29 tff(650,plain,(
% 3.12/2.29 ![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))),
% 3.12/2.29 inference(skolemize,[status(sab)],[649])).
% 3.12/2.29 tff(651,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[650, 643])).
% 3.12/2.29 tff(652,plain,
% 3.12/2.29 (((~![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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(653,plain,
% 3.12/2.29 ((~![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))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(654,plain,
% 3.12/2.29 ((~![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)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[653, 652])).
% 3.12/2.29 tff(655,plain,
% 3.12/2.29 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[654, 651, 641])).
% 3.12/2.29 tff(656,plain,
% 3.12/2.29 (^[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))))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(657,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[656])).
% 3.12/2.29 tff(658,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(659,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')).
% 3.12/2.29 tff(660,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[659, 658])).
% 3.12/2.29 tff(661,plain,(
% 3.12/2.29 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 3.12/2.29 inference(skolemize,[status(sab)],[660])).
% 3.12/2.29 tff(662,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[661, 657])).
% 3.12/2.29 tff(663,plain,
% 3.12/2.29 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_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)))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(664,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(665,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[664, 663])).
% 3.12/2.29 tff(666,plain,
% 3.12/2.29 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[665, 662, 655])).
% 3.12/2.29 tff(667,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)), introduced(assumption)).
% 3.12/2.29 tff(668,plain,
% 3.12/2.29 (^[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)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(669,plain,
% 3.12/2.29 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[668])).
% 3.12/2.29 tff(670,plain,
% 3.12/2.29 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(671,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_53')).
% 3.12/2.29 tff(672,plain,
% 3.12/2.29 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[671, 670])).
% 3.12/2.29 tff(673,plain,(
% 3.12/2.29 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 3.12/2.29 inference(skolemize,[status(sab)],[672])).
% 3.12/2.29 tff(674,plain,
% 3.12/2.29 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[673, 669])).
% 3.12/2.29 tff(675,plain,
% 3.12/2.29 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(676,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(677,plain,
% 3.12/2.29 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[676, 675])).
% 3.12/2.29 tff(678,plain,
% 3.12/2.29 (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)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[677, 674])).
% 3.12/2.29 tff(679,plain,
% 3.12/2.29 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[678, 667])).
% 3.12/2.29 tff(680,plain,
% 3.12/2.29 (^[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)))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(681,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[680])).
% 3.12/2.29 tff(682,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(683,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')).
% 3.12/2.29 tff(684,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[683, 682])).
% 3.12/2.29 tff(685,plain,(
% 3.12/2.29 ![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))),
% 3.12/2.29 inference(skolemize,[status(sab)],[684])).
% 3.12/2.29 tff(686,plain,
% 3.12/2.29 (![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))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[685, 681])).
% 3.12/2.29 tff(687,plain,
% 3.12/2.29 (((~![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_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(688,plain,
% 3.12/2.29 ((~![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_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(689,plain,
% 3.12/2.29 ((~![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_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[688, 687])).
% 3.12/2.29 tff(690,plain,
% 3.12/2.29 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 3.12/2.29 inference(unit_resolution,[status(thm)],[689, 686, 679])).
% 3.12/2.29 tff(691,plain,
% 3.12/2.29 (^[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))))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(692,plain,
% 3.12/2.29 (![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)))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[691])).
% 3.12/2.29 tff(693,plain,
% 3.12/2.29 (![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)))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(694,plain,
% 3.12/2.29 (^[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))))),
% 3.12/2.29 inference(bind,[status(th)],[])).
% 3.12/2.29 tff(695,plain,
% 3.12/2.29 (![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)))),
% 3.12/2.29 inference(quant_intro,[status(thm)],[694])).
% 3.12/2.29 tff(696,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) | (~m_cell_v_token(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_62')).
% 3.12/2.29 tff(697,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[696, 695])).
% 3.12/2.29 tff(698,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[697, 693])).
% 3.12/2.29 tff(699,plain,(
% 3.12/2.29 ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 3.12/2.29 inference(skolemize,[status(sab)],[698])).
% 3.12/2.29 tff(700,plain,
% 3.12/2.29 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 3.12/2.29 inference(modus_ponens,[status(thm)],[699, 692])).
% 3.12/2.29 tff(701,plain,
% 3.12/2.29 (((~![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)))),
% 3.12/2.29 inference(rewrite,[status(thm)],[])).
% 3.12/2.29 tff(702,plain,
% 3.12/2.29 ((~![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)))),
% 3.12/2.29 inference(quant_inst,[status(thm)],[])).
% 3.12/2.29 tff(703,plain,
% 3.12/2.29 ((~![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))),
% 3.20/2.29 inference(modus_ponens,[status(thm)],[702, 701])).
% 3.20/2.29 tff(704,plain,
% 3.20/2.29 (~m_cell_v_token(c_e_h_1, s0)),
% 3.20/2.29 inference(unit_resolution,[status(thm)],[703, 700, 690])).
% 3.20/2.29 tff(705,plain,
% 3.20/2.29 (^[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)))),
% 3.20/2.29 inference(bind,[status(th)],[])).
% 3.20/2.29 tff(706,plain,
% 3.20/2.29 (![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))),
% 3.20/2.29 inference(quant_intro,[status(thm)],[705])).
% 3.20/2.29 tff(707,plain,
% 3.20/2.29 (![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))),
% 3.20/2.29 inference(rewrite,[status(thm)],[])).
% 3.20/2.29 tff(708,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')).
% 3.20/2.29 tff(709,plain,
% 3.20/2.29 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 3.20/2.29 inference(modus_ponens,[status(thm)],[708, 707])).
% 3.20/2.29 tff(710,plain,(
% 3.20/2.29 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 3.20/2.29 inference(skolemize,[status(sab)],[709])).
% 3.20/2.29 tff(711,plain,
% 3.20/2.29 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 3.20/2.29 inference(modus_ponens,[status(thm)],[710, 706])).
% 3.20/2.29 tff(712,plain,
% 3.20/2.29 (((~![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))),
% 3.20/2.29 inference(rewrite,[status(thm)],[])).
% 3.20/2.29 tff(713,plain,
% 3.20/2.29 ((~![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))),
% 3.20/2.29 inference(quant_inst,[status(thm)],[])).
% 3.20/2.29 tff(714,plain,
% 3.20/2.29 ((~![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)),
% 3.20/2.29 inference(modus_ponens,[status(thm)],[713, 712])).
% 3.20/2.29 tff(715,plain,
% 3.20/2.29 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 3.20/2.29 inference(unit_resolution,[status(thm)],[714, 711, 704])).
% 3.20/2.29 tff(716,plain,
% 3.20/2.29 (((~![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))),
% 3.20/2.29 inference(rewrite,[status(thm)],[])).
% 3.20/2.29 tff(717,plain,
% 3.20/2.29 ((~![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))),
% 3.20/2.29 inference(quant_inst,[status(thm)],[])).
% 3.20/2.29 tff(718,plain,
% 3.20/2.29 ((~![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)),
% 3.20/2.29 inference(modus_ponens,[status(thm)],[717, 716])).
% 3.20/2.29 tff(719,plain,
% 3.20/2.29 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 3.20/2.29 inference(unit_resolution,[status(thm)],[718, 686, 715])).
% 3.20/2.29 tff(720,plain,
% 3.20/2.30 (^[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)))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(721,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[720])).
% 3.20/2.30 tff(722,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(723,plain,
% 3.20/2.30 (^[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)))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(724,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[723])).
% 3.20/2.30 tff(725,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')).
% 3.20/2.30 tff(726,plain,
% 3.20/2.30 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[725, 724])).
% 3.20/2.30 tff(727,plain,
% 3.20/2.30 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[726, 722])).
% 3.20/2.30 tff(728,plain,(
% 3.20/2.30 ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 3.20/2.30 inference(skolemize,[status(sab)],[727])).
% 3.20/2.30 tff(729,plain,
% 3.20/2.30 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[728, 721])).
% 3.20/2.30 tff(730,plain,
% 3.20/2.30 (((~![I0: $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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(731,plain,
% 3.20/2.30 ((~![I0: $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))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(732,plain,
% 3.20/2.30 ((~![I0: $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)),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[731, 730])).
% 3.20/2.30 tff(733,plain,
% 3.20/2.30 (~node9(c_e_h_1, c_m, s0)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[732, 729, 667])).
% 3.20/2.30 tff(734,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), introduced(assumption)).
% 3.20/2.30 tff(735,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)), introduced(assumption)).
% 3.20/2.30 tff(736,plain,
% 3.20/2.30 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[689, 686, 735])).
% 3.20/2.30 tff(737,plain,
% 3.20/2.30 (~m_cell_v_token(c_e_h_1, s0)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[703, 700, 736])).
% 3.20/2.30 tff(738,plain,
% 3.20/2.30 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[714, 711, 737])).
% 3.20/2.30 tff(739,plain,
% 3.20/2.30 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[718, 686, 738])).
% 3.20/2.30 tff(740,plain,
% 3.20/2.30 (^[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)))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(741,plain,
% 3.20/2.30 (![I0: $i, X: $i] : (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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[740])).
% 3.20/2.30 tff(742,plain,
% 3.20/2.30 (![I0: $i, X: $i] : (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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(743,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')).
% 3.20/2.30 tff(744,plain,
% 3.20/2.30 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[743, 742])).
% 3.20/2.30 tff(745,plain,(
% 3.20/2.30 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 3.20/2.30 inference(skolemize,[status(sab)],[744])).
% 3.20/2.30 tff(746,plain,
% 3.20/2.30 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[745, 741])).
% 3.20/2.30 tff(747,plain,
% 3.20/2.30 (((~![I0: $i, X: $i] : (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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(748,plain,
% 3.20/2.30 ((~![I0: $i, X: $i] : (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))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(749,plain,
% 3.20/2.30 ((~![I0: $i, X: $i] : (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)),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[748, 747])).
% 3.20/2.30 tff(750,plain,
% 3.20/2.30 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[749, 746, 739])).
% 3.20/2.30 tff(751,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), introduced(assumption)).
% 3.20/2.30 tff(752,assumption,(node11(c_e_h_1, c_n, s0, s1)), introduced(assumption)).
% 3.20/2.30 tff(753,plain,
% 3.20/2.30 (^[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))))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(754,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[753])).
% 3.20/2.30 tff(755,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_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)))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(756,plain,
% 3.20/2.30 (^[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)))))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(757,plain,
% 3.20/2.30 (![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)))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[756])).
% 3.20/2.30 tff(758,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')).
% 3.20/2.30 tff(759,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[758, 757])).
% 3.20/2.30 tff(760,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[759, 755])).
% 3.20/2.30 tff(761,plain,(
% 3.20/2.30 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 3.20/2.30 inference(skolemize,[status(sab)],[760])).
% 3.20/2.30 tff(762,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[761, 754])).
% 3.20/2.30 tff(763,plain,
% 3.20/2.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(764,plain,
% 3.20/2.30 ((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)))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(765,plain,
% 3.20/2.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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))))),
% 3.20/2.30 inference(monotonicity,[status(thm)],[764])).
% 3.20/2.30 tff(766,plain,
% 3.20/2.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 3.20/2.30 inference(transitivity,[status(thm)],[765, 763])).
% 3.20/2.30 tff(767,plain,
% 3.20/2.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(768,plain,
% 3.20/2.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[767, 766])).
% 3.20/2.30 tff(769,plain,
% 3.20/2.30 ($false),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[768, 762, 735, 751, 752])).
% 3.20/2.30 tff(770,plain,((~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, s1)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.30 tff(771,plain,
% 3.20/2.30 (~node11(c_e_h_1, c_n, s0, s1)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[770, 751, 735])).
% 3.20/2.30 tff(772,plain,
% 3.20/2.30 (^[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)))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(773,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[772])).
% 3.20/2.30 tff(774,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(775,plain,
% 3.20/2.30 (^[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)))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(776,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[775])).
% 3.20/2.30 tff(777,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')).
% 3.20/2.30 tff(778,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[777, 776])).
% 3.20/2.30 tff(779,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[778, 774])).
% 3.20/2.30 tff(780,plain,(
% 3.20/2.30 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 3.20/2.30 inference(skolemize,[status(sab)],[779])).
% 3.20/2.30 tff(781,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[780, 773])).
% 3.20/2.30 tff(782,plain,
% 3.20/2.30 (((~![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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(783,plain,
% 3.20/2.30 ((~![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))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(784,plain,
% 3.20/2.30 ((~![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)),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[783, 782])).
% 3.20/2.30 tff(785,plain,
% 3.20/2.30 (node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[784, 781, 96])).
% 3.20/2.30 tff(786,plain,
% 3.20/2.30 (node10(c_e_h_1, c_n, s0, s1)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[785, 771])).
% 3.20/2.30 tff(787,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s0)), introduced(assumption)).
% 3.20/2.30 tff(788,plain,
% 3.20/2.30 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(789,plain,
% 3.20/2.30 ($false),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[788, 133, 787])).
% 3.20/2.30 tff(790,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.30 tff(791,plain,
% 3.20/2.30 (^[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)))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(792,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[791])).
% 3.20/2.30 tff(793,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(794,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')).
% 3.20/2.30 tff(795,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[794, 793])).
% 3.20/2.30 tff(796,plain,(
% 3.20/2.30 ![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))),
% 3.20/2.30 inference(skolemize,[status(sab)],[795])).
% 3.20/2.30 tff(797,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[796, 792])).
% 3.20/2.30 tff(798,plain,
% 3.20/2.30 (((~![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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(799,plain,
% 3.20/2.30 ((~![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))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(800,plain,
% 3.20/2.30 ((~![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)),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[799, 798])).
% 3.20/2.30 tff(801,plain,
% 3.20/2.30 (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)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[800, 797])).
% 3.20/2.30 tff(802,plain,
% 3.20/2.30 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[801, 790])).
% 3.20/2.30 tff(803,plain,
% 3.20/2.30 (^[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)))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(804,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[803])).
% 3.20/2.30 tff(805,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(806,plain,
% 3.20/2.30 (^[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))))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(807,plain,
% 3.20/2.30 (![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))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[806])).
% 3.20/2.30 tff(808,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')).
% 3.20/2.30 tff(809,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[808, 807])).
% 3.20/2.30 tff(810,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[809, 805])).
% 3.20/2.30 tff(811,plain,(
% 3.20/2.30 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 3.20/2.30 inference(skolemize,[status(sab)],[810])).
% 3.20/2.30 tff(812,plain,
% 3.20/2.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[811, 804])).
% 3.20/2.30 tff(813,plain,
% 3.20/2.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, 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_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(814,plain,
% 3.20/2.30 (((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(815,plain,
% 3.20/2.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0))))),
% 3.20/2.30 inference(monotonicity,[status(thm)],[814])).
% 3.20/2.30 tff(816,plain,
% 3.20/2.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)))),
% 3.20/2.30 inference(transitivity,[status(thm)],[815, 813])).
% 3.20/2.30 tff(817,plain,
% 3.20/2.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, 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))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(818,plain,
% 3.20/2.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[817, 816])).
% 3.20/2.30 tff(819,plain,
% 3.20/2.30 ($false),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[818, 812, 751, 802, 786, 750])).
% 3.20/2.30 tff(820,plain,(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, s0))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.30 tff(821,plain,
% 3.20/2.30 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[820, 679])).
% 3.20/2.30 tff(822,plain,
% 3.20/2.30 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, 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)))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(823,plain,
% 3.20/2.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, 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)))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(824,plain,
% 3.20/2.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, 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))),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[823, 822])).
% 3.20/2.30 tff(825,plain,
% 3.20/2.30 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[824, 662, 821])).
% 3.20/2.30 tff(826,plain,
% 3.20/2.30 (((~![I0: $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))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(827,plain,
% 3.20/2.30 ((~![I0: $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))),
% 3.20/2.30 inference(quant_inst,[status(thm)],[])).
% 3.20/2.30 tff(828,plain,
% 3.20/2.30 ((~![I0: $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)),
% 3.20/2.30 inference(modus_ponens,[status(thm)],[827, 826])).
% 3.20/2.30 tff(829,plain,
% 3.20/2.30 (~node9(c_e_h_1, c_m, s1)),
% 3.20/2.30 inference(unit_resolution,[status(thm)],[828, 729, 825])).
% 3.20/2.30 tff(830,assumption,(~node9(c_e_h_1, c_m, s1)), introduced(assumption)).
% 3.20/2.30 tff(831,assumption,(node10(c_e_h_1, c_m, s1, s2)), introduced(assumption)).
% 3.20/2.30 tff(832,plain,
% 3.20/2.30 (^[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))))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(833,plain,
% 3.20/2.30 (![Y: $i, I0: $i, 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)))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[832])).
% 3.20/2.30 tff(834,plain,
% 3.20/2.30 (![Y: $i, I0: $i, 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)))),
% 3.20/2.30 inference(rewrite,[status(thm)],[])).
% 3.20/2.30 tff(835,plain,
% 3.20/2.30 (^[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))))),
% 3.20/2.30 inference(bind,[status(th)],[])).
% 3.20/2.30 tff(836,plain,
% 3.20/2.30 (![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)))),
% 3.20/2.30 inference(quant_intro,[status(thm)],[835])).
% 3.20/2.30 tff(837,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')).
% 3.20/2.31 tff(838,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[837, 836])).
% 3.20/2.31 tff(839,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[838, 834])).
% 3.20/2.31 tff(840,plain,(
% 3.20/2.31 ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 3.20/2.31 inference(skolemize,[status(sab)],[839])).
% 3.20/2.31 tff(841,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[840, 833])).
% 3.20/2.31 tff(842,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s1, s2)) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, 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)))) | (~node10(c_e_h_1, c_m, s1, s2)) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(843,plain,
% 3.20/2.31 ((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))) <=> ((~node10(c_e_h_1, c_m, s1, s2)) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(844,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, 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)))) | ((~node10(c_e_h_1, c_m, s1, s2)) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))))),
% 3.20/2.31 inference(monotonicity,[status(thm)],[843])).
% 3.20/2.31 tff(845,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, 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)))) | (~node10(c_e_h_1, c_m, s1, s2)) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)))),
% 3.20/2.31 inference(transitivity,[status(thm)],[844, 842])).
% 3.20/2.31 tff(846,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, 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)))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(847,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s1, s2)) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[846, 845])).
% 3.20/2.31 tff(848,plain,
% 3.20/2.31 ($false),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[847, 841, 734, 831, 830])).
% 3.20/2.31 tff(849,plain,((~node10(c_e_h_1, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | node9(c_e_h_1, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.31 tff(850,plain,
% 3.20/2.31 (~node10(c_e_h_1, c_m, s1, s2)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[849, 829, 734])).
% 3.20/2.31 tff(851,plain,
% 3.20/2.31 (((~![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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(852,plain,
% 3.20/2.31 ((~![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))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(853,plain,
% 3.20/2.31 ((~![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)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[852, 851])).
% 3.20/2.31 tff(854,plain,
% 3.20/2.31 (node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[853, 781, 181])).
% 3.20/2.31 tff(855,plain,
% 3.20/2.31 (node11(c_e_h_1, c_m, s1, s2)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[854, 850])).
% 3.20/2.31 tff(856,assumption,(node11(c_e_h_1, c_m, s1, s2)), introduced(assumption)).
% 3.20/2.31 tff(857,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), introduced(assumption)).
% 3.20/2.31 tff(858,plain,
% 3.20/2.31 (^[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)))),
% 3.20/2.31 inference(bind,[status(th)],[])).
% 3.20/2.31 tff(859,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_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))),
% 3.20/2.31 inference(quant_intro,[status(thm)],[858])).
% 3.20/2.31 tff(860,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(861,plain,
% 3.20/2.31 (^[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)))),
% 3.20/2.31 inference(bind,[status(th)],[])).
% 3.20/2.31 tff(862,plain,
% 3.20/2.31 (![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))),
% 3.20/2.31 inference(quant_intro,[status(thm)],[861])).
% 3.20/2.31 tff(863,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')).
% 3.20/2.31 tff(864,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[863, 862])).
% 3.20/2.31 tff(865,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[864, 860])).
% 3.20/2.31 tff(866,plain,(
% 3.20/2.31 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 3.20/2.31 inference(skolemize,[status(sab)],[865])).
% 3.20/2.31 tff(867,plain,
% 3.20/2.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[866, 859])).
% 3.20/2.31 tff(868,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(869,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(870,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[869, 868])).
% 3.20/2.31 tff(871,plain,
% 3.20/2.31 ($false),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[870, 867, 857, 734, 856])).
% 3.20/2.31 tff(872,plain,((~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.31 tff(873,plain,
% 3.20/2.31 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[872, 855, 734])).
% 3.20/2.31 tff(874,assumption,(~node9(c_e_h_1, c_m, s0)), introduced(assumption)).
% 3.20/2.31 tff(875,assumption,(node10(c_e_h_1, c_m, s0, s1)), introduced(assumption)).
% 3.20/2.31 tff(876,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), introduced(assumption)).
% 3.20/2.31 tff(877,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, 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)))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(878,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, 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)))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(879,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[878, 877])).
% 3.20/2.31 tff(880,plain,
% 3.20/2.31 ($false),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[879, 841, 876, 875, 874])).
% 3.20/2.31 tff(881,plain,((~node10(c_e_h_1, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | node9(c_e_h_1, c_m, s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.31 tff(882,plain,
% 3.20/2.31 (~node10(c_e_h_1, c_m, s0, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[881, 873, 733])).
% 3.20/2.31 tff(883,plain,
% 3.20/2.31 (((~![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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(884,plain,
% 3.20/2.31 ((~![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))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(885,plain,
% 3.20/2.31 ((~![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)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[884, 883])).
% 3.20/2.31 tff(886,plain,
% 3.20/2.31 (node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[885, 781, 96])).
% 3.20/2.31 tff(887,plain,
% 3.20/2.31 (node11(c_e_h_1, c_m, s0, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[886, 882])).
% 3.20/2.31 tff(888,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(889,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | 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))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(890,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[889, 888])).
% 3.20/2.31 tff(891,plain,
% 3.20/2.31 ($false),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[890, 867, 873, 887, 719])).
% 3.20/2.31 tff(892,plain,(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_m, s2))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.31 tff(893,plain,
% 3.20/2.31 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[892, 666])).
% 3.20/2.31 tff(894,plain,
% 3.20/2.31 (^[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)))),
% 3.20/2.31 inference(bind,[status(th)],[])).
% 3.20/2.31 tff(895,plain,
% 3.20/2.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![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))),
% 3.20/2.31 inference(quant_intro,[status(thm)],[894])).
% 3.20/2.31 tff(896,plain,
% 3.20/2.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(897,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')).
% 3.20/2.31 tff(898,plain,
% 3.20/2.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[897, 896])).
% 3.20/2.31 tff(899,plain,(
% 3.20/2.31 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 3.20/2.31 inference(skolemize,[status(sab)],[898])).
% 3.20/2.31 tff(900,plain,
% 3.20/2.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[899, 895])).
% 3.20/2.31 tff(901,plain,
% 3.20/2.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(902,plain,
% 3.20/2.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(903,plain,
% 3.20/2.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[902, 901])).
% 3.20/2.31 tff(904,plain,
% 3.20/2.31 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[903, 900, 893])).
% 3.20/2.31 tff(905,plain,
% 3.20/2.31 (^[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)))),
% 3.20/2.31 inference(bind,[status(th)],[])).
% 3.20/2.31 tff(906,plain,
% 3.20/2.31 (![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))),
% 3.20/2.31 inference(quant_intro,[status(thm)],[905])).
% 3.20/2.31 tff(907,plain,
% 3.20/2.31 (![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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(908,plain,
% 3.20/2.31 (^[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)))),
% 3.20/2.31 inference(bind,[status(th)],[])).
% 3.20/2.31 tff(909,plain,
% 3.20/2.31 (![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))),
% 3.20/2.31 inference(quant_intro,[status(thm)],[908])).
% 3.20/2.31 tff(910,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')).
% 3.20/2.31 tff(911,plain,
% 3.20/2.31 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[910, 909])).
% 3.20/2.31 tff(912,plain,
% 3.20/2.31 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[911, 907])).
% 3.20/2.31 tff(913,plain,(
% 3.20/2.31 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 3.20/2.31 inference(skolemize,[status(sab)],[912])).
% 3.20/2.31 tff(914,plain,
% 3.20/2.31 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[913, 906])).
% 3.20/2.31 tff(915,plain,
% 3.20/2.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(916,plain,
% 3.20/2.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(917,plain,
% 3.20/2.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[916, 915])).
% 3.20/2.31 tff(918,plain,
% 3.20/2.31 (~node20(c_e_h_1, c_r, s2)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[917, 914, 904])).
% 3.20/2.31 tff(919,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(920,plain,
% 3.20/2.31 ((node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(921,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3))))),
% 3.20/2.31 inference(monotonicity,[status(thm)],[920])).
% 3.20/2.31 tff(922,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 3.20/2.31 inference(transitivity,[status(thm)],[921, 919])).
% 3.20/2.31 tff(923,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(924,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[923, 922])).
% 3.20/2.31 tff(925,plain,
% 3.20/2.31 ($false),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[924, 301, 918, 615, 616])).
% 3.20/2.31 tff(926,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,[]))).
% 3.20/2.31 tff(927,plain,
% 3.20/2.31 (~node21(c_e_h_1, c_r, s2, s3)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[926, 615])).
% 3.20/2.31 tff(928,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 3.20/2.31 tff(929,assumption,(node21(c_e_h_1, c_r, s1, s2)), introduced(assumption)).
% 3.20/2.31 tff(930,plain,
% 3.20/2.31 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[714, 711, 627])).
% 3.20/2.31 tff(931,plain,
% 3.20/2.31 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[718, 686, 930])).
% 3.20/2.31 tff(932,plain,
% 3.20/2.31 (~node9(c_e_h_1, c_m, s0)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[732, 729, 666])).
% 3.20/2.31 tff(933,plain,
% 3.20/2.31 ((~node10(c_e_h_1, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[881, 932])).
% 3.20/2.31 tff(934,plain,
% 3.20/2.31 (~node10(c_e_h_1, c_m, s0, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[933, 876])).
% 3.20/2.31 tff(935,plain,
% 3.20/2.31 (node11(c_e_h_1, c_m, s0, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[886, 934])).
% 3.20/2.31 tff(936,plain,
% 3.20/2.31 ($false),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[890, 867, 876, 935, 931])).
% 3.20/2.31 tff(937,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.31 tff(938,plain,
% 3.20/2.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, 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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(939,plain,
% 3.20/2.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(940,plain,
% 3.20/2.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[939, 938])).
% 3.20/2.31 tff(941,plain,
% 3.20/2.31 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[940, 900, 937])).
% 3.20/2.31 tff(942,plain,
% 3.20/2.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, 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))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(943,plain,
% 3.20/2.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(944,plain,
% 3.20/2.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[943, 942])).
% 3.20/2.31 tff(945,plain,
% 3.20/2.31 (~node20(c_e_h_1, c_r, s1)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[944, 914, 941])).
% 3.20/2.31 tff(946,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(947,plain,
% 3.20/2.31 ((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))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 3.20/2.31 inference(rewrite,[status(thm)],[])).
% 3.20/2.31 tff(948,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, 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)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2))))),
% 3.20/2.31 inference(monotonicity,[status(thm)],[947])).
% 3.20/2.31 tff(949,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, 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)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 3.20/2.31 inference(transitivity,[status(thm)],[948, 946])).
% 3.20/2.31 tff(950,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 3.20/2.31 inference(quant_inst,[status(thm)],[])).
% 3.20/2.31 tff(951,plain,
% 3.20/2.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1) | (~node21(c_e_h_1, c_r, s1, s2))),
% 3.20/2.31 inference(modus_ponens,[status(thm)],[950, 949])).
% 3.20/2.31 tff(952,plain,
% 3.20/2.31 ($false),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[951, 301, 945, 929, 928])).
% 3.20/2.31 tff(953,plain,((~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.31 tff(954,plain,
% 3.20/2.31 (~node21(c_e_h_1, c_r, s1, s2)),
% 3.20/2.31 inference(unit_resolution,[status(thm)],[953, 928])).
% 3.20/2.31 tff(955,plain,
% 3.20/2.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(956,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(957,plain,
% 3.20/2.32 ((~![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)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[956, 955])).
% 3.20/2.32 tff(958,plain,
% 3.20/2.32 (node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[957, 317, 181])).
% 3.20/2.32 tff(959,plain,
% 3.20/2.32 (node22(c_e_h_1, c_r, s1, s2)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[958, 954])).
% 3.20/2.32 tff(960,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s1)), introduced(assumption)).
% 3.20/2.32 tff(961,assumption,(node21(c_e_h_1, c_r, s0, s1)), introduced(assumption)).
% 3.20/2.32 tff(962,plain,
% 3.20/2.32 (((~![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, s0)) | m_c_h_element_v_out(c_e_h_1, 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_1, c_r, s0)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(963,plain,
% 3.20/2.32 ((~![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, s0)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(964,plain,
% 3.20/2.32 ((~![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, s0)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[963, 962])).
% 3.20/2.32 tff(965,plain,
% 3.20/2.32 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s0)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[964, 366, 790])).
% 3.20/2.32 tff(966,plain,
% 3.20/2.32 (((~![I0: $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, s0)) | m_and_h_gate_v_in1(c_e_h_1, 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_1, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s0))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(967,plain,
% 3.20/2.32 ((~![I0: $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, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s0))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(968,plain,
% 3.20/2.32 ((~![I0: $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, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s0)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[967, 966])).
% 3.20/2.32 tff(969,plain,
% 3.20/2.32 (~node20(c_e_h_1, c_r, s0)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[968, 287, 965])).
% 3.20/2.32 tff(970,plain,
% 3.20/2.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, 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)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(971,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(972,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[971, 970])).
% 3.20/2.32 tff(973,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[972, 301, 969, 961, 960])).
% 3.20/2.32 tff(974,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,[]))).
% 3.20/2.32 tff(975,plain,
% 3.20/2.32 (~node21(c_e_h_1, c_r, s0, s1)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[974, 960])).
% 3.20/2.32 tff(976,plain,
% 3.20/2.32 (((~![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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(977,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(978,plain,
% 3.20/2.32 ((~![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)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[977, 976])).
% 3.20/2.32 tff(979,plain,
% 3.20/2.32 (node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[978, 317, 96])).
% 3.20/2.32 tff(980,plain,
% 3.20/2.32 (node22(c_e_h_1, c_r, s0, s1)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[979, 975])).
% 3.20/2.32 tff(981,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s0)), introduced(assumption)).
% 3.20/2.32 tff(982,plain,
% 3.20/2.32 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(983,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[982, 9, 981])).
% 3.20/2.32 tff(984,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(985,plain,
% 3.20/2.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, 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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(986,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(987,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[986, 985])).
% 3.20/2.32 tff(988,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[987, 332, 984, 980, 960])).
% 3.20/2.32 tff(989,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(990,plain,
% 3.20/2.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, 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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(991,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(992,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[991, 990])).
% 3.20/2.32 tff(993,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[992, 332, 989, 959, 928])).
% 3.20/2.32 tff(994,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(995,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 3.20/2.32 tff(996,assumption,(node22(c_e_h_1, c_r, s2, s3)), introduced(assumption)).
% 3.20/2.32 tff(997,plain,
% 3.20/2.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, 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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(998,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(999,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[998, 997])).
% 3.20/2.32 tff(1000,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[999, 332, 615, 996, 995])).
% 3.20/2.32 tff(1001,plain,((~node22(c_e_h_1, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(1002,plain,
% 3.20/2.32 ((~node22(c_e_h_1, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1001, 994])).
% 3.20/2.32 tff(1003,plain,
% 3.20/2.32 (~node22(c_e_h_1, c_r, s2, s3)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1002, 615])).
% 3.20/2.32 tff(1004,plain,
% 3.20/2.32 (((~![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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1005,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1006,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 3.20/2.32 tff(1007,plain,
% 3.20/2.32 (node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1006, 317, 388])).
% 3.20/2.32 tff(1008,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1007, 1003, 927])).
% 3.20/2.32 tff(1009,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(1010,assumption,(m_user_v_ack(c_e_h_1, c_u, s3)), introduced(assumption)).
% 3.20/2.32 tff(1011,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 3.20/2.32 tff(1012,plain,
% 3.20/2.32 (((~![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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1013,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1014,plain,
% 3.20/2.32 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 3.20/2.32 tff(1015,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1014, 608, 1011, 1010])).
% 3.20/2.32 tff(1016,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,[]))).
% 3.20/2.32 tff(1017,plain,
% 3.20/2.32 (~m_user_v_ack(c_e_h_1, c_u, s3)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1016, 1009])).
% 3.20/2.32 tff(1018,assumption,(~m_user_v_ack(c_e_h_1, c_u, s3)), introduced(assumption)).
% 3.20/2.32 tff(1019,assumption,(node23(s3)), introduced(assumption)).
% 3.20/2.32 tff(1020,plain,
% 3.20/2.32 (^[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))))),
% 3.20/2.32 inference(bind,[status(th)],[])).
% 3.20/2.32 tff(1021,plain,
% 3.20/2.32 (![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)))),
% 3.20/2.32 inference(quant_intro,[status(thm)],[1020])).
% 3.20/2.32 tff(1022,plain,
% 3.20/2.32 (![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)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1023,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty1')).
% 3.20/2.32 tff(1024,plain,
% 3.20/2.32 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 3.20/2.32 tff(1025,plain,(
% 3.20/2.32 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 3.20/2.32 inference(skolemize,[status(sab)],[1024])).
% 3.20/2.32 tff(1026,plain,
% 3.20/2.32 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1025, 1021])).
% 3.20/2.32 tff(1027,plain,
% 3.20/2.32 (((~![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)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1028,plain,
% 3.20/2.32 ((~![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)))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1029,plain,
% 3.20/2.32 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 3.20/2.32 tff(1030,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1029, 1026, 1019, 1018])).
% 3.20/2.32 tff(1031,plain,((~node23(s3)) | m_user_v_ack(c_e_h_1, c_u, s3)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(1032,plain,
% 3.20/2.32 (~node23(s3)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1031, 1017])).
% 3.20/2.32 tff(1033,assumption,(node26(s3)), introduced(assumption)).
% 3.20/2.32 tff(1034,assumption,(~m_user_v_ack(c_e_h_3, c_u, s3)), introduced(assumption)).
% 3.20/2.32 tff(1035,plain,
% 3.20/2.32 (^[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)))),
% 3.20/2.32 inference(bind,[status(th)],[])).
% 3.20/2.32 tff(1036,plain,
% 3.20/2.32 (![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))),
% 3.20/2.32 inference(quant_intro,[status(thm)],[1035])).
% 3.20/2.32 tff(1037,plain,
% 3.20/2.32 (![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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1038,plain,
% 3.20/2.32 (^[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)))),
% 3.20/2.32 inference(bind,[status(th)],[])).
% 3.20/2.32 tff(1039,plain,
% 3.20/2.32 (![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))),
% 3.20/2.32 inference(quant_intro,[status(thm)],[1038])).
% 3.20/2.32 tff(1040,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty4')).
% 3.20/2.32 tff(1041,plain,
% 3.20/2.32 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 3.20/2.32 tff(1042,plain,
% 3.20/2.32 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1041, 1037])).
% 3.20/2.32 tff(1043,plain,(
% 3.20/2.32 ![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 3.20/2.32 inference(skolemize,[status(sab)],[1042])).
% 3.20/2.32 tff(1044,plain,
% 3.20/2.32 (![X: $i] : ((~node24(X)) | m_user_v_ack(c_e_h_3, c_u, X))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1043, 1036])).
% 3.20/2.32 tff(1045,plain,
% 3.20/2.32 (((~![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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1046,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1047,plain,
% 3.20/2.32 ((~![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)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 3.20/2.32 tff(1048,plain,
% 3.20/2.32 (~node24(s3)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1047, 1044, 1034])).
% 3.20/2.32 tff(1049,plain,
% 3.20/2.32 (^[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))))),
% 3.20/2.32 inference(bind,[status(th)],[])).
% 3.20/2.32 tff(1050,plain,
% 3.20/2.32 (![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)))),
% 3.20/2.32 inference(quant_intro,[status(thm)],[1049])).
% 3.20/2.32 tff(1051,plain,
% 3.20/2.32 (![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)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1052,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty6')).
% 3.20/2.32 tff(1053,plain,
% 3.20/2.32 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 3.20/2.32 tff(1054,plain,(
% 3.20/2.32 ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 3.20/2.32 inference(skolemize,[status(sab)],[1053])).
% 3.20/2.32 tff(1055,plain,
% 3.20/2.32 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 3.20/2.32 tff(1056,plain,
% 3.20/2.32 (((~![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)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1057,plain,
% 3.20/2.32 ((~![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)))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1058,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 3.20/2.32 tff(1059,plain,
% 3.20/2.32 (~node25(s3)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1058, 1055, 1034])).
% 3.20/2.32 tff(1060,assumption,(~node23(s3)), introduced(assumption)).
% 3.20/2.32 tff(1061,plain,
% 3.20/2.32 (^[X: $i] : refl((node23(X) | node24(X) | node25(X) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X))))),
% 3.20/2.32 inference(bind,[status(th)],[])).
% 3.20/2.32 tff(1062,plain,
% 3.20/2.32 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 3.20/2.32 inference(quant_intro,[status(thm)],[1061])).
% 3.20/2.32 tff(1063,plain,
% 3.20/2.32 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1064,plain,
% 3.20/2.32 (^[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)))))),
% 3.20/2.32 inference(bind,[status(th)],[])).
% 3.20/2.32 tff(1065,plain,
% 3.20/2.32 (![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 3.20/2.32 inference(quant_intro,[status(thm)],[1064])).
% 3.20/2.32 tff(1066,axiom,(![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty7')).
% 3.20/2.32 tff(1067,plain,
% 3.20/2.32 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 3.20/2.32 tff(1068,plain,
% 3.20/2.32 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1067, 1063])).
% 3.20/2.32 tff(1069,plain,(
% 3.20/2.32 ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 3.20/2.32 inference(skolemize,[status(sab)],[1068])).
% 3.20/2.32 tff(1070,plain,
% 3.20/2.32 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1069, 1062])).
% 3.20/2.32 tff(1071,plain,
% 3.20/2.32 (((~![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)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1072,plain,
% 3.20/2.32 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1073,plain,
% 3.20/2.32 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s3) | node24(s3) | node25(s3) | (~node26(s3))),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 3.20/2.32 tff(1074,plain,
% 3.20/2.32 (node24(s3) | node25(s3) | (~node26(s3))),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1073, 1070, 1060])).
% 3.20/2.32 tff(1075,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1074, 1059, 1048, 1033])).
% 3.20/2.32 tff(1076,plain,(m_user_v_ack(c_e_h_3, c_u, s3) | (~node26(s3)) | node23(s3)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(1077,plain,
% 3.20/2.32 (m_user_v_ack(c_e_h_3, c_u, s3) | (~node26(s3))),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1076, 1032])).
% 3.20/2.32 tff(1078,plain,
% 3.20/2.32 (~node26(s3)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1077, 614])).
% 3.20/2.32 tff(1079,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s1)), introduced(assumption)).
% 3.20/2.32 tff(1080,plain,
% 3.20/2.32 (((~![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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1081,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1082,plain,
% 3.20/2.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 3.20/2.32 tff(1083,plain,
% 3.20/2.32 ($false),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1082, 366, 152, 1079])).
% 3.20/2.32 tff(1084,plain,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.32 tff(1085,plain,
% 3.20/2.32 (((~![I0: $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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1086,plain,
% 3.20/2.32 ((~![I0: $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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1087,plain,
% 3.20/2.32 ((~![I0: $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)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 3.20/2.32 tff(1088,plain,
% 3.20/2.32 (~node20(c_e_h_3, c_r, s1)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1087, 287, 1084])).
% 3.20/2.32 tff(1089,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 3.20/2.32 tff(1090,assumption,(node21(c_e_h_3, c_r, s0, s1)), introduced(assumption)).
% 3.20/2.32 tff(1091,plain,
% 3.20/2.32 (((~![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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1092,plain,
% 3.20/2.32 ((~![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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1093,plain,
% 3.20/2.32 ((~![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)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 3.20/2.32 tff(1094,plain,
% 3.20/2.32 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1093, 366, 136])).
% 3.20/2.32 tff(1095,plain,
% 3.20/2.32 (((~![I0: $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))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1096,plain,
% 3.20/2.32 ((~![I0: $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))),
% 3.20/2.32 inference(quant_inst,[status(thm)],[])).
% 3.20/2.32 tff(1097,plain,
% 3.20/2.32 ((~![I0: $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)),
% 3.20/2.32 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 3.20/2.32 tff(1098,plain,
% 3.20/2.32 (~node20(c_e_h_3, c_r, s0)),
% 3.20/2.32 inference(unit_resolution,[status(thm)],[1097, 287, 1094])).
% 3.20/2.32 tff(1099,plain,
% 3.20/2.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 3.20/2.32 inference(rewrite,[status(thm)],[])).
% 3.20/2.32 tff(1100,plain,
% 3.20/2.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1101,plain,
% 3.20/2.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 3.20/2.33 tff(1102,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1101, 301, 1098, 1090, 1089])).
% 3.20/2.33 tff(1103,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,[]))).
% 3.20/2.33 tff(1104,plain,
% 3.20/2.33 (~node21(c_e_h_3, c_r, s0, s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1103, 1089])).
% 3.20/2.33 tff(1105,plain,
% 3.20/2.33 (((~![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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1106,plain,
% 3.20/2.33 ((~![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))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1107,plain,
% 3.20/2.33 ((~![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)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 3.20/2.33 tff(1108,plain,
% 3.20/2.33 (node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1107, 317, 96])).
% 3.20/2.33 tff(1109,plain,
% 3.20/2.33 (node22(c_e_h_3, c_r, s0, s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1108, 1104])).
% 3.20/2.33 tff(1110,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s0)), introduced(assumption)).
% 3.20/2.33 tff(1111,plain,
% 3.20/2.33 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1112,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1111, 9, 1110])).
% 3.20/2.33 tff(1113,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.33 tff(1114,plain,
% 3.20/2.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1115,plain,
% 3.20/2.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1116,plain,
% 3.20/2.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 3.20/2.33 tff(1117,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1116, 332, 1113, 1109, 1089])).
% 3.20/2.33 tff(1118,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.33 tff(1119,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 3.20/2.33 tff(1120,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 3.20/2.33 tff(1121,assumption,(~node20(c_e_h_3, c_r, s1)), introduced(assumption)).
% 3.20/2.33 tff(1122,assumption,(node21(c_e_h_3, c_r, s1, s2)), introduced(assumption)).
% 3.20/2.33 tff(1123,plain,
% 3.20/2.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1124,plain,
% 3.20/2.33 ((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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1125,plain,
% 3.20/2.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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))))),
% 3.20/2.33 inference(monotonicity,[status(thm)],[1124])).
% 3.20/2.33 tff(1126,plain,
% 3.20/2.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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)))),
% 3.20/2.33 inference(transitivity,[status(thm)],[1125, 1123])).
% 3.20/2.33 tff(1127,plain,
% 3.20/2.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1128,plain,
% 3.20/2.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s1) | (~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 3.20/2.33 tff(1129,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1128, 301, 1122, 1121, 1119])).
% 3.20/2.33 tff(1130,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,[]))).
% 3.20/2.33 tff(1131,plain,
% 3.20/2.33 (~node21(c_e_h_3, c_r, s1, s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1130, 1119, 1121])).
% 3.20/2.33 tff(1132,plain,
% 3.20/2.33 (((~![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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1133,plain,
% 3.20/2.33 ((~![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))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1134,plain,
% 3.20/2.33 ((~![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)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 3.20/2.33 tff(1135,plain,
% 3.20/2.33 (node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1134, 317, 181])).
% 3.20/2.33 tff(1136,plain,
% 3.20/2.33 (node22(c_e_h_3, c_r, s1, s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1135, 1131])).
% 3.20/2.33 tff(1137,plain,
% 3.20/2.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1138,plain,
% 3.20/2.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_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))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1139,plain,
% 3.20/2.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 3.20/2.33 tff(1140,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1139, 332, 1136, 1120, 1119])).
% 3.20/2.33 tff(1141,plain,((~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) | node20(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.33 tff(1142,plain,
% 3.20/2.33 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | node20(c_e_h_3, c_r, s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1141, 1118])).
% 3.20/2.33 tff(1143,plain,
% 3.20/2.33 (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1142, 1088])).
% 3.20/2.33 tff(1144,assumption,(m_user_v_ack(c_e_h_3, c_u, s2)), introduced(assumption)).
% 3.20/2.33 tff(1145,plain,
% 3.20/2.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, 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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1146,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1147,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 3.20/2.33 tff(1148,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1147, 608, 1144, 1143])).
% 3.20/2.33 tff(1149,plain,(~m_user_v_ack(c_e_h_3, c_u, s2)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.33 tff(1150,plain,
% 3.20/2.33 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | ((~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1151,plain,
% 3.20/2.33 ((m_user_v_ack(c_e_h_3, c_u, s2) | (~node25(s2))) <=> ((~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1152,plain,
% 3.20/2.33 (((~![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)))) | ((~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2)))),
% 3.20/2.33 inference(monotonicity,[status(thm)],[1151])).
% 3.20/2.33 tff(1153,plain,
% 3.20/2.33 (((~![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)))) | (~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2))),
% 3.20/2.33 inference(transitivity,[status(thm)],[1152, 1150])).
% 3.20/2.33 tff(1154,plain,
% 3.20/2.33 ((~![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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1155,plain,
% 3.20/2.33 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s2)) | m_user_v_ack(c_e_h_3, c_u, s2)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 3.20/2.33 tff(1156,plain,
% 3.20/2.33 (~node25(s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1155, 1055, 1149])).
% 3.20/2.33 tff(1157,plain,
% 3.20/2.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1158,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1159,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 3.20/2.33 tff(1160,plain,
% 3.20/2.33 (~m_user_v_ack(c_e_h_1, c_u, s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1159, 608, 994])).
% 3.20/2.33 tff(1161,plain,
% 3.20/2.33 (^[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))))),
% 3.20/2.33 inference(bind,[status(th)],[])).
% 3.20/2.33 tff(1162,plain,
% 3.20/2.33 (![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)))),
% 3.20/2.33 inference(quant_intro,[status(thm)],[1161])).
% 3.20/2.33 tff(1163,plain,
% 3.20/2.33 (![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1164,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty3')).
% 3.20/2.33 tff(1165,plain,
% 3.20/2.33 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 3.20/2.33 tff(1166,plain,(
% 3.20/2.33 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 3.20/2.33 inference(skolemize,[status(sab)],[1165])).
% 3.20/2.33 tff(1167,plain,
% 3.20/2.33 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1166, 1162])).
% 3.20/2.33 tff(1168,plain,
% 3.20/2.33 (((~![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1169,plain,
% 3.20/2.33 ((~![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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1170,plain,
% 3.20/2.33 ((~![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))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 3.20/2.33 tff(1171,plain,
% 3.20/2.33 (~node24(s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1170, 1167, 1160])).
% 3.20/2.33 tff(1172,plain,
% 3.20/2.33 (((~![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1173,plain,
% 3.20/2.33 ((~![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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1174,plain,
% 3.20/2.33 ((~![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))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 3.20/2.33 tff(1175,plain,
% 3.20/2.33 (~node23(s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1174, 1026, 1160])).
% 3.20/2.33 tff(1176,plain,
% 3.20/2.33 (((~![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1177,plain,
% 3.20/2.33 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1178,plain,
% 3.20/2.33 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s2) | node24(s2) | node25(s2) | (~node26(s2))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 3.20/2.33 tff(1179,plain,
% 3.20/2.33 (node25(s2) | (~node26(s2))),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1178, 1070, 1175, 1171])).
% 3.20/2.33 tff(1180,plain,
% 3.20/2.33 (~node26(s2)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1179, 1156])).
% 3.20/2.33 tff(1181,assumption,(~node26(s4)), introduced(assumption)).
% 3.20/2.33 tff(1182,assumption,(~node26(s3)), introduced(assumption)).
% 3.20/2.33 tff(1183,assumption,(~node26(s2)), introduced(assumption)).
% 3.20/2.33 tff(1184,plain,
% 3.20/2.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1185,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1186,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 3.20/2.33 tff(1187,plain,
% 3.20/2.33 (~m_user_v_ack(c_e_h_3, c_u, s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1186, 608, 1118])).
% 3.20/2.33 tff(1188,plain,
% 3.20/2.33 (((~![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, s1) | (~node25(s1)))) <=> ((~![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, s1) | (~node25(s1)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1189,plain,
% 3.20/2.33 ((~![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, s1) | (~node25(s1)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1190,plain,
% 3.20/2.33 ((~![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, s1) | (~node25(s1))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 3.20/2.33 tff(1191,plain,
% 3.20/2.33 (~node25(s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1190, 1055, 1187])).
% 3.20/2.33 tff(1192,plain,
% 3.20/2.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1193,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1194,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 3.20/2.33 tff(1195,plain,
% 3.20/2.33 (~m_user_v_ack(c_e_h_1, c_u, s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1194, 608, 989])).
% 3.20/2.33 tff(1196,plain,
% 3.20/2.33 (((~![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1197,plain,
% 3.20/2.33 ((~![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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1198,plain,
% 3.20/2.33 ((~![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))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 3.20/2.33 tff(1199,plain,
% 3.20/2.33 (~node24(s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1198, 1167, 1195])).
% 3.20/2.33 tff(1200,plain,
% 3.20/2.33 (((~![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1201,plain,
% 3.20/2.33 ((~![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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1202,plain,
% 3.20/2.33 ((~![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))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 3.20/2.33 tff(1203,plain,
% 3.20/2.33 (~node23(s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1202, 1026, 1195])).
% 3.20/2.33 tff(1204,plain,
% 3.20/2.33 (((~![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1205,plain,
% 3.20/2.33 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1206,plain,
% 3.20/2.33 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s1) | node24(s1) | node25(s1) | (~node26(s1))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 3.20/2.33 tff(1207,plain,
% 3.20/2.33 (node25(s1) | (~node26(s1))),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1206, 1070, 1203, 1199])).
% 3.20/2.33 tff(1208,plain,
% 3.20/2.33 (~node26(s1)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1207, 1191])).
% 3.20/2.33 tff(1209,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s0)), introduced(assumption)).
% 3.20/2.33 tff(1210,plain,
% 3.20/2.33 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1211,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1210, 9, 1209])).
% 3.20/2.33 tff(1212,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.33 tff(1213,plain,
% 3.20/2.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1214,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1215,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 3.20/2.33 tff(1216,plain,
% 3.20/2.33 (~m_user_v_ack(c_e_h_2, c_u, s0)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1215, 608, 1212])).
% 3.20/2.33 tff(1217,assumption,(node25(s0)), introduced(assumption)).
% 3.20/2.33 tff(1218,plain,
% 3.20/2.33 (^[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))))),
% 3.20/2.33 inference(bind,[status(th)],[])).
% 3.20/2.33 tff(1219,plain,
% 3.20/2.33 (![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)))),
% 3.20/2.33 inference(quant_intro,[status(thm)],[1218])).
% 3.20/2.33 tff(1220,plain,
% 3.20/2.33 (![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1221,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty5')).
% 3.20/2.33 tff(1222,plain,
% 3.20/2.33 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 3.20/2.33 tff(1223,plain,(
% 3.20/2.33 ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 3.20/2.33 inference(skolemize,[status(sab)],[1222])).
% 3.20/2.33 tff(1224,plain,
% 3.20/2.33 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1223, 1219])).
% 3.20/2.33 tff(1225,plain,
% 3.20/2.33 (((~![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)))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1226,plain,
% 3.20/2.33 ((~![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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1227,plain,
% 3.20/2.33 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0))),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 3.20/2.33 tff(1228,plain,
% 3.20/2.33 ($false),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1227, 1224, 1217, 1216])).
% 3.20/2.33 tff(1229,plain,(~node25(s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.33 tff(1230,plain,
% 3.20/2.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_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))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1231,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1232,plain,
% 3.20/2.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 3.20/2.33 tff(1233,plain,
% 3.20/2.33 (~m_user_v_ack(c_e_h_1, c_u, s0)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1232, 608, 984])).
% 3.20/2.33 tff(1234,plain,
% 3.20/2.33 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1235,plain,
% 3.20/2.33 ((m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0))) <=> ((~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 3.20/2.33 inference(rewrite,[status(thm)],[])).
% 3.20/2.33 tff(1236,plain,
% 3.20/2.33 (((~![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)))) | ((~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0)))),
% 3.20/2.33 inference(monotonicity,[status(thm)],[1235])).
% 3.20/2.33 tff(1237,plain,
% 3.20/2.33 (((~![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)))) | (~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 3.20/2.33 inference(transitivity,[status(thm)],[1236, 1234])).
% 3.20/2.33 tff(1238,plain,
% 3.20/2.33 ((~![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)))),
% 3.20/2.33 inference(quant_inst,[status(thm)],[])).
% 3.20/2.33 tff(1239,plain,
% 3.20/2.33 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s0)) | m_user_v_ack(c_e_h_1, c_u, s0)),
% 3.20/2.33 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 3.20/2.33 tff(1240,plain,
% 3.20/2.33 (~node24(s0)),
% 3.20/2.33 inference(unit_resolution,[status(thm)],[1239, 1167, 1233])).
% 3.20/2.33 tff(1241,plain,
% 3.20/2.33 (((~![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, s0) | (~node23(s0)))) <=> ((~![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, s0) | (~node23(s0)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1242,plain,
% 3.20/2.34 ((~![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, s0) | (~node23(s0)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1243,plain,
% 3.20/2.34 ((~![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, s0) | (~node23(s0))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 3.20/2.34 tff(1244,plain,
% 3.20/2.34 (~node23(s0)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1243, 1026, 1233])).
% 3.20/2.34 tff(1245,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1246,plain,
% 3.20/2.34 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1247,plain,
% 3.20/2.34 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s0) | node24(s0) | node25(s0) | (~node26(s0))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 3.20/2.34 tff(1248,plain,
% 3.20/2.34 (node25(s0) | (~node26(s0))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1247, 1070, 1244, 1240])).
% 3.20/2.34 tff(1249,plain,
% 3.20/2.34 (~node26(s0)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1248, 1229])).
% 3.20/2.34 tff(1250,plain,
% 3.20/2.34 (until27(s0) <=> until27(s0)),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1251,axiom,(until27(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty15')).
% 3.20/2.34 tff(1252,plain,
% 3.20/2.34 (until27(s0)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 3.20/2.34 tff(1253,plain,
% 3.20/2.34 (^[X: $i] : refl(((~until27(X)) | node26(X) | xuntil28(X)) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1254,plain,
% 3.20/2.34 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1253])).
% 3.20/2.34 tff(1255,plain,
% 3.20/2.34 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1256,plain,
% 3.20/2.34 (^[X: $i] : rewrite(((node26(X) | xuntil28(X)) | (~until27(X))) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1257,plain,
% 3.20/2.34 (![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X))) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1256])).
% 3.20/2.34 tff(1258,axiom,(![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty8')).
% 3.20/2.34 tff(1259,plain,
% 3.20/2.34 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 3.20/2.34 tff(1260,plain,
% 3.20/2.34 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1259, 1255])).
% 3.20/2.34 tff(1261,plain,(
% 3.20/2.34 ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 3.20/2.34 inference(skolemize,[status(sab)],[1260])).
% 3.20/2.34 tff(1262,plain,
% 3.20/2.34 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1261, 1254])).
% 3.20/2.34 tff(1263,plain,
% 3.20/2.34 (((~![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))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1264,plain,
% 3.20/2.34 (((~until27(s0)) | node26(s0) | xuntil28(s0)) <=> (xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1265,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(monotonicity,[status(thm)],[1264])).
% 3.20/2.34 tff(1266,plain,
% 3.20/2.34 (((~![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))),
% 3.20/2.34 inference(transitivity,[status(thm)],[1265, 1263])).
% 3.20/2.34 tff(1267,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1268,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 3.20/2.34 tff(1269,plain,
% 3.20/2.34 (xuntil28(s0) | node26(s0)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1268, 1262, 1252])).
% 3.20/2.34 tff(1270,plain,
% 3.20/2.34 (xuntil28(s0)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1269, 1249])).
% 3.20/2.34 tff(1271,plain,
% 3.20/2.34 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1272,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1271])).
% 3.20/2.34 tff(1273,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1274,plain,
% 3.20/2.34 (^[Y: $i, X: $i] : rewrite(((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1275,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1274])).
% 3.20/2.34 tff(1276,axiom,(![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty9')).
% 3.20/2.34 tff(1277,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 3.20/2.34 tff(1278,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1277, 1273])).
% 3.20/2.34 tff(1279,plain,(
% 3.20/2.34 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 3.20/2.34 inference(skolemize,[status(sab)],[1278])).
% 3.20/2.34 tff(1280,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1279, 1272])).
% 3.20/2.34 tff(1281,plain,
% 3.20/2.34 (((~![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))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1282,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1283,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 3.20/2.34 tff(1284,plain,
% 3.20/2.34 ((~xuntil28(s0)) | until27(s1)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1283, 92, 1280])).
% 3.20/2.34 tff(1285,plain,
% 3.20/2.34 (until27(s1)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1284, 1270])).
% 3.20/2.34 tff(1286,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1287,plain,
% 3.20/2.34 (((~until27(s1)) | node26(s1) | xuntil28(s1)) <=> (xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1288,plain,
% 3.20/2.34 (((~![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))))),
% 3.20/2.34 inference(monotonicity,[status(thm)],[1287])).
% 3.20/2.34 tff(1289,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(transitivity,[status(thm)],[1288, 1286])).
% 3.20/2.34 tff(1290,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1291,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 3.20/2.34 tff(1292,plain,
% 3.20/2.34 (xuntil28(s1) | node26(s1)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1291, 1262, 1285])).
% 3.20/2.34 tff(1293,plain,
% 3.20/2.34 (xuntil28(s1)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1292, 1208])).
% 3.20/2.34 tff(1294,plain,
% 3.20/2.34 (((~![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))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1295,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1296,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 3.20/2.34 tff(1297,plain,
% 3.20/2.34 ((~xuntil28(s1)) | until27(s2)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1296, 177, 1280])).
% 3.20/2.34 tff(1298,plain,
% 3.20/2.34 (until27(s2)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1297, 1293])).
% 3.20/2.34 tff(1299,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1300,plain,
% 3.20/2.34 (((~until27(s2)) | node26(s2) | xuntil28(s2)) <=> (xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1301,plain,
% 3.20/2.34 (((~![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))))),
% 3.20/2.34 inference(monotonicity,[status(thm)],[1300])).
% 3.20/2.34 tff(1302,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(transitivity,[status(thm)],[1301, 1299])).
% 3.20/2.34 tff(1303,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1304,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 3.20/2.34 tff(1305,plain,
% 3.20/2.34 (xuntil28(s2) | node26(s2)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1304, 1262, 1298])).
% 3.20/2.34 tff(1306,plain,
% 3.20/2.34 (xuntil28(s2)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1305, 1183])).
% 3.20/2.34 tff(1307,plain,
% 3.20/2.34 (((~![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))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1308,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1309,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 3.20/2.34 tff(1310,plain,
% 3.20/2.34 ((~xuntil28(s2)) | until27(s3)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1309, 384, 1280])).
% 3.20/2.34 tff(1311,plain,
% 3.20/2.34 (until27(s3)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1310, 1306])).
% 3.20/2.34 tff(1312,plain,
% 3.20/2.34 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1313,plain,
% 3.20/2.34 (((~until27(s3)) | node26(s3) | xuntil28(s3)) <=> (xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1314,plain,
% 3.20/2.34 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3))))),
% 3.20/2.34 inference(monotonicity,[status(thm)],[1313])).
% 3.20/2.34 tff(1315,plain,
% 3.20/2.34 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 3.20/2.34 inference(transitivity,[status(thm)],[1314, 1312])).
% 3.20/2.34 tff(1316,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1317,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 3.20/2.34 tff(1318,plain,
% 3.20/2.34 (xuntil28(s3) | node26(s3)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1317, 1262, 1311])).
% 3.20/2.34 tff(1319,plain,
% 3.20/2.34 (xuntil28(s3)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1318, 1182])).
% 3.20/2.34 tff(1320,plain,
% 3.20/2.34 (succ(s3, s4) <=> succ(s3, s4)),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1321,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 3.20/2.34 tff(1322,plain,
% 3.20/2.34 (succ(s3, s4)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 3.20/2.34 tff(1323,plain,
% 3.20/2.34 (((~![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))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1324,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1325,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 3.20/2.34 tff(1326,plain,
% 3.20/2.34 ((~xuntil28(s3)) | until27(s4)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1325, 1322, 1280])).
% 3.20/2.34 tff(1327,plain,
% 3.20/2.34 (until27(s4)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1326, 1319])).
% 3.20/2.34 tff(1328,plain,
% 3.20/2.34 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1329,plain,
% 3.20/2.34 (((~until27(s4)) | node26(s4) | xuntil28(s4)) <=> (xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1330,plain,
% 3.20/2.34 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4))))),
% 3.20/2.34 inference(monotonicity,[status(thm)],[1329])).
% 3.20/2.34 tff(1331,plain,
% 3.20/2.34 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 3.20/2.34 inference(transitivity,[status(thm)],[1330, 1328])).
% 3.20/2.34 tff(1332,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1333,plain,
% 3.20/2.34 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 3.20/2.34 tff(1334,plain,
% 3.20/2.34 (xuntil28(s4) | node26(s4)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1333, 1262, 1327])).
% 3.20/2.34 tff(1335,plain,
% 3.20/2.34 (xuntil28(s4)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1334, 1181])).
% 3.20/2.34 tff(1336,plain,
% 3.20/2.34 (^[X: $i] : refl(((~last(X)) | (~xuntil2p30(X))) <=> ((~last(X)) | (~xuntil2p30(X))))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1337,plain,
% 3.20/2.34 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1336])).
% 3.20/2.34 tff(1338,plain,
% 3.20/2.34 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1339,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty14')).
% 3.20/2.34 tff(1340,plain,
% 3.20/2.34 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 3.20/2.34 tff(1341,plain,(
% 3.20/2.34 ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(skolemize,[status(sab)],[1340])).
% 3.20/2.34 tff(1342,plain,
% 3.20/2.34 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1341, 1337])).
% 3.20/2.34 tff(1343,plain,
% 3.20/2.34 (last(s4) <=> last(s4)),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1344,axiom,(last(s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 3.20/2.34 tff(1345,plain,
% 3.20/2.34 (last(s4)),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 3.20/2.34 tff(1346,plain,
% 3.20/2.34 (((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s4)) | (~xuntil2p30(s4)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s4)) | (~xuntil2p30(s4)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1347,plain,
% 3.20/2.34 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s4)) | (~xuntil2p30(s4)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1348,plain,
% 3.20/2.34 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s4)) | (~xuntil2p30(s4))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 3.20/2.34 tff(1349,plain,
% 3.20/2.34 (~xuntil2p30(s4)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1348, 1345, 1342])).
% 3.20/2.34 tff(1350,plain,
% 3.20/2.34 (^[X: $i] : refl((node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1351,plain,
% 3.20/2.34 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1350])).
% 3.20/2.34 tff(1352,plain,
% 3.20/2.34 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1353,plain,
% 3.20/2.34 (^[X: $i] : rewrite(((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1354,plain,
% 3.20/2.34 (![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1353])).
% 3.20/2.34 tff(1355,axiom,(![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty12')).
% 3.20/2.34 tff(1356,plain,
% 3.20/2.34 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 3.20/2.34 tff(1357,plain,
% 3.20/2.34 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1356, 1352])).
% 3.20/2.34 tff(1358,plain,(
% 3.20/2.34 ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 3.20/2.34 inference(skolemize,[status(sab)],[1357])).
% 3.20/2.34 tff(1359,plain,
% 3.20/2.34 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1358, 1351])).
% 3.20/2.34 tff(1360,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1361,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1362,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 3.20/2.34 tff(1363,plain,
% 3.20/2.34 (node26(s4) | (~until2p29(s4))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1362, 1359, 1349])).
% 3.20/2.34 tff(1364,plain,
% 3.20/2.34 (~until2p29(s4)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1363, 1181])).
% 3.20/2.34 tff(1365,plain,
% 3.20/2.34 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1366,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1365])).
% 3.20/2.34 tff(1367,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1368,plain,
% 3.20/2.34 (^[Y: $i, X: $i] : rewrite(((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1369,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1368])).
% 3.20/2.34 tff(1370,axiom,(![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty13')).
% 3.20/2.34 tff(1371,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 3.20/2.34 tff(1372,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1371, 1367])).
% 3.20/2.34 tff(1373,plain,(
% 3.20/2.34 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(skolemize,[status(sab)],[1372])).
% 3.20/2.34 tff(1374,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1373, 1366])).
% 3.20/2.34 tff(1375,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1376,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1377,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 3.20/2.34 tff(1378,plain,
% 3.20/2.34 (until2p29(s4) | (~xuntil2p30(s3))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1377, 1322, 1374])).
% 3.20/2.34 tff(1379,plain,
% 3.20/2.34 (~xuntil2p30(s3)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1378, 1364])).
% 3.20/2.34 tff(1380,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1381,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1382,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 3.20/2.34 tff(1383,plain,
% 3.20/2.34 (xuntil2p30(s3) | (~until2p29(s3))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1382, 1359, 1182])).
% 3.20/2.34 tff(1384,plain,
% 3.20/2.34 (~until2p29(s3)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1383, 1379])).
% 3.20/2.34 tff(1385,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1386,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1387,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 3.20/2.34 tff(1388,plain,
% 3.20/2.34 (until2p29(s3) | (~xuntil2p30(s2))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1387, 384, 1374])).
% 3.20/2.34 tff(1389,plain,
% 3.20/2.34 (~xuntil2p30(s2)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1388, 1384])).
% 3.20/2.34 tff(1390,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1391,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1392,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 3.20/2.34 tff(1393,plain,
% 3.20/2.34 (xuntil2p30(s2) | (~until2p29(s2))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1392, 1359, 1183])).
% 3.20/2.34 tff(1394,plain,
% 3.20/2.34 (~until2p29(s2)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1393, 1389])).
% 3.20/2.34 tff(1395,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1396,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1397,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 3.20/2.34 tff(1398,plain,
% 3.20/2.34 (until2p29(s2) | (~xuntil2p30(s1))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1397, 177, 1374])).
% 3.20/2.34 tff(1399,plain,
% 3.20/2.34 (~xuntil2p30(s1)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1398, 1394])).
% 3.20/2.34 tff(1400,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1401,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1402,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 3.20/2.34 tff(1403,plain,
% 3.20/2.34 (xuntil2p30(s1) | (~until2p29(s1))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1402, 1359, 1208])).
% 3.20/2.34 tff(1404,plain,
% 3.20/2.34 (~until2p29(s1)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1403, 1399])).
% 3.20/2.34 tff(1405,plain,
% 3.20/2.34 (^[Y: $i, X: $i] : refl(((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1406,plain,
% 3.20/2.34 (![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))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1405])).
% 3.20/2.34 tff(1407,plain,
% 3.20/2.34 (![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))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1408,plain,
% 3.20/2.34 (^[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))))),
% 3.20/2.34 inference(bind,[status(th)],[])).
% 3.20/2.34 tff(1409,plain,
% 3.20/2.34 (![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))),
% 3.20/2.34 inference(quant_intro,[status(thm)],[1408])).
% 3.20/2.34 tff(1410,axiom,(![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty11')).
% 3.20/2.34 tff(1411,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 3.20/2.34 tff(1412,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1411, 1407])).
% 3.20/2.34 tff(1413,plain,(
% 3.20/2.34 ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 3.20/2.34 inference(skolemize,[status(sab)],[1412])).
% 3.20/2.34 tff(1414,plain,
% 3.20/2.34 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1413, 1406])).
% 3.20/2.34 tff(1415,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1416,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1417,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 3.20/2.34 tff(1418,plain,
% 3.20/2.34 (until2p29(s1) | (~xuntil2p30(s0))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1417, 92, 1374])).
% 3.20/2.34 tff(1419,plain,
% 3.20/2.34 (~xuntil2p30(s0)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1418, 1404])).
% 3.20/2.34 tff(1420,plain,
% 3.20/2.34 (((~![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)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1421,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1422,plain,
% 3.20/2.34 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 3.20/2.34 tff(1423,plain,
% 3.20/2.34 (xuntil2p30(s0) | (~until2p29(s0))),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1422, 1359, 1249])).
% 3.20/2.34 tff(1424,plain,
% 3.20/2.34 (~until2p29(s0)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1423, 1419])).
% 3.20/2.34 tff(1425,assumption,(~until2p29(s0)), introduced(assumption)).
% 3.20/2.34 tff(1426,assumption,(xuntil28(s4)), introduced(assumption)).
% 3.20/2.34 tff(1427,assumption,(trans(s4, s0)), introduced(assumption)).
% 3.20/2.34 tff(1428,plain,
% 3.20/2.34 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1429,plain,
% 3.20/2.34 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0)) <=> ((~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1430,plain,
% 3.20/2.34 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0))))),
% 3.20/2.34 inference(monotonicity,[status(thm)],[1429])).
% 3.20/2.34 tff(1431,plain,
% 3.20/2.34 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0)))),
% 3.20/2.34 inference(transitivity,[status(thm)],[1430, 1428])).
% 3.20/2.34 tff(1432,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s0)) | until2p29(s0))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1433,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s4)) | (~xuntil28(s4)) | until2p29(s0) | (~trans(s4, s0))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 3.20/2.34 tff(1434,plain,
% 3.20/2.34 ($false),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1433, 1345, 1427, 1414, 1426, 1425])).
% 3.20/2.34 tff(1435,plain,((~trans(s4, s0)) | (~xuntil28(s4)) | until2p29(s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.34 tff(1436,plain,
% 3.20/2.34 (~trans(s4, s0)),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1435, 1335, 1424])).
% 3.20/2.34 tff(1437,assumption,(~until2p29(s4)), introduced(assumption)).
% 3.20/2.34 tff(1438,assumption,(trans(s4, s4)), introduced(assumption)).
% 3.20/2.34 tff(1439,plain,
% 3.20/2.34 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1440,plain,
% 3.20/2.34 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4)) <=> (until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))),
% 3.20/2.34 inference(rewrite,[status(thm)],[])).
% 3.20/2.34 tff(1441,plain,
% 3.20/2.34 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4))))),
% 3.20/2.34 inference(monotonicity,[status(thm)],[1440])).
% 3.20/2.34 tff(1442,plain,
% 3.20/2.34 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)))),
% 3.20/2.34 inference(transitivity,[status(thm)],[1441, 1439])).
% 3.20/2.34 tff(1443,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4)) | until2p29(s4))),
% 3.20/2.34 inference(quant_inst,[status(thm)],[])).
% 3.20/2.34 tff(1444,plain,
% 3.20/2.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s4))),
% 3.20/2.34 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 3.20/2.34 tff(1445,plain,
% 3.20/2.34 ($false),
% 3.20/2.34 inference(unit_resolution,[status(thm)],[1444, 1345, 1438, 1414, 1437, 1426])).
% 3.20/2.35 tff(1446,plain,((~trans(s4, s4)) | until2p29(s4) | (~xuntil28(s4))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.35 tff(1447,plain,
% 3.20/2.35 (~trans(s4, s4)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1446, 1364, 1335])).
% 3.20/2.35 tff(1448,assumption,(~until2p29(s3)), introduced(assumption)).
% 3.20/2.35 tff(1449,assumption,(trans(s4, s3)), introduced(assumption)).
% 3.20/2.35 tff(1450,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1451,plain,
% 3.20/2.35 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3)) <=> (until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1452,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3))))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1451])).
% 3.20/2.35 tff(1453,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1452, 1450])).
% 3.20/2.35 tff(1454,plain,
% 3.20/2.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3)) | until2p29(s3))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1455,plain,
% 3.20/2.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s3))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 3.20/2.35 tff(1456,plain,
% 3.20/2.35 ($false),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1455, 1345, 1449, 1414, 1448, 1426])).
% 3.20/2.35 tff(1457,plain,((~trans(s4, s3)) | until2p29(s3) | (~xuntil28(s4))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.35 tff(1458,plain,
% 3.20/2.35 (~trans(s4, s3)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1457, 1384, 1335])).
% 3.20/2.35 tff(1459,plain,
% 3.20/2.35 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 3.20/2.35 inference(bind,[status(th)],[])).
% 3.20/2.35 tff(1460,plain,
% 3.20/2.35 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 3.20/2.35 inference(quant_intro,[status(thm)],[1459])).
% 3.20/2.35 tff(1461,plain,
% 3.20/2.35 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1462,plain,
% 3.20/2.35 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 3.20/2.35 inference(bind,[status(th)],[])).
% 3.20/2.35 tff(1463,plain,
% 3.20/2.35 (![X: $i] : ((loop | (~last(X))) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 3.20/2.35 inference(quant_intro,[status(thm)],[1462])).
% 3.20/2.35 tff(1464,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty10')).
% 3.20/2.35 tff(1465,plain,
% 3.20/2.35 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 3.20/2.35 tff(1466,plain,
% 3.20/2.35 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1465, 1461])).
% 3.20/2.35 tff(1467,plain,(
% 3.20/2.35 ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 3.20/2.35 inference(skolemize,[status(sab)],[1466])).
% 3.20/2.35 tff(1468,plain,
% 3.20/2.35 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1467, 1460])).
% 3.20/2.35 tff(1469,plain,
% 3.20/2.35 (((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s4)) | (~xuntil28(s4)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s4)) | (~xuntil28(s4)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1470,plain,
% 3.20/2.35 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s4)) | (~xuntil28(s4)))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1471,plain,
% 3.20/2.35 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s4)) | (~xuntil28(s4))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 3.20/2.35 tff(1472,plain,
% 3.20/2.35 (loop | (~xuntil28(s4))),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1471, 1345, 1468])).
% 3.20/2.35 tff(1473,plain,
% 3.20/2.35 (loop),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1472, 1335])).
% 3.20/2.35 tff(1474,assumption,(~until2p29(s2)), introduced(assumption)).
% 3.20/2.35 tff(1475,assumption,(trans(s4, s2)), introduced(assumption)).
% 3.20/2.35 tff(1476,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1477,plain,
% 3.20/2.35 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2)) <=> (until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1478,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2))))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1477])).
% 3.20/2.35 tff(1479,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1478, 1476])).
% 3.20/2.35 tff(1480,plain,
% 3.20/2.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2)) | until2p29(s2))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1481,plain,
% 3.20/2.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s2))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 3.20/2.35 tff(1482,plain,
% 3.20/2.35 ($false),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1481, 1345, 1475, 1414, 1474, 1426])).
% 3.20/2.35 tff(1483,plain,((~trans(s4, s2)) | until2p29(s2) | (~xuntil28(s4))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.35 tff(1484,plain,
% 3.20/2.35 (~trans(s4, s2)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1483, 1394, 1335])).
% 3.20/2.35 tff(1485,plain,
% 3.20/2.35 (((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1486,plain,
% 3.20/2.35 ((((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3)) | trans(s4, s4)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1487,plain,
% 3.20/2.35 ((((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2)) | trans(s4, s3)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1488,plain,
% 3.20/2.35 ((((~loop) | trans(s4, s0) | trans(s4, s1)) | trans(s4, s2)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1489,plain,
% 3.20/2.35 ((((~loop) | trans(s4, s0)) | trans(s4, s1)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1490,plain,
% 3.20/2.35 (((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) <=> (((~loop) | trans(s4, s0) | trans(s4, s1)) | trans(s4, s2))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1489])).
% 3.20/2.35 tff(1491,plain,
% 3.20/2.35 (((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1490, 1488])).
% 3.20/2.35 tff(1492,plain,
% 3.20/2.35 ((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) <=> (((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2)) | trans(s4, s3))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1491])).
% 3.20/2.35 tff(1493,plain,
% 3.20/2.35 ((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1492, 1487])).
% 3.20/2.35 tff(1494,plain,
% 3.20/2.35 (((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) | trans(s4, s4)) <=> (((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3)) | trans(s4, s4))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1493])).
% 3.20/2.35 tff(1495,plain,
% 3.20/2.35 (((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) | trans(s4, s4)) <=> ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1494, 1486])).
% 3.20/2.35 tff(1496,axiom,((((((~loop) | trans(s4, s0)) | trans(s4, s1)) | trans(s4, s2)) | trans(s4, s3)) | trans(s4, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 3.20/2.35 tff(1497,plain,
% 3.20/2.35 ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4)),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 3.20/2.35 tff(1498,plain,
% 3.20/2.35 ((~loop) | trans(s4, s0) | trans(s4, s1) | trans(s4, s2) | trans(s4, s3) | trans(s4, s4)),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1497, 1485])).
% 3.20/2.35 tff(1499,plain,
% 3.20/2.35 (trans(s4, s1)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1498, 1484, 1473, 1458, 1447, 1436])).
% 3.20/2.35 tff(1500,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1501,plain,
% 3.20/2.35 (((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1)) <=> (until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1502,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1))))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1501])).
% 3.20/2.35 tff(1503,plain,
% 3.20/2.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1502, 1500])).
% 3.20/2.35 tff(1504,plain,
% 3.20/2.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1)) | until2p29(s1))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1505,plain,
% 3.20/2.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s4)) | (~xuntil28(s4)) | (~trans(s4, s1))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 3.20/2.35 tff(1506,plain,
% 3.20/2.35 ($false),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1505, 1345, 1499, 1414, 1404, 1335])).
% 3.20/2.35 tff(1507,plain,(node26(s4) | node26(s2) | node26(s3)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.35 tff(1508,plain,
% 3.20/2.35 (node26(s4) | node26(s3)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1507, 1180])).
% 3.20/2.35 tff(1509,plain,
% 3.20/2.35 (node26(s4)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1508, 1078])).
% 3.20/2.35 tff(1510,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 3.20/2.35 tff(1511,assumption,(node11(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 3.20/2.35 tff(1512,plain,
% 3.20/2.35 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[820, 655])).
% 3.20/2.35 tff(1513,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1514,plain,
% 3.20/2.35 ((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)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1515,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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))))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1514])).
% 3.20/2.35 tff(1516,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1515, 1513])).
% 3.20/2.35 tff(1517,plain,
% 3.20/2.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~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)))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1518,plain,
% 3.20/2.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 3.20/2.35 tff(1519,plain,
% 3.20/2.35 ($false),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1518, 762, 1512, 1510, 1511])).
% 3.20/2.35 tff(1520,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,[]))).
% 3.20/2.35 tff(1521,plain,
% 3.20/2.35 (~node11(c_e_h_1, c_n, s1, s2)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1520, 1510])).
% 3.20/2.35 tff(1522,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s0)), introduced(assumption)).
% 3.20/2.35 tff(1523,plain,
% 3.20/2.35 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1524,plain,
% 3.20/2.35 ($false),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1523, 9, 1522])).
% 3.20/2.35 tff(1525,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.35 tff(1526,plain,
% 3.20/2.35 (((~![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))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1527,plain,
% 3.20/2.35 ((~![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))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1528,plain,
% 3.20/2.35 ((~![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)),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 3.20/2.35 tff(1529,plain,
% 3.20/2.35 (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1528, 39, 1525])).
% 3.20/2.35 tff(1530,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s0)), introduced(assumption)).
% 3.20/2.35 tff(1531,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s1)), introduced(assumption)).
% 3.20/2.35 tff(1532,assumption,(node18(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 3.20/2.35 tff(1533,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node18(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1534,plain,
% 3.20/2.35 (((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1535,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node18(c_e_h_1, c_e, s0, s1))))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1534])).
% 3.20/2.35 tff(1536,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1535, 1533])).
% 3.20/2.35 tff(1537,plain,
% 3.20/2.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1538,plain,
% 3.20/2.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node18(c_e_h_1, c_e, s0, s1))),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 3.20/2.35 tff(1539,plain,
% 3.20/2.35 ($false),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1538, 164, 1531, 790, 1532])).
% 3.20/2.35 tff(1540,plain,((~node18(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,[]))).
% 3.20/2.35 tff(1541,plain,
% 3.20/2.35 (~node18(c_e_h_1, c_e, s0, s1)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1540, 1531])).
% 3.20/2.35 tff(1542,plain,
% 3.20/2.35 (((~![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))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1543,plain,
% 3.20/2.35 ((~![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))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1544,plain,
% 3.20/2.35 ((~![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)),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 3.20/2.35 tff(1545,plain,
% 3.20/2.35 (node19(c_e_h_1, c_e, s0, s1)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1544, 103, 96])).
% 3.20/2.35 tff(1546,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | (~node19(c_e_h_1, c_e, s0, s1)) | node18(c_e_h_1, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s0) | (~node19(c_e_h_1, c_e, s0, s1)) | node18(c_e_h_1, c_e, s0, s1))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1547,plain,
% 3.20/2.35 ((node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))) <=> (node17(c_e_h_1, c_e, s0) | (~node19(c_e_h_1, c_e, s0, s1)) | node18(c_e_h_1, c_e, s0, s1))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.35 tff(1548,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | (~node19(c_e_h_1, c_e, s0, s1)) | node18(c_e_h_1, c_e, s0, s1)))),
% 3.20/2.35 inference(monotonicity,[status(thm)],[1547])).
% 3.20/2.35 tff(1549,plain,
% 3.20/2.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s0) | (~node19(c_e_h_1, c_e, s0, s1)) | node18(c_e_h_1, c_e, s0, s1))),
% 3.20/2.35 inference(transitivity,[status(thm)],[1548, 1546])).
% 3.20/2.35 tff(1550,plain,
% 3.20/2.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 3.20/2.35 inference(quant_inst,[status(thm)],[])).
% 3.20/2.35 tff(1551,plain,
% 3.20/2.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s0) | (~node19(c_e_h_1, c_e, s0, s1)) | node18(c_e_h_1, c_e, s0, s1)),
% 3.20/2.35 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 3.20/2.35 tff(1552,plain,
% 3.20/2.35 (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1551, 195, 1545])).
% 3.20/2.35 tff(1553,plain,
% 3.20/2.35 (node17(c_e_h_1, c_e, s0)),
% 3.20/2.35 inference(unit_resolution,[status(thm)],[1552, 1541])).
% 3.20/2.35 tff(1554,plain,
% 3.20/2.35 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 3.20/2.35 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1555,plain,
% 3.20/2.36 ((m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1556,plain,
% 3.20/2.36 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0))))),
% 3.20/2.36 inference(monotonicity,[status(thm)],[1555])).
% 3.20/2.36 tff(1557,plain,
% 3.20/2.36 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 3.20/2.36 inference(transitivity,[status(thm)],[1556, 1554])).
% 3.20/2.36 tff(1558,plain,
% 3.20/2.36 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1559,plain,
% 3.20/2.36 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0))),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 3.20/2.36 tff(1560,plain,
% 3.20/2.36 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1559, 351, 1553])).
% 3.20/2.36 tff(1561,plain,
% 3.20/2.36 (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1560, 1530])).
% 3.20/2.36 tff(1562,assumption,(node15(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 3.20/2.36 tff(1563,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(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))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1564,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(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))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1565,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 3.20/2.36 tff(1566,plain,
% 3.20/2.36 ($false),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1565, 146, 1531, 790, 1562])).
% 3.20/2.36 tff(1567,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,[]))).
% 3.20/2.36 tff(1568,plain,
% 3.20/2.36 (~node15(c_e_h_1, c_e, s0, s1)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1567, 1531])).
% 3.20/2.36 tff(1569,assumption,(node14(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 3.20/2.36 tff(1570,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_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)))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1571,plain,
% 3.20/2.36 (((~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)))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1572,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_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))))),
% 3.20/2.36 inference(monotonicity,[status(thm)],[1571])).
% 3.20/2.36 tff(1573,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_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)))),
% 3.20/2.36 inference(transitivity,[status(thm)],[1572, 1570])).
% 3.20/2.36 tff(1574,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_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)))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1575,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1))),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 3.20/2.36 tff(1576,plain,
% 3.20/2.36 ($false),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1575, 73, 1531, 1569, 1530])).
% 3.20/2.36 tff(1577,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,[]))).
% 3.20/2.36 tff(1578,plain,
% 3.20/2.36 (~node14(c_e_h_1, c_e, s0, s1)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1577, 1530, 1531])).
% 3.20/2.36 tff(1579,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node14(c_e_h_1, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(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) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node14(c_e_h_1, c_e, s0, s1))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1580,plain,
% 3.20/2.36 ((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))) <=> (node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node14(c_e_h_1, c_e, s0, s1))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1581,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))) | (node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node14(c_e_h_1, c_e, s0, s1)))),
% 3.20/2.36 inference(monotonicity,[status(thm)],[1580])).
% 3.20/2.36 tff(1582,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node14(c_e_h_1, c_e, s0, s1))),
% 3.20/2.36 inference(transitivity,[status(thm)],[1581, 1579])).
% 3.20/2.36 tff(1583,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_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)))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1584,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node14(c_e_h_1, c_e, s0, s1)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 3.20/2.36 tff(1585,plain,
% 3.20/2.36 (node16(c_e_h_1, c_e, s0) | node15(c_e_h_1, c_e, s0, s1) | node14(c_e_h_1, c_e, s0, s1)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1584, 117, 1545])).
% 3.20/2.36 tff(1586,plain,
% 3.20/2.36 (node16(c_e_h_1, c_e, s0)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1585, 1578, 1568])).
% 3.20/2.36 tff(1587,plain,
% 3.20/2.36 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_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))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1588,plain,
% 3.20/2.36 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_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))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1589,plain,
% 3.20/2.36 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 3.20/2.36 tff(1590,plain,
% 3.20/2.36 ($false),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1589, 54, 1586, 1561, 1530])).
% 3.20/2.36 tff(1591,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.36 tff(1592,plain,
% 3.20/2.36 (~m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1591, 1529])).
% 3.20/2.36 tff(1593,plain,
% 3.20/2.36 (((~![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))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1594,plain,
% 3.20/2.36 ((~![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))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1595,plain,
% 3.20/2.36 ((~![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)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 3.20/2.36 tff(1596,plain,
% 3.20/2.36 (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)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1595, 797])).
% 3.20/2.36 tff(1597,plain,
% 3.20/2.36 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1596, 1592])).
% 3.20/2.36 tff(1598,plain,
% 3.20/2.36 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_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))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1599,plain,
% 3.20/2.36 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1600,plain,
% 3.20/2.36 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 3.20/2.36 tff(1601,plain,
% 3.20/2.36 (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)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1600, 746])).
% 3.20/2.36 tff(1602,plain,
% 3.20/2.36 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1601, 937])).
% 3.20/2.36 tff(1603,assumption,(node10(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 3.20/2.36 tff(1604,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)), introduced(assumption)).
% 3.20/2.36 tff(1605,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)), introduced(assumption)).
% 3.20/2.36 tff(1606,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1607,plain,
% 3.20/2.36 (((~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_in2(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1608,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_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_in2(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2))))),
% 3.20/2.36 inference(monotonicity,[status(thm)],[1607])).
% 3.20/2.36 tff(1609,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_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_in2(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)))),
% 3.20/2.36 inference(transitivity,[status(thm)],[1608, 1606])).
% 3.20/2.36 tff(1610,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_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))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1611,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2))),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 3.20/2.36 tff(1612,plain,
% 3.20/2.36 ($false),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1611, 812, 1605, 1604, 1510, 1603])).
% 3.20/2.36 tff(1613,plain,((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | (~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_n, s2)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.36 tff(1614,plain,
% 3.20/2.36 ((~node10(c_e_h_1, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1613, 1602, 1597])).
% 3.20/2.36 tff(1615,plain,
% 3.20/2.36 (~node10(c_e_h_1, c_n, s1, s2)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1614, 1510])).
% 3.20/2.36 tff(1616,plain,
% 3.20/2.36 (((~![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))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1617,plain,
% 3.20/2.36 ((~![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))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1618,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 3.20/2.36 tff(1619,plain,
% 3.20/2.36 (node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1618, 781, 181])).
% 3.20/2.36 tff(1620,plain,
% 3.20/2.36 ($false),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1619, 1615, 1521])).
% 3.20/2.36 tff(1621,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.36 tff(1622,plain,
% 3.20/2.36 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_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)))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1623,plain,
% 3.20/2.36 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1624,plain,
% 3.20/2.36 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 3.20/2.36 tff(1625,plain,
% 3.20/2.36 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1624, 662, 1621])).
% 3.20/2.36 tff(1626,plain,
% 3.20/2.36 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_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))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1627,plain,
% 3.20/2.36 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1628,plain,
% 3.20/2.36 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 3.20/2.36 tff(1629,plain,
% 3.20/2.36 (~node9(c_e_h_1, c_m, s2)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1628, 729, 1625])).
% 3.20/2.36 tff(1630,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 3.20/2.36 tff(1631,assumption,(node11(c_e_h_1, c_m, s2, s3)), introduced(assumption)).
% 3.20/2.36 tff(1632,plain,
% 3.20/2.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_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))),
% 3.20/2.36 inference(rewrite,[status(thm)],[])).
% 3.20/2.36 tff(1633,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_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))),
% 3.20/2.36 inference(quant_inst,[status(thm)],[])).
% 3.20/2.36 tff(1634,plain,
% 3.20/2.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 3.20/2.36 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 3.20/2.36 tff(1635,plain,
% 3.20/2.36 ($false),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1634, 867, 893, 1630, 1631])).
% 3.20/2.36 tff(1636,plain,((~node11(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 3.20/2.36 tff(1637,plain,
% 3.20/2.36 (~node11(c_e_h_1, c_m, s2, s3)),
% 3.20/2.36 inference(unit_resolution,[status(thm)],[1636, 1630])).
% 3.20/2.36 tff(1638,plain,
% 3.20/2.36 (((~![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))),
% 3.20/2.37 inference(rewrite,[status(thm)],[])).
% 3.20/2.37 tff(1639,plain,
% 3.20/2.37 ((~![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))),
% 3.20/2.37 inference(quant_inst,[status(thm)],[])).
% 3.20/2.37 tff(1640,plain,
% 3.20/2.37 ((~![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)),
% 3.20/2.37 inference(modus_ponens,[status(thm)],[1639, 1638])).
% 3.20/2.37 tff(1641,plain,
% 3.20/2.37 (node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 3.20/2.37 inference(unit_resolution,[status(thm)],[1640, 781, 388])).
% 3.20/2.37 tff(1642,plain,
% 3.20/2.37 (node10(c_e_h_1, c_m, s2, s3)),
% 3.20/2.37 inference(unit_resolution,[status(thm)],[1641, 1637])).
% 3.20/2.37 tff(1643,plain,
% 3.20/2.37 (((~![Y: $i, I0: $i, 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) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 3.20/2.37 inference(rewrite,[status(thm)],[])).
% 3.20/2.37 tff(1644,plain,
% 3.20/2.37 ((~![Y: $i, I0: $i, 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)))),
% 3.20/2.37 inference(quant_inst,[status(thm)],[])).
% 3.20/2.37 tff(1645,plain,
% 3.20/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3))),
% 3.20/2.37 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 3.20/2.37 tff(1646,plain,
% 3.20/2.37 ($false),
% 3.20/2.37 inference(unit_resolution,[status(thm)],[1645, 841, 1630, 1642, 1629])).
% 3.20/2.37 tff(1647,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.37 tff(1648,plain,
% 3.20/2.37 (((~![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))),
% 3.20/2.37 inference(rewrite,[status(thm)],[])).
% 3.20/2.37 tff(1649,plain,
% 3.20/2.37 ((~![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))),
% 3.20/2.37 inference(quant_inst,[status(thm)],[])).
% 3.20/2.37 tff(1650,plain,
% 3.20/2.37 ((~![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)),
% 3.20/2.37 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 3.20/2.37 tff(1651,plain,
% 3.20/2.37 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 3.20/2.37 inference(unit_resolution,[status(thm)],[1650, 900, 1647])).
% 3.20/2.37 tff(1652,plain,
% 3.20/2.37 (((~![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))),
% 3.20/2.37 inference(rewrite,[status(thm)],[])).
% 3.20/2.37 tff(1653,plain,
% 3.20/2.37 ((~![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))),
% 3.20/2.37 inference(quant_inst,[status(thm)],[])).
% 3.20/2.37 tff(1654,plain,
% 3.20/2.37 ((~![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)),
% 3.20/2.37 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 3.20/2.37 tff(1655,plain,
% 3.20/2.37 (~node20(c_e_h_1, c_r, s3)),
% 3.20/2.37 inference(unit_resolution,[status(thm)],[1654, 914, 1651])).
% 3.20/2.37 tff(1656,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 3.20/2.37 tff(1657,assumption,(node22(c_e_h_1, c_r, s3, s4)), introduced(assumption)).
% 3.20/2.37 tff(1658,plain,
% 3.20/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_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))),
% 3.20/2.37 inference(rewrite,[status(thm)],[])).
% 3.20/2.37 tff(1659,plain,
% 3.20/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 3.20/2.37 inference(quant_inst,[status(thm)],[])).
% 3.20/2.37 tff(1660,plain,
% 3.20/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 3.20/2.37 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 3.20/2.37 tff(1661,plain,
% 3.20/2.37 ($false),
% 3.20/2.37 inference(unit_resolution,[status(thm)],[1660, 332, 1657, 1656, 1011])).
% 3.20/2.37 tff(1662,plain,((~node22(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 3.20/2.37 tff(1663,plain,
% 3.20/2.37 (~node22(c_e_h_1, c_r, s3, s4)),
% 3.20/2.37 inference(unit_resolution,[status(thm)],[1662, 1656, 1011])).
% 3.20/2.37 tff(1664,assumption,(~node20(c_e_h_1, c_r, s3)), introduced(assumption)).
% 3.20/2.37 tff(1665,assumption,(node21(c_e_h_1, c_r, s3, s4)), introduced(assumption)).
% 3.20/2.37 tff(1666,plain,
% 3.20/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (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) | (~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)))),
% 3.20/2.37 inference(rewrite,[status(thm)],[])).
% 3.20/2.37 tff(1667,plain,
% 3.20/2.37 ((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))) <=> (node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)))),
% 3.20/2.37 inference(rewrite,[status(thm)],[])).
% 3.20/2.37 tff(1668,plain,
% 3.20/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4))))),
% 3.20/2.37 inference(monotonicity,[status(thm)],[1667])).
% 3.20/2.37 tff(1669,plain,
% 3.20/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)))),
% 3.20/2.37 inference(transitivity,[status(thm)],[1668, 1666])).
% 3.20/2.37 tff(1670,plain,
% 3.20/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (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)))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1671,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 3.28/2.37 tff(1672,plain,
% 3.28/2.37 ($false),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1671, 301, 1665, 1664, 1656])).
% 3.28/2.37 tff(1673,plain,((~node21(c_e_h_1, c_r, s3, s4)) | node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4))), inference(lemma,lemma(discharge,[]))).
% 3.28/2.37 tff(1674,plain,
% 3.28/2.37 (~node21(c_e_h_1, c_r, s3, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1673, 1656, 1664])).
% 3.28/2.37 tff(1675,plain,
% 3.28/2.37 (((~![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))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1676,plain,
% 3.28/2.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1677,plain,
% 3.28/2.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 3.28/2.37 tff(1678,plain,
% 3.28/2.37 (trans(s3, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1677, 1322, 89])).
% 3.28/2.37 tff(1679,plain,
% 3.28/2.37 (((~![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))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1680,plain,
% 3.28/2.37 ((~![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))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1681,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 3.28/2.37 tff(1682,plain,
% 3.28/2.37 (node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1681, 317, 1678])).
% 3.28/2.37 tff(1683,plain,
% 3.28/2.37 ($false),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1682, 1674, 1663])).
% 3.28/2.37 tff(1684,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.37 tff(1685,plain,
% 3.28/2.37 ((~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)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1684, 1655])).
% 3.28/2.37 tff(1686,plain,
% 3.28/2.37 (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1685, 1009])).
% 3.28/2.37 tff(1687,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 3.28/2.37 tff(1688,assumption,(m_user_v_ack(c_e_h_1, c_u, s4)), introduced(assumption)).
% 3.28/2.37 tff(1689,plain,
% 3.28/2.37 (((~![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))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1690,plain,
% 3.28/2.37 ((~![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))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1691,plain,
% 3.28/2.37 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 3.28/2.37 tff(1692,plain,
% 3.28/2.37 ($false),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1691, 608, 1688, 1687])).
% 3.28/2.37 tff(1693,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,[]))).
% 3.28/2.37 tff(1694,plain,
% 3.28/2.37 (~m_user_v_ack(c_e_h_1, c_u, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1693, 1686])).
% 3.28/2.37 tff(1695,plain,
% 3.28/2.37 (((~![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))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1696,plain,
% 3.28/2.37 ((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))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1697,plain,
% 3.28/2.37 (((~![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)))),
% 3.28/2.37 inference(monotonicity,[status(thm)],[1696])).
% 3.28/2.37 tff(1698,plain,
% 3.28/2.37 (((~![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))),
% 3.28/2.37 inference(transitivity,[status(thm)],[1697, 1695])).
% 3.28/2.37 tff(1699,plain,
% 3.28/2.37 ((~![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)))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1700,plain,
% 3.28/2.37 ((~![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)),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 3.28/2.37 tff(1701,plain,
% 3.28/2.37 (~node24(s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1700, 1167, 1694])).
% 3.28/2.37 tff(1702,plain,
% 3.28/2.37 (((~![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)))) | m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1703,plain,
% 3.28/2.37 ((~![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)))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1704,plain,
% 3.28/2.37 ((~![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))),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 3.28/2.37 tff(1705,plain,
% 3.28/2.37 (~node23(s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1704, 1026, 1694])).
% 3.28/2.37 tff(1706,plain,
% 3.28/2.37 (((~![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)))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1707,plain,
% 3.28/2.37 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1708,plain,
% 3.28/2.37 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s4) | node24(s4) | node25(s4) | (~node26(s4))),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 3.28/2.37 tff(1709,plain,
% 3.28/2.37 (node25(s4) | (~node26(s4))),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1708, 1070, 1705, 1701])).
% 3.28/2.37 tff(1710,plain,
% 3.28/2.37 (node25(s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1709, 1509])).
% 3.28/2.37 tff(1711,plain,
% 3.28/2.37 (((~![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, s4) | (~node25(s4)))) <=> ((~![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, s4) | (~node25(s4)))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1712,plain,
% 3.28/2.37 ((~![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, s4) | (~node25(s4)))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1713,plain,
% 3.28/2.37 ((~![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, s4) | (~node25(s4))),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 3.28/2.37 tff(1714,plain,
% 3.28/2.37 (m_user_v_ack(c_e_h_3, c_u, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1713, 1055, 1710])).
% 3.28/2.37 tff(1715,plain,
% 3.28/2.37 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1716,plain,
% 3.28/2.37 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1717,plain,
% 3.28/2.37 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 3.28/2.37 tff(1718,plain,
% 3.28/2.37 (m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1717, 608, 1714])).
% 3.28/2.37 tff(1719,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s4)), introduced(assumption)).
% 3.28/2.37 tff(1720,assumption,(~node20(c_e_h_3, c_r, s3)), introduced(assumption)).
% 3.28/2.37 tff(1721,assumption,(node21(c_e_h_3, c_r, s3, s4)), introduced(assumption)).
% 3.28/2.37 tff(1722,plain,
% 3.28/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1723,plain,
% 3.28/2.37 ((node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1724,plain,
% 3.28/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4))))),
% 3.28/2.37 inference(monotonicity,[status(thm)],[1723])).
% 3.28/2.37 tff(1725,plain,
% 3.28/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 3.28/2.37 inference(transitivity,[status(thm)],[1724, 1722])).
% 3.28/2.37 tff(1726,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1727,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4))),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 3.28/2.37 tff(1728,plain,
% 3.28/2.37 ($false),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1727, 301, 1721, 1720, 1719])).
% 3.28/2.37 tff(1729,plain,((~node21(c_e_h_3, c_r, s3, s4)) | node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4))), inference(lemma,lemma(discharge,[]))).
% 3.28/2.37 tff(1730,plain,
% 3.28/2.37 (~node21(c_e_h_3, c_r, s3, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1729, 1719, 1720])).
% 3.28/2.37 tff(1731,plain,
% 3.28/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1732,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1733,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4)),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 3.28/2.37 tff(1734,plain,
% 3.28/2.37 (node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1733, 317, 1678])).
% 3.28/2.37 tff(1735,plain,
% 3.28/2.37 (node22(c_e_h_3, c_r, s3, s4)),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1734, 1730])).
% 3.28/2.37 tff(1736,plain,
% 3.28/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1737,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 3.28/2.37 inference(quant_inst,[status(thm)],[])).
% 3.28/2.37 tff(1738,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 3.28/2.37 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 3.28/2.37 tff(1739,plain,
% 3.28/2.37 ($false),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1738, 332, 1735, 373, 1719])).
% 3.28/2.37 tff(1740,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3) | node20(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.37 tff(1741,plain,
% 3.28/2.37 ($false),
% 3.28/2.37 inference(unit_resolution,[status(thm)],[1740, 1718, 600, 373])).
% 3.28/2.37 tff(1742,plain,(m_and_h_gate_v_out(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.37 tff(1743,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 3.28/2.37 tff(1744,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 3.28/2.37 tff(1745,assumption,(node22(c_e_h_3, c_r, s2, s3)), introduced(assumption)).
% 3.28/2.37 tff(1746,plain,
% 3.28/2.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(1747,plain,
% 3.28/2.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 3.28/2.38 inference(quant_inst,[status(thm)],[])).
% 3.28/2.38 tff(1748,plain,
% 3.28/2.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 3.28/2.38 tff(1749,plain,
% 3.28/2.38 ($false),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1748, 332, 1745, 1743, 1744])).
% 3.28/2.38 tff(1750,plain,((~node22(c_e_h_3, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.38 tff(1751,plain,
% 3.28/2.38 ((~node22(c_e_h_3, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1750, 1143])).
% 3.28/2.38 tff(1752,plain,
% 3.28/2.38 (~node22(c_e_h_3, c_r, s2, s3)),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1751, 1743])).
% 3.28/2.38 tff(1753,assumption,(~node20(c_e_h_3, c_r, s2)), introduced(assumption)).
% 3.28/2.38 tff(1754,assumption,(node21(c_e_h_3, c_r, s2, s3)), introduced(assumption)).
% 3.28/2.38 tff(1755,plain,
% 3.28/2.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_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)))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(1756,plain,
% 3.28/2.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 3.28/2.38 inference(quant_inst,[status(thm)],[])).
% 3.28/2.38 tff(1757,plain,
% 3.28/2.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 3.28/2.38 tff(1758,plain,
% 3.28/2.38 ($false),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1757, 301, 1754, 1753, 1743])).
% 3.28/2.38 tff(1759,plain,((~node21(c_e_h_3, c_r, s2, s3)) | node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3))), inference(lemma,lemma(discharge,[]))).
% 3.28/2.38 tff(1760,plain,
% 3.28/2.38 (~node21(c_e_h_3, c_r, s2, s3)),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1759, 1743, 1753])).
% 3.28/2.38 tff(1761,plain,
% 3.28/2.38 (((~![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))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(1762,plain,
% 3.28/2.38 ((~![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))),
% 3.28/2.38 inference(quant_inst,[status(thm)],[])).
% 3.28/2.38 tff(1763,plain,
% 3.28/2.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 3.28/2.38 tff(1764,plain,
% 3.28/2.38 (node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1763, 317, 388])).
% 3.28/2.38 tff(1765,plain,
% 3.28/2.38 ($false),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1764, 1760, 1752])).
% 3.28/2.38 tff(1766,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.38 tff(1767,plain,
% 3.28/2.38 (node20(c_e_h_3, c_r, s2)),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1766, 1742])).
% 3.28/2.38 tff(1768,plain,
% 3.28/2.38 (((~![I0: $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))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(1769,plain,
% 3.28/2.38 ((~![I0: $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))),
% 3.28/2.38 inference(quant_inst,[status(thm)],[])).
% 3.28/2.38 tff(1770,plain,
% 3.28/2.38 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[1769, 1768])).
% 3.28/2.38 tff(1771,plain,
% 3.28/2.38 ($false),
% 3.28/2.38 inference(unit_resolution,[status(thm)],[1770, 287, 1767, 372])).
% 3.28/2.38 % SZS output end Proof
%------------------------------------------------------------------------------