TSTP Solution File: SWV422-1.060 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV422-1.060 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 15:14:29 EDT 2022
% Result : Unsatisfiable 0.61s 0.63s
% Output : Proof 2.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWV422-1.060 : TPTP v8.1.0. Released v3.5.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n014.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun Sep 4 03:18:15 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.61/0.63 % SZS status Unsatisfiable
% 0.61/0.63 % SZS output start Proof
% 0.61/0.63 tff(always25_type, type, (
% 0.61/0.63 always25: $i > $o)).
% 0.61/0.63 tff(s19_type, type, (
% 0.61/0.63 s19: $i)).
% 0.61/0.63 tff(s20_type, type, (
% 0.61/0.63 s20: $i)).
% 0.61/0.63 tff(m_main_v_state2_type, type, (
% 0.61/0.63 m_main_v_state2: ( $i * $i ) > $o)).
% 0.61/0.63 tff(c_c2_type, type, (
% 0.61/0.63 c_c2: $i)).
% 0.61/0.63 tff(node9_type, type, (
% 0.61/0.63 node9: $i > $o)).
% 0.61/0.63 tff(c_n2_type, type, (
% 0.61/0.63 c_n2: $i)).
% 0.61/0.63 tff(node13_type, type, (
% 0.61/0.63 node13: ( $i * $i ) > $o)).
% 0.61/0.63 tff(s18_type, type, (
% 0.61/0.63 s18: $i)).
% 0.61/0.63 tff(node12_type, type, (
% 0.61/0.63 node12: $i > $o)).
% 0.61/0.63 tff(m_main_v_turn_type, type, (
% 0.61/0.63 m_main_v_turn: ( $i * $i ) > $o)).
% 0.61/0.63 tff(c_2_type, type, (
% 0.61/0.63 c_2: $i)).
% 0.61/0.63 tff(c_1_type, type, (
% 0.61/0.63 c_1: $i)).
% 0.61/0.63 tff(m_main_v_state1_type, type, (
% 0.61/0.63 m_main_v_state1: ( $i * $i ) > $o)).
% 0.61/0.63 tff(c_t1_type, type, (
% 0.61/0.63 c_t1: $i)).
% 0.61/0.63 tff(s17_type, type, (
% 0.61/0.63 s17: $i)).
% 0.61/0.63 tff(node6_type, type, (
% 0.61/0.63 node6: ( $i * $i ) > $o)).
% 0.61/0.63 tff(s16_type, type, (
% 0.61/0.63 s16: $i)).
% 0.61/0.63 tff(node1_type, type, (
% 0.61/0.63 node1: $i > $o)).
% 0.61/0.63 tff(c_n1_type, type, (
% 0.61/0.63 c_n1: $i)).
% 0.61/0.63 tff(s15_type, type, (
% 0.61/0.63 s15: $i)).
% 0.61/0.63 tff(node5_type, type, (
% 0.61/0.63 node5: $i > $o)).
% 0.61/0.63 tff(s14_type, type, (
% 0.61/0.63 s14: $i)).
% 0.61/0.63 tff(c_c1_type, type, (
% 0.61/0.63 c_c1: $i)).
% 0.61/0.63 tff(node3_type, type, (
% 0.61/0.63 node3: $i > $o)).
% 0.61/0.63 tff(s13_type, type, (
% 0.61/0.63 s13: $i)).
% 0.61/0.63 tff(s12_type, type, (
% 0.61/0.63 s12: $i)).
% 0.61/0.63 tff(c_t2_type, type, (
% 0.61/0.63 c_t2: $i)).
% 0.61/0.63 tff(s11_type, type, (
% 0.61/0.63 s11: $i)).
% 0.61/0.63 tff(s10_type, type, (
% 0.61/0.63 s10: $i)).
% 0.61/0.63 tff(s9_type, type, (
% 0.61/0.63 s9: $i)).
% 0.61/0.63 tff(s8_type, type, (
% 0.61/0.63 s8: $i)).
% 0.61/0.63 tff(s7_type, type, (
% 0.61/0.63 s7: $i)).
% 0.61/0.63 tff(s6_type, type, (
% 0.61/0.63 s6: $i)).
% 0.61/0.63 tff(s5_type, type, (
% 0.61/0.63 s5: $i)).
% 0.61/0.63 tff(s4_type, type, (
% 0.61/0.63 s4: $i)).
% 0.61/0.63 tff(s3_type, type, (
% 0.61/0.63 s3: $i)).
% 0.61/0.63 tff(s2_type, type, (
% 0.61/0.63 s2: $i)).
% 0.61/0.63 tff(s1_type, type, (
% 0.61/0.63 s1: $i)).
% 0.61/0.63 tff(node8_type, type, (
% 0.61/0.63 node8: $i > $o)).
% 0.61/0.63 tff(s0_type, type, (
% 0.61/0.63 s0: $i)).
% 0.61/0.63 tff(node14_type, type, (
% 0.61/0.63 node14: ( $i * $i ) > $o)).
% 0.61/0.63 tff(trans_type, type, (
% 0.61/0.63 trans: ( $i * $i ) > $o)).
% 0.61/0.63 tff(succ_type, type, (
% 0.61/0.63 succ: ( $i * $i ) > $o)).
% 0.61/0.63 tff(node17_type, type, (
% 0.61/0.63 node17: ( $i * $i ) > $o)).
% 0.61/0.63 tff(node15_type, type, (
% 0.61/0.63 node15: $i > $o)).
% 0.61/0.63 tff(node16_type, type, (
% 0.61/0.63 node16: $i > $o)).
% 0.61/0.63 tff(node18_type, type, (
% 0.61/0.63 node18: ( $i * $i ) > $o)).
% 0.61/0.63 tff(node11_type, type, (
% 0.61/0.63 node11: $i > $o)).
% 0.61/0.63 tff(node7_type, type, (
% 0.61/0.63 node7: ( $i * $i ) > $o)).
% 0.61/0.63 tff(node10_type, type, (
% 0.61/0.63 node10: $i > $o)).
% 0.61/0.63 tff(node4_type, type, (
% 0.61/0.63 node4: $i > $o)).
% 0.61/0.63 tff(node2_type, type, (
% 0.61/0.63 node2: $i > $o)).
% 0.61/0.63 tff(s59_type, type, (
% 0.61/0.63 s59: $i)).
% 0.61/0.63 tff(node26_type, type, (
% 0.61/0.63 node26: $i > $o)).
% 0.61/0.63 tff(s58_type, type, (
% 0.61/0.63 s58: $i)).
% 0.61/0.63 tff(xuntil28_type, type, (
% 0.61/0.63 xuntil28: $i > $o)).
% 0.61/0.63 tff(until27_type, type, (
% 0.61/0.63 until27: $i > $o)).
% 0.61/0.63 tff(s57_type, type, (
% 0.61/0.63 s57: $i)).
% 0.61/0.63 tff(s56_type, type, (
% 0.61/0.63 s56: $i)).
% 0.61/0.63 tff(s55_type, type, (
% 0.61/0.63 s55: $i)).
% 0.61/0.63 tff(s54_type, type, (
% 0.61/0.63 s54: $i)).
% 0.61/0.63 tff(s53_type, type, (
% 0.61/0.63 s53: $i)).
% 0.61/0.63 tff(s52_type, type, (
% 0.61/0.63 s52: $i)).
% 0.61/0.63 tff(s51_type, type, (
% 0.61/0.63 s51: $i)).
% 0.61/0.63 tff(s50_type, type, (
% 0.61/0.63 s50: $i)).
% 0.61/0.63 tff(s49_type, type, (
% 0.61/0.63 s49: $i)).
% 0.61/0.63 tff(s48_type, type, (
% 0.61/0.63 s48: $i)).
% 0.61/0.63 tff(s47_type, type, (
% 0.61/0.63 s47: $i)).
% 0.61/0.63 tff(s46_type, type, (
% 0.61/0.63 s46: $i)).
% 0.61/0.63 tff(s45_type, type, (
% 0.61/0.63 s45: $i)).
% 0.61/0.63 tff(s44_type, type, (
% 0.61/0.63 s44: $i)).
% 0.61/0.63 tff(s43_type, type, (
% 0.61/0.63 s43: $i)).
% 0.61/0.63 tff(s42_type, type, (
% 0.61/0.63 s42: $i)).
% 0.61/0.63 tff(s41_type, type, (
% 0.61/0.63 s41: $i)).
% 0.61/0.63 tff(s40_type, type, (
% 0.61/0.63 s40: $i)).
% 0.61/0.63 tff(s39_type, type, (
% 0.61/0.63 s39: $i)).
% 0.61/0.63 tff(s38_type, type, (
% 0.61/0.63 s38: $i)).
% 0.61/0.63 tff(s37_type, type, (
% 0.61/0.63 s37: $i)).
% 0.61/0.63 tff(s36_type, type, (
% 0.61/0.63 s36: $i)).
% 0.61/0.63 tff(s35_type, type, (
% 0.61/0.63 s35: $i)).
% 0.61/0.63 tff(s34_type, type, (
% 0.61/0.63 s34: $i)).
% 0.61/0.63 tff(s33_type, type, (
% 0.61/0.63 s33: $i)).
% 0.61/0.63 tff(s32_type, type, (
% 0.61/0.63 s32: $i)).
% 0.61/0.63 tff(s31_type, type, (
% 0.61/0.63 s31: $i)).
% 0.61/0.63 tff(s30_type, type, (
% 0.61/0.63 s30: $i)).
% 0.61/0.63 tff(s29_type, type, (
% 0.61/0.63 s29: $i)).
% 0.61/0.63 tff(s28_type, type, (
% 0.61/0.63 s28: $i)).
% 0.61/0.63 tff(s27_type, type, (
% 0.61/0.63 s27: $i)).
% 0.61/0.63 tff(s26_type, type, (
% 0.61/0.63 s26: $i)).
% 0.61/0.63 tff(s25_type, type, (
% 0.61/0.63 s25: $i)).
% 0.61/0.63 tff(s24_type, type, (
% 0.61/0.63 s24: $i)).
% 0.61/0.63 tff(s23_type, type, (
% 0.61/0.63 s23: $i)).
% 0.61/0.63 tff(s22_type, type, (
% 0.61/0.63 s22: $i)).
% 0.61/0.63 tff(s21_type, type, (
% 0.61/0.63 s21: $i)).
% 0.61/0.63 tff(until2p29_type, type, (
% 0.61/0.63 until2p29: $i > $o)).
% 0.61/0.63 tff(xuntil2p30_type, type, (
% 0.61/0.63 xuntil2p30: $i > $o)).
% 0.61/0.63 tff(last_type, type, (
% 0.61/0.63 last: $i > $o)).
% 0.61/0.63 tff(loop_type, type, (
% 0.61/0.63 loop: $o)).
% 0.61/0.63 tff(1,plain,
% 0.61/0.63 (m_main_v_state1(s0, c_n1) <=> m_main_v_state1(s0, c_n1)),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(2,axiom,(m_main_v_state1(s0, c_n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_11')).
% 0.61/0.63 tff(3,plain,
% 0.61/0.63 (m_main_v_state1(s0, c_n1)),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.61/0.63 tff(4,plain,
% 0.61/0.63 (^[X: $i] : refl(((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1))))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(5,plain,
% 0.61/0.63 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1))) <=> ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[4])).
% 0.61/0.63 tff(6,plain,
% 0.61/0.63 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1))) <=> ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(7,axiom,(![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_2')).
% 0.61/0.63 tff(8,plain,
% 0.61/0.63 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.61/0.63 tff(9,plain,(
% 0.61/0.63 ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.61/0.63 inference(skolemize,[status(sab)],[8])).
% 0.61/0.63 tff(10,plain,
% 0.61/0.63 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.61/0.63 tff(11,plain,
% 0.61/0.63 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state1(s0, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state1(s0, c_t1)))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(12,plain,
% 0.61/0.63 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state1(s0, c_t1)))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(13,plain,
% 0.61/0.63 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state1(s0, c_t1))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.61/0.63 tff(14,plain,
% 0.61/0.63 (~m_main_v_state1(s0, c_t1)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.61/0.63 tff(15,plain,
% 0.61/0.63 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node8(X))) <=> (m_main_v_state1(X, c_t1) | (~node8(X))))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(16,plain,
% 0.61/0.63 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[15])).
% 0.61/0.63 tff(17,plain,
% 0.61/0.63 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(18,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_36')).
% 0.61/0.63 tff(19,plain,
% 0.61/0.63 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.61/0.63 tff(20,plain,(
% 0.61/0.63 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.61/0.63 inference(skolemize,[status(sab)],[19])).
% 0.61/0.63 tff(21,plain,
% 0.61/0.63 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.61/0.63 tff(22,plain,
% 0.61/0.63 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | (m_main_v_state1(s0, c_t1) | (~node8(s0)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | m_main_v_state1(s0, c_t1) | (~node8(s0)))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(23,plain,
% 0.61/0.63 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | (m_main_v_state1(s0, c_t1) | (~node8(s0)))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(24,plain,
% 0.61/0.63 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | m_main_v_state1(s0, c_t1) | (~node8(s0))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.61/0.63 tff(25,plain,
% 0.61/0.63 (~node8(s0)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 0.61/0.63 tff(26,plain,
% 0.61/0.63 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(27,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[26])).
% 0.61/0.63 tff(28,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(29,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound61')).
% 0.61/0.63 tff(30,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.61/0.63 tff(31,plain,(
% 0.61/0.63 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.61/0.63 inference(skolemize,[status(sab)],[30])).
% 0.61/0.63 tff(32,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.61/0.63 tff(33,plain,
% 0.61/0.63 (succ(s0, s1) <=> succ(s0, s1)),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(34,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 0.61/0.63 tff(35,plain,
% 0.61/0.63 (succ(s0, s1)),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.61/0.63 tff(36,plain,
% 0.61/0.63 (((~![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))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(37,plain,
% 0.61/0.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(38,plain,
% 0.61/0.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.61/0.63 tff(39,plain,
% 0.61/0.63 (trans(s0, s1)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[38, 35, 32])).
% 0.61/0.63 tff(40,plain,
% 0.61/0.63 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node14(X, Y)) <=> ((~trans(X, Y)) | node14(X, Y)))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(41,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[40])).
% 0.61/0.63 tff(42,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(43,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_55')).
% 0.61/0.63 tff(44,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.61/0.63 tff(45,plain,(
% 0.61/0.63 ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.61/0.63 inference(skolemize,[status(sab)],[44])).
% 0.61/0.63 tff(46,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.61/0.63 tff(47,plain,
% 0.61/0.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s0, s1)) | node14(s0, s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s0, s1)) | node14(s0, s1))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(48,plain,
% 0.61/0.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s0, s1)) | node14(s0, s1))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(49,plain,
% 0.61/0.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s0, s1)) | node14(s0, s1)),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.61/0.63 tff(50,plain,
% 0.61/0.63 (node14(s0, s1)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[49, 46, 39])).
% 0.61/0.63 tff(51,plain,
% 0.61/0.63 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(52,plain,
% 0.61/0.63 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[51])).
% 0.61/0.64 tff(53,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(54,plain,
% 0.61/0.64 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((node8(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_n1))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X))), ((((node8(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_t2)) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X)) | m_main_v_state2(Y, c_t2)))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X)) | m_main_v_state2(Y, c_t2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | m_main_v_state2(Y, c_t2))), ((((node8(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_t2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | m_main_v_state2(Y, c_t2)))), (((((node8(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))), (((((node8(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(55,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((((node8(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[54])).
% 0.61/0.64 tff(56,axiom,(![Y: $i, X: $i] : ((((node8(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_49')).
% 0.61/0.64 tff(57,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.61/0.64 tff(58,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.61/0.64 tff(59,plain,(
% 0.61/0.64 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.61/0.64 inference(skolemize,[status(sab)],[58])).
% 0.61/0.64 tff(60,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.61/0.64 tff(61,plain,
% 0.61/0.64 (m_main_v_state2(s0, c_n2) <=> m_main_v_state2(s0, c_n2)),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(62,axiom,(m_main_v_state2(s0, c_n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_12')).
% 0.61/0.64 tff(63,plain,
% 0.61/0.64 (m_main_v_state2(s0, c_n2)),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.61/0.64 tff(64,plain,
% 0.61/0.64 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | m_main_v_state2(s1, c_t2) | (~node14(s0, s1)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | m_main_v_state2(s1, c_t2) | (~node14(s0, s1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(65,plain,
% 0.61/0.64 (((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | (~node14(s0, s1)) | m_main_v_state2(s1, c_t2)) <=> ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | m_main_v_state2(s1, c_t2) | (~node14(s0, s1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(66,plain,
% 0.61/0.64 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | (~node14(s0, s1)) | m_main_v_state2(s1, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | m_main_v_state2(s1, c_t2) | (~node14(s0, s1))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[65])).
% 0.61/0.64 tff(67,plain,
% 0.61/0.64 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | (~node14(s0, s1)) | m_main_v_state2(s1, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | m_main_v_state2(s1, c_t2) | (~node14(s0, s1)))),
% 0.61/0.64 inference(transitivity,[status(thm)],[66, 64])).
% 0.61/0.64 tff(68,plain,
% 0.61/0.64 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | (~node14(s0, s1)) | m_main_v_state2(s1, c_t2))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(69,plain,
% 0.61/0.64 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node8(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node8(s0) | m_main_v_state2(s1, c_t2) | (~node14(s0, s1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.61/0.64 tff(70,plain,
% 0.61/0.64 (m_main_v_state2(s1, c_t2)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[69, 3, 63, 60, 50, 25])).
% 0.61/0.64 tff(71,plain,
% 0.61/0.64 (^[X: $i] : refl(((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2))) <=> ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(72,plain,
% 0.61/0.64 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2))) <=> ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[71])).
% 0.61/0.64 tff(73,plain,
% 0.61/0.64 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2))) <=> ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(74,axiom,(![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_6')).
% 0.61/0.64 tff(75,plain,
% 0.61/0.64 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.61/0.64 tff(76,plain,(
% 0.61/0.64 ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.61/0.64 inference(skolemize,[status(sab)],[75])).
% 0.61/0.64 tff(77,plain,
% 0.61/0.64 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.61/0.64 tff(78,plain,
% 0.61/0.64 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s1, c_n2)) | (~m_main_v_state2(s1, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s1, c_n2)) | (~m_main_v_state2(s1, c_t2)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(79,plain,
% 0.61/0.64 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s1, c_n2)) | (~m_main_v_state2(s1, c_t2)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(80,plain,
% 0.61/0.64 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s1, c_n2)) | (~m_main_v_state2(s1, c_t2))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.61/0.64 tff(81,plain,
% 0.61/0.64 (~m_main_v_state2(s1, c_n2)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[80, 77, 70])).
% 0.61/0.64 tff(82,plain,
% 0.61/0.64 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node9(X))) <=> (m_main_v_state2(X, c_n2) | (~node9(X))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(83,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[82])).
% 0.61/0.64 tff(84,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(85,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_37')).
% 0.61/0.64 tff(86,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.61/0.64 tff(87,plain,(
% 0.61/0.64 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.61/0.64 inference(skolemize,[status(sab)],[86])).
% 0.61/0.64 tff(88,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.61/0.64 tff(89,plain,
% 0.61/0.64 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s1, c_n2) | (~node9(s1)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s1, c_n2) | (~node9(s1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(90,plain,
% 0.61/0.64 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s1, c_n2) | (~node9(s1)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(91,plain,
% 0.61/0.64 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s1, c_n2) | (~node9(s1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.61/0.64 tff(92,plain,
% 0.61/0.64 (~node9(s1)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[91, 88, 81])).
% 0.61/0.64 tff(93,plain,
% 0.61/0.64 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s0, c_n2)) | (~m_main_v_state2(s0, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s0, c_n2)) | (~m_main_v_state2(s0, c_t2)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(94,plain,
% 0.61/0.64 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s0, c_n2)) | (~m_main_v_state2(s0, c_t2)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(95,plain,
% 0.61/0.64 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s0, c_n2)) | (~m_main_v_state2(s0, c_t2))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.61/0.64 tff(96,plain,
% 0.61/0.64 (~m_main_v_state2(s0, c_t2)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[95, 77, 63])).
% 0.61/0.64 tff(97,plain,
% 0.61/0.64 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node15(X))) <=> (m_main_v_state2(X, c_t2) | (~node15(X))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(98,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[97])).
% 0.61/0.64 tff(99,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(100,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_57')).
% 0.61/0.64 tff(101,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.61/0.64 tff(102,plain,(
% 0.61/0.64 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.61/0.64 inference(skolemize,[status(sab)],[101])).
% 0.61/0.64 tff(103,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.61/0.64 tff(104,plain,
% 0.61/0.64 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s0, c_t2) | (~node15(s0)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s0, c_t2) | (~node15(s0)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(105,plain,
% 0.61/0.64 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s0, c_t2) | (~node15(s0)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(106,plain,
% 0.61/0.64 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s0, c_t2) | (~node15(s0))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.61/0.64 tff(107,plain,
% 0.61/0.64 (~node15(s0)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[106, 103, 96])).
% 0.61/0.64 tff(108,plain,
% 0.61/0.64 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node16(X))) <=> (m_main_v_state1(X, c_t1) | (~node16(X))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(109,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[108])).
% 0.61/0.64 tff(110,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(111,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_59')).
% 0.61/0.64 tff(112,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.61/0.64 tff(113,plain,(
% 0.61/0.64 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.61/0.64 inference(skolemize,[status(sab)],[112])).
% 0.61/0.64 tff(114,plain,
% 0.61/0.64 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.61/0.64 tff(115,plain,
% 0.61/0.64 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | (m_main_v_state1(s0, c_t1) | (~node16(s0)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | m_main_v_state1(s0, c_t1) | (~node16(s0)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(116,plain,
% 0.61/0.64 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | (m_main_v_state1(s0, c_t1) | (~node16(s0)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(117,plain,
% 0.61/0.64 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | m_main_v_state1(s0, c_t1) | (~node16(s0))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.61/0.64 tff(118,plain,
% 0.61/0.64 (~node16(s0)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[117, 114, 14])).
% 0.61/0.64 tff(119,plain,
% 0.61/0.64 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node18(X, Y)) <=> ((~trans(X, Y)) | node18(X, Y)))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(120,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[119])).
% 0.61/0.64 tff(121,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(122,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_65')).
% 0.61/0.64 tff(123,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.61/0.64 tff(124,plain,(
% 0.61/0.64 ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.61/0.64 inference(skolemize,[status(sab)],[123])).
% 0.61/0.64 tff(125,plain,
% 0.61/0.64 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.61/0.64 tff(126,plain,
% 0.61/0.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s0, s1)) | node18(s0, s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s0, s1)) | node18(s0, s1))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(127,plain,
% 0.61/0.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s0, s1)) | node18(s0, s1))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(128,plain,
% 0.61/0.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s0, s1)) | node18(s0, s1)),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.61/0.65 tff(129,plain,
% 0.61/0.65 (node18(s0, s1)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[128, 125, 39])).
% 0.61/0.65 tff(130,plain,
% 0.61/0.65 (^[Y: $i, X: $i] : refl((node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y))) <=> (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(131,plain,
% 0.61/0.65 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y))) <=> ![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[130])).
% 0.61/0.65 tff(132,plain,
% 0.61/0.65 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y))) <=> ![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(133,plain,
% 0.61/0.65 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((node15(X) | node16(X)) | node17(X, Y)) <=> (node15(X) | node16(X) | node17(X, Y))), ((((node15(X) | node16(X)) | node17(X, Y)) | (~node18(X, Y))) <=> ((node15(X) | node16(X) | node17(X, Y)) | (~node18(X, Y))))), rewrite(((node15(X) | node16(X) | node17(X, Y)) | (~node18(X, Y))) <=> (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))), ((((node15(X) | node16(X)) | node17(X, Y)) | (~node18(X, Y))) <=> (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(134,plain,
% 0.61/0.65 (![Y: $i, X: $i] : (((node15(X) | node16(X)) | node17(X, Y)) | (~node18(X, Y))) <=> ![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[133])).
% 0.61/0.65 tff(135,axiom,(![Y: $i, X: $i] : (((node15(X) | node16(X)) | node17(X, Y)) | (~node18(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_64')).
% 0.61/0.65 tff(136,plain,
% 0.61/0.65 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.61/0.65 tff(137,plain,
% 0.61/0.65 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.61/0.65 tff(138,plain,(
% 0.61/0.65 ![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.61/0.65 inference(skolemize,[status(sab)],[137])).
% 0.61/0.65 tff(139,plain,
% 0.61/0.65 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.61/0.65 tff(140,plain,
% 0.61/0.65 (((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1)))) <=> ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(141,plain,
% 0.61/0.65 ((node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1))) <=> (node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(142,plain,
% 0.61/0.65 (((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1)))) <=> ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[141])).
% 0.61/0.65 tff(143,plain,
% 0.61/0.65 (((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1)))) <=> ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.61/0.65 inference(transitivity,[status(thm)],[142, 140])).
% 0.61/0.65 tff(144,plain,
% 0.61/0.65 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(145,plain,
% 0.61/0.65 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.61/0.65 tff(146,plain,
% 0.61/0.65 (node17(s0, s1)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[145, 139, 129, 118, 107])).
% 0.61/0.65 tff(147,plain,
% 0.61/0.65 (m_main_v_turn(s0, c_1) <=> m_main_v_turn(s0, c_1)),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(148,axiom,(m_main_v_turn(s0, c_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_13')).
% 0.61/0.65 tff(149,plain,
% 0.61/0.65 (m_main_v_turn(s0, c_1)),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.61/0.65 tff(150,plain,
% 0.61/0.65 (^[X: $i] : refl(((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2))) <=> ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(151,plain,
% 0.61/0.65 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2))) <=> ![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[150])).
% 0.61/0.65 tff(152,plain,
% 0.61/0.65 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2))) <=> ![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(153,axiom,(![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_10')).
% 0.61/0.65 tff(154,plain,
% 0.61/0.65 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.61/0.65 tff(155,plain,(
% 0.61/0.65 ![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.61/0.65 inference(skolemize,[status(sab)],[154])).
% 0.61/0.65 tff(156,plain,
% 0.61/0.65 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.61/0.65 tff(157,plain,
% 0.61/0.65 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s0, c_1)) | (~m_main_v_turn(s0, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s0, c_1)) | (~m_main_v_turn(s0, c_2)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(158,plain,
% 0.61/0.65 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s0, c_1)) | (~m_main_v_turn(s0, c_2)))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(159,plain,
% 0.61/0.65 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s0, c_1)) | (~m_main_v_turn(s0, c_2))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.61/0.65 tff(160,plain,
% 0.61/0.65 (~m_main_v_turn(s0, c_2)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[159, 156, 149])).
% 0.61/0.65 tff(161,plain,
% 0.61/0.65 (^[V: $i, Y: $i, X: $i] : refl(((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V))) <=> ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(162,plain,
% 0.61/0.65 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V))) <=> ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[161])).
% 0.61/0.65 tff(163,plain,
% 0.61/0.65 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V))) <=> ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(164,plain,
% 0.61/0.65 (^[V: $i, Y: $i, X: $i] : rewrite((((~m_main_v_turn(Y, V)) | m_main_v_turn(X, V)) | (~node17(X, Y))) <=> ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(165,plain,
% 0.61/0.65 (![V: $i, Y: $i, X: $i] : (((~m_main_v_turn(Y, V)) | m_main_v_turn(X, V)) | (~node17(X, Y))) <=> ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[164])).
% 0.61/0.65 tff(166,axiom,(![V: $i, Y: $i, X: $i] : (((~m_main_v_turn(Y, V)) | m_main_v_turn(X, V)) | (~node17(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_61')).
% 0.61/0.65 tff(167,plain,
% 0.61/0.65 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.61/0.65 tff(168,plain,
% 0.61/0.65 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.61/0.65 tff(169,plain,(
% 0.61/0.65 ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.61/0.65 inference(skolemize,[status(sab)],[168])).
% 0.61/0.65 tff(170,plain,
% 0.61/0.65 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.61/0.65 tff(171,plain,
% 0.61/0.65 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | (m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)) | (~node17(s0, s1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)) | (~node17(s0, s1)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(172,plain,
% 0.61/0.65 (((~node17(s0, s1)) | m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2))) <=> (m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)) | (~node17(s0, s1)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(173,plain,
% 0.61/0.65 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s0, s1)) | m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | (m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)) | (~node17(s0, s1))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[172])).
% 0.61/0.65 tff(174,plain,
% 0.61/0.65 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s0, s1)) | m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)) | (~node17(s0, s1)))),
% 0.61/0.65 inference(transitivity,[status(thm)],[173, 171])).
% 0.61/0.65 tff(175,plain,
% 0.61/0.65 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s0, s1)) | m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(176,plain,
% 0.61/0.65 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s0, c_2) | (~m_main_v_turn(s1, c_2)) | (~node17(s0, s1))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.61/0.65 tff(177,plain,
% 0.61/0.65 (~m_main_v_turn(s1, c_2)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[176, 170, 160, 146])).
% 0.61/0.65 tff(178,plain,
% 0.61/0.65 (^[X: $i] : refl((m_main_v_turn(X, c_2) | (~node12(X))) <=> (m_main_v_turn(X, c_2) | (~node12(X))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(179,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X))) <=> ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[178])).
% 0.61/0.65 tff(180,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X))) <=> ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(181,axiom,(![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_45')).
% 0.61/0.65 tff(182,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.61/0.65 tff(183,plain,(
% 0.61/0.65 ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.61/0.65 inference(skolemize,[status(sab)],[182])).
% 0.61/0.65 tff(184,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.61/0.65 tff(185,plain,
% 0.61/0.65 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s1, c_2) | (~node12(s1)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s1, c_2) | (~node12(s1)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(186,plain,
% 0.61/0.65 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s1, c_2) | (~node12(s1)))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(187,plain,
% 0.61/0.65 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s1, c_2) | (~node12(s1))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.61/0.65 tff(188,plain,
% 0.61/0.65 (~node12(s1)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[187, 184, 177])).
% 0.61/0.65 tff(189,plain,
% 0.61/0.65 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node1(X))) <=> (m_main_v_state2(X, c_t2) | (~node1(X))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(190,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[189])).
% 0.61/0.65 tff(191,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(192,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_15')).
% 0.61/0.65 tff(193,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.61/0.65 tff(194,plain,(
% 0.61/0.65 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.61/0.65 inference(skolemize,[status(sab)],[193])).
% 0.61/0.65 tff(195,plain,
% 0.61/0.65 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.61/0.65 tff(196,plain,
% 0.61/0.65 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s0, c_t2) | (~node1(s0)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s0, c_t2) | (~node1(s0)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(197,plain,
% 0.61/0.65 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s0, c_t2) | (~node1(s0)))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(198,plain,
% 0.61/0.65 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s0, c_t2) | (~node1(s0))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.61/0.65 tff(199,plain,
% 0.61/0.65 (~node1(s0)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[198, 195, 96])).
% 0.61/0.65 tff(200,plain,
% 0.61/0.65 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node7(X, Y)) <=> ((~trans(X, Y)) | node7(X, Y)))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(201,plain,
% 0.61/0.65 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[200])).
% 0.61/0.65 tff(202,plain,
% 0.61/0.65 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(203,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_34')).
% 0.61/0.65 tff(204,plain,
% 0.61/0.65 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.61/0.65 tff(205,plain,(
% 0.61/0.65 ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.61/0.65 inference(skolemize,[status(sab)],[204])).
% 0.61/0.65 tff(206,plain,
% 0.61/0.65 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.61/0.65 tff(207,plain,
% 0.61/0.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s0, s1)) | node7(s0, s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s0, s1)) | node7(s0, s1))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(208,plain,
% 0.61/0.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s0, s1)) | node7(s0, s1))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(209,plain,
% 0.61/0.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s0, s1)) | node7(s0, s1)),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.61/0.65 tff(210,plain,
% 0.61/0.65 (node7(s0, s1)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[209, 206, 39])).
% 0.61/0.65 tff(211,plain,
% 0.61/0.65 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(212,plain,
% 0.61/0.65 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[211])).
% 0.61/0.66 tff(213,plain,
% 0.61/0.66 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(214,plain,
% 0.61/0.66 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((node1(X) | (~m_main_v_state1(X, c_n1))) | (~m_main_v_state2(X, c_n2))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X))), ((((node1(X) | (~m_main_v_state1(X, c_n1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_t1)) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X)) | m_main_v_state1(Y, c_t1)))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X)) | m_main_v_state1(Y, c_t1)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | m_main_v_state1(Y, c_t1))), ((((node1(X) | (~m_main_v_state1(X, c_n1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_t1)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | m_main_v_state1(Y, c_t1)))), (((((node1(X) | (~m_main_v_state1(X, c_n1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))), (((((node1(X) | (~m_main_v_state1(X, c_n1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(215,plain,
% 0.61/0.66 (![Y: $i, X: $i] : ((((node1(X) | (~m_main_v_state1(X, c_n1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[214])).
% 0.61/0.66 tff(216,axiom,(![Y: $i, X: $i] : ((((node1(X) | (~m_main_v_state1(X, c_n1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_28')).
% 0.61/0.66 tff(217,plain,
% 0.61/0.66 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.61/0.66 tff(218,plain,
% 0.61/0.66 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.61/0.66 tff(219,plain,(
% 0.61/0.66 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.61/0.66 inference(skolemize,[status(sab)],[218])).
% 0.61/0.66 tff(220,plain,
% 0.61/0.66 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.61/0.66 tff(221,plain,
% 0.61/0.66 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | m_main_v_state1(s1, c_t1) | (~node7(s0, s1)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | m_main_v_state1(s1, c_t1) | (~node7(s0, s1)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(222,plain,
% 0.61/0.66 (((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | (~node7(s0, s1)) | m_main_v_state1(s1, c_t1)) <=> ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | m_main_v_state1(s1, c_t1) | (~node7(s0, s1)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(223,plain,
% 0.61/0.66 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | (~node7(s0, s1)) | m_main_v_state1(s1, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | m_main_v_state1(s1, c_t1) | (~node7(s0, s1))))),
% 0.61/0.66 inference(monotonicity,[status(thm)],[222])).
% 0.61/0.66 tff(224,plain,
% 0.61/0.66 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | (~node7(s0, s1)) | m_main_v_state1(s1, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | m_main_v_state1(s1, c_t1) | (~node7(s0, s1)))),
% 0.61/0.66 inference(transitivity,[status(thm)],[223, 221])).
% 0.61/0.66 tff(225,plain,
% 0.61/0.66 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | (~node7(s0, s1)) | m_main_v_state1(s1, c_t1))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(226,plain,
% 0.61/0.66 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s0, c_n1)) | (~m_main_v_state2(s0, c_n2)) | node1(s0) | m_main_v_state1(s1, c_t1) | (~node7(s0, s1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.61/0.66 tff(227,plain,
% 0.61/0.66 (m_main_v_state1(s1, c_t1)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[226, 3, 63, 220, 210, 199])).
% 0.61/0.66 tff(228,plain,
% 0.61/0.66 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s1, c_n1)) | (~m_main_v_state1(s1, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s1, c_n1)) | (~m_main_v_state1(s1, c_t1)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(229,plain,
% 0.61/0.66 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s1, c_n1)) | (~m_main_v_state1(s1, c_t1)))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(230,plain,
% 0.61/0.66 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s1, c_n1)) | (~m_main_v_state1(s1, c_t1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.61/0.66 tff(231,plain,
% 0.61/0.66 (~m_main_v_state1(s1, c_n1)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[230, 10, 227])).
% 0.61/0.66 tff(232,plain,
% 0.61/0.66 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node11(X))) <=> (m_main_v_state1(X, c_n1) | (~node11(X))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(233,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[232])).
% 0.61/0.66 tff(234,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(235,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_42')).
% 0.61/0.66 tff(236,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.61/0.66 tff(237,plain,(
% 0.61/0.66 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.61/0.66 inference(skolemize,[status(sab)],[236])).
% 0.61/0.66 tff(238,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.61/0.66 tff(239,plain,
% 0.61/0.66 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s1, c_n1) | (~node11(s1)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s1, c_n1) | (~node11(s1)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(240,plain,
% 0.61/0.66 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s1, c_n1) | (~node11(s1)))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(241,plain,
% 0.61/0.66 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s1, c_n1) | (~node11(s1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.61/0.66 tff(242,plain,
% 0.61/0.66 (~node11(s1)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[241, 238, 231])).
% 0.61/0.66 tff(243,plain,
% 0.61/0.66 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node10(X))) <=> (m_main_v_state2(X, c_n2) | (~node10(X))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(244,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[243])).
% 0.61/0.66 tff(245,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(246,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_39')).
% 0.61/0.66 tff(247,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.61/0.66 tff(248,plain,(
% 0.61/0.66 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.61/0.66 inference(skolemize,[status(sab)],[247])).
% 0.61/0.66 tff(249,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.61/0.66 tff(250,plain,
% 0.61/0.66 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s1, c_n2) | (~node10(s1)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s1, c_n2) | (~node10(s1)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(251,plain,
% 0.61/0.66 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s1, c_n2) | (~node10(s1)))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(252,plain,
% 0.61/0.66 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s1, c_n2) | (~node10(s1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.61/0.66 tff(253,plain,
% 0.61/0.66 (~node10(s1)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[252, 249, 81])).
% 0.61/0.66 tff(254,plain,
% 0.61/0.66 (^[X: $i] : refl(((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2))) <=> ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(255,plain,
% 0.61/0.66 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2))) <=> ![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[254])).
% 0.61/0.66 tff(256,plain,
% 0.61/0.66 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2))) <=> ![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(257,axiom,(![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_8')).
% 0.61/0.66 tff(258,plain,
% 0.61/0.66 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.61/0.66 tff(259,plain,(
% 0.61/0.66 ![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.61/0.66 inference(skolemize,[status(sab)],[258])).
% 0.61/0.66 tff(260,plain,
% 0.61/0.66 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.61/0.66 tff(261,plain,
% 0.61/0.66 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s1, c_t2)) | (~m_main_v_state2(s1, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_state2(s1, c_c2)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(262,plain,
% 0.61/0.66 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s1, c_t2)) | (~m_main_v_state2(s1, c_c2)))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(263,plain,
% 0.61/0.66 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_state2(s1, c_c2))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.61/0.66 tff(264,plain,
% 0.61/0.66 (~m_main_v_state2(s1, c_c2)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[263, 260, 70])).
% 0.61/0.66 tff(265,plain,
% 0.61/0.66 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node8(X))) <=> (m_main_v_state2(X, c_n2) | (~node8(X))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(266,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[265])).
% 0.61/0.66 tff(267,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(268,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_35')).
% 0.61/0.66 tff(269,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.61/0.66 tff(270,plain,(
% 0.61/0.66 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.61/0.66 inference(skolemize,[status(sab)],[269])).
% 0.61/0.66 tff(271,plain,
% 0.61/0.66 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.61/0.66 tff(272,plain,
% 0.61/0.66 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s1, c_n2) | (~node8(s1)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s1, c_n2) | (~node8(s1)))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(273,plain,
% 0.61/0.66 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s1, c_n2) | (~node8(s1)))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(274,plain,
% 0.61/0.66 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s1, c_n2) | (~node8(s1))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.61/0.66 tff(275,plain,
% 0.61/0.66 (~node8(s1)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[274, 271, 81])).
% 0.61/0.66 tff(276,plain,
% 0.61/0.66 (succ(s1, s2) <=> succ(s1, s2)),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(277,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 0.61/0.66 tff(278,plain,
% 0.61/0.66 (succ(s1, s2)),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.61/0.66 tff(279,plain,
% 0.61/0.66 (((~![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))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(280,plain,
% 0.61/0.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(281,plain,
% 0.61/0.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.61/0.66 tff(282,plain,
% 0.61/0.66 (trans(s1, s2)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[281, 278, 32])).
% 0.61/0.66 tff(283,plain,
% 0.61/0.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s1, s2)) | node14(s1, s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s1, s2)) | node14(s1, s2))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(284,plain,
% 0.61/0.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s1, s2)) | node14(s1, s2))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(285,plain,
% 0.61/0.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s1, s2)) | node14(s1, s2)),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.61/0.66 tff(286,plain,
% 0.61/0.66 (node14(s1, s2)),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[285, 46, 282])).
% 0.61/0.66 tff(287,plain,
% 0.61/0.66 (^[Y: $i, X: $i] : refl((m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y))) <=> (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y))))),
% 0.61/0.67 inference(bind,[status(th)],[])).
% 0.61/0.67 tff(288,plain,
% 0.61/0.67 (![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y))) <=> ![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))),
% 0.61/0.67 inference(quant_intro,[status(thm)],[287])).
% 0.61/0.67 tff(289,plain,
% 0.61/0.67 (![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y))) <=> ![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(290,plain,
% 0.61/0.67 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((node8(X) | node9(X)) | node10(X)) <=> (node9(X) | node8(X) | node10(X))), ((((node8(X) | node9(X)) | node10(X)) | node11(X)) <=> ((node9(X) | node8(X) | node10(X)) | node11(X)))), rewrite(((node9(X) | node8(X) | node10(X)) | node11(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X))), ((((node8(X) | node9(X)) | node10(X)) | node11(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X)))), (((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) <=> ((node9(X) | node8(X) | node10(X) | node11(X)) | node12(X)))), rewrite(((node9(X) | node8(X) | node10(X) | node11(X)) | node12(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X) | node12(X))), (((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X) | node12(X)))), ((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) <=> ((node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | m_main_v_state2(X, c_c2)))), rewrite(((node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | m_main_v_state2(X, c_c2)) <=> (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X))), ((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) <=> (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X)))), (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) | node13(X, Y)) <=> ((m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | node13(X, Y)))), rewrite(((m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | node13(X, Y)) <=> (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y))), (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) | node13(X, Y)) <=> (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y)))), ((((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) | node13(X, Y)) | (~node14(X, Y))) <=> ((m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y)) | (~node14(X, Y))))), rewrite(((m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y)) | (~node14(X, Y))) <=> (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))), ((((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) | node13(X, Y)) | (~node14(X, Y))) <=> (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))))),
% 0.61/0.67 inference(bind,[status(th)],[])).
% 0.61/0.67 tff(291,plain,
% 0.61/0.67 (![Y: $i, X: $i] : (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) | node13(X, Y)) | (~node14(X, Y))) <=> ![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))),
% 0.61/0.67 inference(quant_intro,[status(thm)],[290])).
% 0.61/0.67 tff(292,axiom,(![Y: $i, X: $i] : (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | m_main_v_state2(X, c_c2)) | node13(X, Y)) | (~node14(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_54')).
% 0.61/0.67 tff(293,plain,
% 0.61/0.67 (![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.61/0.67 tff(294,plain,
% 0.61/0.67 (![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.61/0.67 tff(295,plain,(
% 0.61/0.67 ![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))),
% 0.61/0.67 inference(skolemize,[status(sab)],[294])).
% 0.61/0.67 tff(296,plain,
% 0.61/0.67 (![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.61/0.67 tff(297,plain,
% 0.61/0.67 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s1, c_c2) | node9(s1) | node8(s1) | node10(s1) | node11(s1) | node12(s1) | node13(s1, s2) | (~node14(s1, s2)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s1, c_c2) | node9(s1) | node8(s1) | node10(s1) | node11(s1) | node12(s1) | node13(s1, s2) | (~node14(s1, s2)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(298,plain,
% 0.61/0.67 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s1, c_c2) | node9(s1) | node8(s1) | node10(s1) | node11(s1) | node12(s1) | node13(s1, s2) | (~node14(s1, s2)))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(299,plain,
% 0.61/0.67 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s1, c_c2) | node9(s1) | node8(s1) | node10(s1) | node11(s1) | node12(s1) | node13(s1, s2) | (~node14(s1, s2))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.61/0.67 tff(300,plain,
% 0.61/0.67 (m_main_v_state2(s1, c_c2) | node9(s1) | node8(s1) | node10(s1) | node11(s1) | node12(s1) | node13(s1, s2)),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[299, 296, 286])).
% 0.61/0.67 tff(301,plain,
% 0.61/0.67 (node13(s1, s2)),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[300, 275, 264, 253, 242, 188, 92])).
% 0.61/0.67 tff(302,plain,
% 0.61/0.67 (^[V: $i, Y: $i, X: $i] : refl(((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V))) <=> ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V))))),
% 0.61/0.67 inference(bind,[status(th)],[])).
% 0.61/0.67 tff(303,plain,
% 0.61/0.67 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V))) <=> ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.61/0.67 inference(quant_intro,[status(thm)],[302])).
% 0.61/0.67 tff(304,plain,
% 0.61/0.67 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V))) <=> ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(305,plain,
% 0.61/0.67 (^[V: $i, Y: $i, X: $i] : rewrite((((~m_main_v_state2(Y, V)) | m_main_v_state2(X, V)) | (~node13(X, Y))) <=> ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V))))),
% 0.61/0.67 inference(bind,[status(th)],[])).
% 0.61/0.67 tff(306,plain,
% 0.61/0.67 (![V: $i, Y: $i, X: $i] : (((~m_main_v_state2(Y, V)) | m_main_v_state2(X, V)) | (~node13(X, Y))) <=> ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.61/0.67 inference(quant_intro,[status(thm)],[305])).
% 0.61/0.67 tff(307,axiom,(![V: $i, Y: $i, X: $i] : (((~m_main_v_state2(Y, V)) | m_main_v_state2(X, V)) | (~node13(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_47')).
% 0.61/0.67 tff(308,plain,
% 0.61/0.67 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.61/0.67 tff(309,plain,
% 0.61/0.67 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.61/0.67 tff(310,plain,(
% 0.61/0.67 ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.61/0.67 inference(skolemize,[status(sab)],[309])).
% 0.61/0.67 tff(311,plain,
% 0.61/0.67 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.61/0.67 tff(312,plain,
% 0.61/0.67 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)) | (~node13(s1, s2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)) | (~node13(s1, s2)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(313,plain,
% 0.61/0.67 (((~node13(s1, s2)) | m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2))) <=> (m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)) | (~node13(s1, s2)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(314,plain,
% 0.61/0.67 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s1, s2)) | m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)) | (~node13(s1, s2))))),
% 0.61/0.67 inference(monotonicity,[status(thm)],[313])).
% 0.61/0.67 tff(315,plain,
% 0.61/0.67 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s1, s2)) | m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)) | (~node13(s1, s2)))),
% 0.61/0.67 inference(transitivity,[status(thm)],[314, 312])).
% 0.61/0.67 tff(316,plain,
% 0.61/0.67 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s1, s2)) | m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(317,plain,
% 0.61/0.67 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s1, c_n2) | (~m_main_v_state2(s2, c_n2)) | (~node13(s1, s2))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.61/0.67 tff(318,plain,
% 0.61/0.67 (~m_main_v_state2(s2, c_n2)),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[317, 311, 81, 301])).
% 0.61/0.67 tff(319,plain,
% 0.61/0.67 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s2, c_n2) | (~node9(s2)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s2, c_n2) | (~node9(s2)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(320,plain,
% 0.61/0.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s2, c_n2) | (~node9(s2)))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(321,plain,
% 0.61/0.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s2, c_n2) | (~node9(s2))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.61/0.67 tff(322,plain,
% 0.61/0.67 (~node9(s2)),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[321, 88, 318])).
% 0.61/0.67 tff(323,plain,
% 0.61/0.67 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node16(X))) <=> (m_main_v_state2(X, c_n2) | (~node16(X))))),
% 0.61/0.67 inference(bind,[status(th)],[])).
% 0.61/0.67 tff(324,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.61/0.67 inference(quant_intro,[status(thm)],[323])).
% 0.61/0.67 tff(325,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(326,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_58')).
% 0.61/0.67 tff(327,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.61/0.67 tff(328,plain,(
% 0.61/0.67 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.61/0.67 inference(skolemize,[status(sab)],[327])).
% 0.61/0.67 tff(329,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.61/0.67 tff(330,plain,
% 0.61/0.67 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s1, c_n2) | (~node16(s1)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s1, c_n2) | (~node16(s1)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(331,plain,
% 0.61/0.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s1, c_n2) | (~node16(s1)))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(332,plain,
% 0.61/0.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s1, c_n2) | (~node16(s1))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.61/0.67 tff(333,plain,
% 0.61/0.67 (~node16(s1)),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[332, 329, 81])).
% 0.61/0.67 tff(334,plain,
% 0.61/0.67 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node15(X))) <=> (m_main_v_state1(X, c_n1) | (~node15(X))))),
% 0.61/0.67 inference(bind,[status(th)],[])).
% 0.61/0.67 tff(335,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.61/0.67 inference(quant_intro,[status(thm)],[334])).
% 0.61/0.67 tff(336,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(337,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_56')).
% 0.61/0.67 tff(338,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.61/0.67 tff(339,plain,(
% 0.61/0.67 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.61/0.67 inference(skolemize,[status(sab)],[338])).
% 0.61/0.67 tff(340,plain,
% 0.61/0.67 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[339, 335])).
% 0.61/0.67 tff(341,plain,
% 0.61/0.67 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s1, c_n1) | (~node15(s1)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s1, c_n1) | (~node15(s1)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(342,plain,
% 0.61/0.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s1, c_n1) | (~node15(s1)))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(343,plain,
% 0.61/0.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s1, c_n1) | (~node15(s1))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.61/0.67 tff(344,plain,
% 0.61/0.67 (~node15(s1)),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[343, 340, 231])).
% 0.61/0.67 tff(345,plain,
% 0.61/0.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s1, s2)) | node18(s1, s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s1, s2)) | node18(s1, s2))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(346,plain,
% 0.61/0.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s1, s2)) | node18(s1, s2))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(347,plain,
% 0.61/0.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s1, s2)) | node18(s1, s2)),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.61/0.67 tff(348,plain,
% 0.61/0.67 (node18(s1, s2)),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[347, 125, 282])).
% 0.61/0.67 tff(349,plain,
% 0.61/0.67 (((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2)))) <=> ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2)))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(350,plain,
% 0.61/0.67 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2)))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(351,plain,
% 0.61/0.68 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.61/0.68 tff(352,plain,
% 0.61/0.68 (node15(s1) | node16(s1) | node17(s1, s2)),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[351, 139, 348])).
% 0.61/0.68 tff(353,plain,
% 0.61/0.68 (node17(s1, s2)),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[352, 344, 333])).
% 0.61/0.68 tff(354,plain,
% 0.61/0.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | (m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)) | (~node17(s1, s2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)) | (~node17(s1, s2)))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(355,plain,
% 0.61/0.68 (((~node17(s1, s2)) | m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2))) <=> (m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)) | (~node17(s1, s2)))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(356,plain,
% 0.61/0.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s1, s2)) | m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | (m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)) | (~node17(s1, s2))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[355])).
% 0.61/0.68 tff(357,plain,
% 0.61/0.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s1, s2)) | m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)) | (~node17(s1, s2)))),
% 0.61/0.68 inference(transitivity,[status(thm)],[356, 354])).
% 0.61/0.68 tff(358,plain,
% 0.61/0.68 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s1, s2)) | m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(359,plain,
% 0.61/0.68 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s1, c_2) | (~m_main_v_turn(s2, c_2)) | (~node17(s1, s2))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.61/0.68 tff(360,plain,
% 0.61/0.68 (~m_main_v_turn(s2, c_2)),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[359, 170, 353, 177])).
% 0.61/0.68 tff(361,plain,
% 0.61/0.68 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s2, c_2) | (~node12(s2)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s2, c_2) | (~node12(s2)))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(362,plain,
% 0.61/0.68 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s2, c_2) | (~node12(s2)))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(363,plain,
% 0.61/0.68 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s2, c_2) | (~node12(s2))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.61/0.68 tff(364,plain,
% 0.61/0.68 (~node12(s2)),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[363, 184, 360])).
% 0.61/0.68 tff(365,plain,
% 0.61/0.68 (^[V: $i, Y: $i, X: $i] : refl(((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V)) <=> ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V)))),
% 0.61/0.68 inference(bind,[status(th)],[])).
% 0.61/0.68 tff(366,plain,
% 0.61/0.68 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V)) <=> ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.61/0.68 inference(quant_intro,[status(thm)],[365])).
% 0.61/0.68 tff(367,plain,
% 0.61/0.68 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V)) <=> ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(368,plain,
% 0.61/0.68 (^[V: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((m_main_v_turn(Y, V) | (~m_main_v_turn(X, V))) <=> ((~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))), (((m_main_v_turn(Y, V) | (~m_main_v_turn(X, V))) | (~node17(X, Y))) <=> (((~m_main_v_turn(X, V)) | m_main_v_turn(Y, V)) | (~node17(X, Y))))), rewrite((((~m_main_v_turn(X, V)) | m_main_v_turn(Y, V)) | (~node17(X, Y))) <=> ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))), (((m_main_v_turn(Y, V) | (~m_main_v_turn(X, V))) | (~node17(X, Y))) <=> ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))))),
% 0.61/0.68 inference(bind,[status(th)],[])).
% 0.61/0.68 tff(369,plain,
% 0.61/0.68 (![V: $i, Y: $i, X: $i] : ((m_main_v_turn(Y, V) | (~m_main_v_turn(X, V))) | (~node17(X, Y))) <=> ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.61/0.68 inference(quant_intro,[status(thm)],[368])).
% 0.61/0.68 tff(370,axiom,(![V: $i, Y: $i, X: $i] : ((m_main_v_turn(Y, V) | (~m_main_v_turn(X, V))) | (~node17(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_60')).
% 0.61/0.68 tff(371,plain,
% 0.61/0.68 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.61/0.68 tff(372,plain,
% 0.61/0.68 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.61/0.68 tff(373,plain,(
% 0.61/0.68 ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.61/0.68 inference(skolemize,[status(sab)],[372])).
% 0.61/0.68 tff(374,plain,
% 0.61/0.68 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[373, 366])).
% 0.61/0.68 tff(375,plain,
% 0.61/0.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | ((~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1) | (~node17(s0, s1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | (~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1) | (~node17(s0, s1)))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(376,plain,
% 0.61/0.68 (((~node17(s0, s1)) | (~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1)) <=> ((~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1) | (~node17(s0, s1)))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(377,plain,
% 0.61/0.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | ((~node17(s0, s1)) | (~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | ((~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1) | (~node17(s0, s1))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[376])).
% 0.61/0.68 tff(378,plain,
% 0.61/0.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | ((~node17(s0, s1)) | (~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | (~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1) | (~node17(s0, s1)))),
% 0.61/0.68 inference(transitivity,[status(thm)],[377, 375])).
% 0.61/0.68 tff(379,plain,
% 0.61/0.68 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | ((~node17(s0, s1)) | (~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(380,plain,
% 0.61/0.68 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))) | (~m_main_v_turn(s0, c_1)) | m_main_v_turn(s1, c_1) | (~node17(s0, s1))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.61/0.68 tff(381,plain,
% 0.61/0.68 (m_main_v_turn(s1, c_1)),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[380, 149, 374, 146])).
% 0.61/0.68 tff(382,plain,
% 0.61/0.68 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node4(X))) <=> (m_main_v_state2(X, c_n2) | (~node4(X))))),
% 0.61/0.68 inference(bind,[status(th)],[])).
% 0.61/0.68 tff(383,plain,
% 0.61/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.61/0.68 inference(quant_intro,[status(thm)],[382])).
% 0.61/0.68 tff(384,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(385,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_21')).
% 0.66/0.68 tff(386,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.66/0.68 tff(387,plain,(
% 0.66/0.68 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.66/0.68 inference(skolemize,[status(sab)],[386])).
% 0.66/0.68 tff(388,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[387, 383])).
% 0.66/0.68 tff(389,plain,
% 0.66/0.68 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s1, c_n2) | (~node4(s1)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s1, c_n2) | (~node4(s1)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(390,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s1, c_n2) | (~node4(s1)))),
% 0.66/0.68 inference(quant_inst,[status(thm)],[])).
% 0.66/0.68 tff(391,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s1, c_n2) | (~node4(s1))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.66/0.68 tff(392,plain,
% 0.66/0.68 (~node4(s1)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[391, 388, 81])).
% 0.66/0.68 tff(393,plain,
% 0.66/0.68 (^[X: $i] : refl((m_main_v_state2(X, c_c2) | (~node3(X))) <=> (m_main_v_state2(X, c_c2) | (~node3(X))))),
% 0.66/0.68 inference(bind,[status(th)],[])).
% 0.66/0.68 tff(394,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X))) <=> ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.66/0.68 inference(quant_intro,[status(thm)],[393])).
% 0.66/0.68 tff(395,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X))) <=> ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(396,axiom,(![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_19')).
% 0.66/0.68 tff(397,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.66/0.68 tff(398,plain,(
% 0.66/0.68 ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.66/0.68 inference(skolemize,[status(sab)],[397])).
% 0.66/0.68 tff(399,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[398, 394])).
% 0.66/0.68 tff(400,plain,
% 0.66/0.68 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s1, c_c2) | (~node3(s1)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s1, c_c2) | (~node3(s1)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(401,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s1, c_c2) | (~node3(s1)))),
% 0.66/0.68 inference(quant_inst,[status(thm)],[])).
% 0.66/0.68 tff(402,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s1, c_c2) | (~node3(s1))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.66/0.68 tff(403,plain,
% 0.66/0.68 (~node3(s1)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[402, 399, 264])).
% 0.66/0.68 tff(404,plain,
% 0.66/0.68 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node2(X))) <=> (m_main_v_state2(X, c_n2) | (~node2(X))))),
% 0.66/0.68 inference(bind,[status(th)],[])).
% 0.66/0.68 tff(405,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.66/0.68 inference(quant_intro,[status(thm)],[404])).
% 0.66/0.68 tff(406,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(407,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_17')).
% 0.66/0.68 tff(408,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.66/0.68 tff(409,plain,(
% 0.66/0.68 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.66/0.68 inference(skolemize,[status(sab)],[408])).
% 0.66/0.68 tff(410,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.66/0.68 tff(411,plain,
% 0.66/0.68 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s1, c_n2) | (~node2(s1)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s1, c_n2) | (~node2(s1)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(412,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s1, c_n2) | (~node2(s1)))),
% 0.66/0.68 inference(quant_inst,[status(thm)],[])).
% 0.66/0.68 tff(413,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s1, c_n2) | (~node2(s1))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.66/0.68 tff(414,plain,
% 0.66/0.68 (~node2(s1)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[413, 410, 81])).
% 0.66/0.68 tff(415,plain,
% 0.66/0.68 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node1(X))) <=> (m_main_v_state1(X, c_n1) | (~node1(X))))),
% 0.66/0.68 inference(bind,[status(th)],[])).
% 0.66/0.68 tff(416,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.66/0.68 inference(quant_intro,[status(thm)],[415])).
% 0.66/0.68 tff(417,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(418,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_14')).
% 0.66/0.68 tff(419,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.66/0.68 tff(420,plain,(
% 0.66/0.68 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.66/0.68 inference(skolemize,[status(sab)],[419])).
% 0.66/0.68 tff(421,plain,
% 0.66/0.68 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[420, 416])).
% 0.66/0.68 tff(422,plain,
% 0.66/0.68 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s1, c_n1) | (~node1(s1)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s1, c_n1) | (~node1(s1)))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(423,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s1, c_n1) | (~node1(s1)))),
% 0.66/0.68 inference(quant_inst,[status(thm)],[])).
% 0.66/0.68 tff(424,plain,
% 0.66/0.68 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s1, c_n1) | (~node1(s1))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.66/0.68 tff(425,plain,
% 0.66/0.68 (~node1(s1)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[424, 421, 231])).
% 0.66/0.68 tff(426,plain,
% 0.66/0.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s1, s2)) | node7(s1, s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s1, s2)) | node7(s1, s2))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(427,plain,
% 0.66/0.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s1, s2)) | node7(s1, s2))),
% 0.66/0.68 inference(quant_inst,[status(thm)],[])).
% 0.66/0.68 tff(428,plain,
% 0.66/0.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s1, s2)) | node7(s1, s2)),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.66/0.68 tff(429,plain,
% 0.66/0.68 (node7(s1, s2)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[428, 206, 282])).
% 0.66/0.68 tff(430,plain,
% 0.66/0.68 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)))),
% 0.66/0.68 inference(bind,[status(th)],[])).
% 0.66/0.68 tff(431,plain,
% 0.66/0.68 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.66/0.68 inference(quant_intro,[status(thm)],[430])).
% 0.66/0.68 tff(432,plain,
% 0.66/0.69 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(433,plain,
% 0.66/0.69 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((node1(X) | node2(X)) | node3(X)) <=> (node1(X) | node2(X) | node3(X))), ((((node1(X) | node2(X)) | node3(X)) | node4(X)) <=> ((node1(X) | node2(X) | node3(X)) | node4(X)))), rewrite(((node1(X) | node2(X) | node3(X)) | node4(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X))), ((((node1(X) | node2(X)) | node3(X)) | node4(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X)))), (((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) <=> ((node1(X) | node2(X) | node3(X) | node4(X)) | (~m_main_v_state1(X, c_t1))))), rewrite(((node1(X) | node2(X) | node3(X) | node4(X)) | (~m_main_v_state1(X, c_t1))) <=> ((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X) | node4(X))), (((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) <=> ((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X) | node4(X)))), ((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) <=> (((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X) | node4(X)) | (~m_main_v_state2(X, c_t2))))), rewrite((((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X) | node4(X)) | (~m_main_v_state2(X, c_t2))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | node1(X) | node2(X) | node3(X) | node4(X))), ((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | node1(X) | node2(X) | node3(X) | node4(X)))), (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | node1(X) | node2(X) | node3(X) | node4(X)) | (~m_main_v_turn(X, c_1))))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | node1(X) | node2(X) | node3(X) | node4(X)) | (~m_main_v_turn(X, c_1))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X))), (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X)))), ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) | m_main_v_state1(Y, c_c1)) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X)) | m_main_v_state1(Y, c_c1)))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X)) | m_main_v_state1(Y, c_c1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | m_main_v_state1(Y, c_c1))), ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) | m_main_v_state1(Y, c_c1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | m_main_v_state1(Y, c_c1)))), (((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))), (((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(434,plain,
% 0.66/0.69 (![Y: $i, X: $i] : ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[433])).
% 0.66/0.69 tff(435,axiom,(![Y: $i, X: $i] : ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_turn(X, c_1))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_31')).
% 0.66/0.69 tff(436,plain,
% 0.66/0.69 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.66/0.69 tff(437,plain,
% 0.66/0.69 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[436, 432])).
% 0.66/0.69 tff(438,plain,(
% 0.66/0.69 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.66/0.69 inference(skolemize,[status(sab)],[437])).
% 0.66/0.69 tff(439,plain,
% 0.66/0.69 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[438, 431])).
% 0.66/0.69 tff(440,plain,
% 0.66/0.69 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state2(s1, c_t2)) | (~m_main_v_state1(s1, c_t1)) | m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | (~m_main_v_turn(s1, c_1)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_state1(s1, c_t1)) | m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | (~m_main_v_turn(s1, c_1)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(441,plain,
% 0.66/0.69 (((~m_main_v_state1(s1, c_t1)) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_turn(s1, c_1)) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | m_main_v_state1(s2, c_c1)) <=> ((~m_main_v_state2(s1, c_t2)) | (~m_main_v_state1(s1, c_t1)) | m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | (~m_main_v_turn(s1, c_1)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(442,plain,
% 0.66/0.69 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s1, c_t1)) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_turn(s1, c_1)) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | m_main_v_state1(s2, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state2(s1, c_t2)) | (~m_main_v_state1(s1, c_t1)) | m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | (~m_main_v_turn(s1, c_1))))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[441])).
% 0.66/0.69 tff(443,plain,
% 0.66/0.69 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s1, c_t1)) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_turn(s1, c_1)) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | m_main_v_state1(s2, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_state1(s1, c_t1)) | m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | (~m_main_v_turn(s1, c_1)))),
% 0.66/0.69 inference(transitivity,[status(thm)],[442, 440])).
% 0.66/0.69 tff(444,plain,
% 0.66/0.69 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s1, c_t1)) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_turn(s1, c_1)) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | m_main_v_state1(s2, c_c1))),
% 0.66/0.69 inference(quant_inst,[status(thm)],[])).
% 0.66/0.69 tff(445,plain,
% 0.66/0.69 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_t2)) | (~m_main_v_turn(X, c_1)) | node1(X) | node2(X) | node3(X) | node4(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state2(s1, c_t2)) | (~m_main_v_state1(s1, c_t1)) | m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~node7(s1, s2)) | (~m_main_v_turn(s1, c_1))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.66/0.69 tff(446,plain,
% 0.66/0.69 (m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~m_main_v_turn(s1, c_1))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[445, 439, 429, 70, 227])).
% 0.66/0.69 tff(447,plain,
% 0.66/0.69 (m_main_v_state1(s2, c_c1)),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[446, 425, 414, 403, 392, 381])).
% 0.66/0.69 tff(448,plain,
% 0.66/0.69 (^[X: $i] : refl(((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(449,plain,
% 0.66/0.69 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1))) <=> ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[448])).
% 0.66/0.69 tff(450,plain,
% 0.66/0.69 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1))) <=> ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(451,axiom,(![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_3')).
% 0.66/0.69 tff(452,plain,
% 0.66/0.69 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.66/0.69 tff(453,plain,(
% 0.66/0.69 ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.69 inference(skolemize,[status(sab)],[452])).
% 0.66/0.69 tff(454,plain,
% 0.66/0.69 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[453, 449])).
% 0.66/0.70 tff(455,plain,
% 0.66/0.70 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s2, c_n1)) | (~m_main_v_state1(s2, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s2, c_n1)) | (~m_main_v_state1(s2, c_c1)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(456,plain,
% 0.66/0.70 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s2, c_n1)) | (~m_main_v_state1(s2, c_c1)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(457,plain,
% 0.66/0.70 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s2, c_n1)) | (~m_main_v_state1(s2, c_c1))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.66/0.70 tff(458,plain,
% 0.66/0.70 (~m_main_v_state1(s2, c_n1)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[457, 454, 447])).
% 0.66/0.70 tff(459,plain,
% 0.66/0.70 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s2, c_n1) | (~node11(s2)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s2, c_n1) | (~node11(s2)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(460,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s2, c_n1) | (~node11(s2)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(461,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s2, c_n1) | (~node11(s2))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.66/0.70 tff(462,plain,
% 0.66/0.70 (~node11(s2)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[461, 238, 458])).
% 0.66/0.70 tff(463,plain,
% 0.66/0.70 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s2, c_n2) | (~node10(s2)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s2, c_n2) | (~node10(s2)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(464,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s2, c_n2) | (~node10(s2)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(465,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s2, c_n2) | (~node10(s2))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.66/0.70 tff(466,plain,
% 0.66/0.70 (~node10(s2)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[465, 249, 318])).
% 0.66/0.70 tff(467,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)) | (~node13(s1, s2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)) | (~node13(s1, s2)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(468,plain,
% 0.66/0.70 (((~node13(s1, s2)) | m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2))) <=> (m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)) | (~node13(s1, s2)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(469,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s1, s2)) | m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)) | (~node13(s1, s2))))),
% 0.66/0.70 inference(monotonicity,[status(thm)],[468])).
% 0.66/0.70 tff(470,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s1, s2)) | m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)) | (~node13(s1, s2)))),
% 0.66/0.70 inference(transitivity,[status(thm)],[469, 467])).
% 0.66/0.70 tff(471,plain,
% 0.66/0.70 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s1, s2)) | m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(472,plain,
% 0.66/0.70 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s1, c_c2) | (~m_main_v_state2(s2, c_c2)) | (~node13(s1, s2))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.66/0.70 tff(473,plain,
% 0.66/0.70 (~m_main_v_state2(s2, c_c2)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[472, 311, 264, 301])).
% 0.66/0.70 tff(474,plain,
% 0.66/0.70 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s2, c_n2) | (~node8(s2)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s2, c_n2) | (~node8(s2)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(475,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s2, c_n2) | (~node8(s2)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(476,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s2, c_n2) | (~node8(s2))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.66/0.70 tff(477,plain,
% 0.66/0.70 (~node8(s2)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[476, 271, 318])).
% 0.66/0.70 tff(478,plain,
% 0.66/0.70 (succ(s2, s3) <=> succ(s2, s3)),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(479,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 0.66/0.70 tff(480,plain,
% 0.66/0.70 (succ(s2, s3)),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.66/0.70 tff(481,plain,
% 0.66/0.70 (((~![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))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(482,plain,
% 0.66/0.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(483,plain,
% 0.66/0.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.66/0.70 tff(484,plain,
% 0.66/0.70 (trans(s2, s3)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[483, 480, 32])).
% 0.66/0.70 tff(485,plain,
% 0.66/0.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s2, s3)) | node14(s2, s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s2, s3)) | node14(s2, s3))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(486,plain,
% 0.66/0.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s2, s3)) | node14(s2, s3))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(487,plain,
% 0.66/0.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s2, s3)) | node14(s2, s3)),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.66/0.70 tff(488,plain,
% 0.66/0.70 (node14(s2, s3)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[487, 46, 484])).
% 0.66/0.70 tff(489,plain,
% 0.66/0.70 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s2, c_c2) | node9(s2) | node8(s2) | node10(s2) | node11(s2) | node12(s2) | node13(s2, s3) | (~node14(s2, s3)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s2, c_c2) | node9(s2) | node8(s2) | node10(s2) | node11(s2) | node12(s2) | node13(s2, s3) | (~node14(s2, s3)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(490,plain,
% 0.66/0.70 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s2, c_c2) | node9(s2) | node8(s2) | node10(s2) | node11(s2) | node12(s2) | node13(s2, s3) | (~node14(s2, s3)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(491,plain,
% 0.66/0.70 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s2, c_c2) | node9(s2) | node8(s2) | node10(s2) | node11(s2) | node12(s2) | node13(s2, s3) | (~node14(s2, s3))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.66/0.70 tff(492,plain,
% 0.66/0.70 (m_main_v_state2(s2, c_c2) | node9(s2) | node8(s2) | node10(s2) | node11(s2) | node12(s2) | node13(s2, s3)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[491, 296, 488])).
% 0.66/0.70 tff(493,plain,
% 0.66/0.70 (node13(s2, s3)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[492, 477, 473, 466, 462, 364, 322])).
% 0.66/0.70 tff(494,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)) | (~node13(s2, s3)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)) | (~node13(s2, s3)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(495,plain,
% 0.66/0.70 (((~node13(s2, s3)) | m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2))) <=> (m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)) | (~node13(s2, s3)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(496,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s2, s3)) | m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)) | (~node13(s2, s3))))),
% 0.66/0.70 inference(monotonicity,[status(thm)],[495])).
% 0.66/0.70 tff(497,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s2, s3)) | m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)) | (~node13(s2, s3)))),
% 0.66/0.70 inference(transitivity,[status(thm)],[496, 494])).
% 0.66/0.70 tff(498,plain,
% 0.66/0.70 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s2, s3)) | m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(499,plain,
% 0.66/0.70 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s2, c_n2) | (~m_main_v_state2(s3, c_n2)) | (~node13(s2, s3))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.66/0.70 tff(500,plain,
% 0.66/0.70 (~m_main_v_state2(s3, c_n2)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[499, 311, 318, 493])).
% 0.66/0.70 tff(501,plain,
% 0.66/0.70 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s3, c_n2) | (~node9(s3)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s3, c_n2) | (~node9(s3)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(502,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s3, c_n2) | (~node9(s3)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(503,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s3, c_n2) | (~node9(s3))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.66/0.70 tff(504,plain,
% 0.66/0.70 (~node9(s3)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[503, 88, 500])).
% 0.66/0.70 tff(505,plain,
% 0.66/0.70 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s3, c_n2) | (~node10(s3)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s3, c_n2) | (~node10(s3)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(506,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s3, c_n2) | (~node10(s3)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(507,plain,
% 0.66/0.70 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s3, c_n2) | (~node10(s3))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.66/0.70 tff(508,plain,
% 0.66/0.70 (~node10(s3)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[507, 249, 500])).
% 0.66/0.70 tff(509,plain,
% 0.66/0.70 (^[V: $i, Y: $i, X: $i] : refl(((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V)) <=> ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V)))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(510,plain,
% 0.66/0.70 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V)) <=> ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[509])).
% 0.66/0.70 tff(511,plain,
% 0.66/0.70 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V)) <=> ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(512,plain,
% 0.66/0.70 (^[V: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((m_main_v_state2(Y, V) | (~m_main_v_state2(X, V))) <=> ((~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))), (((m_main_v_state2(Y, V) | (~m_main_v_state2(X, V))) | (~node13(X, Y))) <=> (((~m_main_v_state2(X, V)) | m_main_v_state2(Y, V)) | (~node13(X, Y))))), rewrite((((~m_main_v_state2(X, V)) | m_main_v_state2(Y, V)) | (~node13(X, Y))) <=> ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))), (((m_main_v_state2(Y, V) | (~m_main_v_state2(X, V))) | (~node13(X, Y))) <=> ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(513,plain,
% 0.66/0.70 (![V: $i, Y: $i, X: $i] : ((m_main_v_state2(Y, V) | (~m_main_v_state2(X, V))) | (~node13(X, Y))) <=> ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[512])).
% 0.66/0.70 tff(514,axiom,(![V: $i, Y: $i, X: $i] : ((m_main_v_state2(Y, V) | (~m_main_v_state2(X, V))) | (~node13(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_46')).
% 0.66/0.70 tff(515,plain,
% 0.66/0.70 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.66/0.70 tff(516,plain,
% 0.66/0.70 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[515, 511])).
% 0.66/0.70 tff(517,plain,(
% 0.66/0.70 ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.66/0.70 inference(skolemize,[status(sab)],[516])).
% 0.66/0.70 tff(518,plain,
% 0.66/0.70 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[517, 510])).
% 0.66/0.70 tff(519,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2) | (~node13(s1, s2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2) | (~node13(s1, s2)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(520,plain,
% 0.66/0.70 (((~node13(s1, s2)) | (~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2)) <=> ((~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2) | (~node13(s1, s2)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(521,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s1, s2)) | (~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2) | (~node13(s1, s2))))),
% 0.66/0.70 inference(monotonicity,[status(thm)],[520])).
% 0.66/0.70 tff(522,plain,
% 0.66/0.70 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s1, s2)) | (~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2) | (~node13(s1, s2)))),
% 0.66/0.70 inference(transitivity,[status(thm)],[521, 519])).
% 0.66/0.70 tff(523,plain,
% 0.66/0.70 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s1, s2)) | (~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(524,plain,
% 0.66/0.71 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s1, c_t2)) | m_main_v_state2(s2, c_t2) | (~node13(s1, s2))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.66/0.71 tff(525,plain,
% 0.66/0.71 (m_main_v_state2(s2, c_t2)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[524, 518, 70, 301])).
% 0.66/0.71 tff(526,plain,
% 0.66/0.71 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2) | (~node13(s2, s3)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2) | (~node13(s2, s3)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(527,plain,
% 0.66/0.71 (((~node13(s2, s3)) | (~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2)) <=> ((~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2) | (~node13(s2, s3)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(528,plain,
% 0.66/0.71 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s2, s3)) | (~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2) | (~node13(s2, s3))))),
% 0.66/0.71 inference(monotonicity,[status(thm)],[527])).
% 0.66/0.71 tff(529,plain,
% 0.66/0.71 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s2, s3)) | (~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2) | (~node13(s2, s3)))),
% 0.66/0.71 inference(transitivity,[status(thm)],[528, 526])).
% 0.66/0.71 tff(530,plain,
% 0.66/0.71 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s2, s3)) | (~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(531,plain,
% 0.66/0.71 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s2, c_t2)) | m_main_v_state2(s3, c_t2) | (~node13(s2, s3))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.66/0.71 tff(532,plain,
% 0.66/0.71 (m_main_v_state2(s3, c_t2)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[531, 518, 525, 493])).
% 0.66/0.71 tff(533,plain,
% 0.66/0.71 (^[X: $i] : refl(((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(534,plain,
% 0.66/0.71 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1))) <=> ![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[533])).
% 0.66/0.71 tff(535,plain,
% 0.66/0.71 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1))) <=> ![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(536,axiom,(![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_4')).
% 0.66/0.71 tff(537,plain,
% 0.66/0.71 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.66/0.71 tff(538,plain,(
% 0.66/0.71 ![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.71 inference(skolemize,[status(sab)],[537])).
% 0.66/0.71 tff(539,plain,
% 0.66/0.71 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[538, 534])).
% 0.66/0.71 tff(540,plain,
% 0.66/0.71 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s2, c_t1)) | (~m_main_v_state1(s2, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s2, c_t1)) | (~m_main_v_state1(s2, c_c1)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(541,plain,
% 0.66/0.71 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s2, c_t1)) | (~m_main_v_state1(s2, c_c1)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(542,plain,
% 0.66/0.71 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s2, c_t1)) | (~m_main_v_state1(s2, c_c1))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.66/0.71 tff(543,plain,
% 0.66/0.71 (~m_main_v_state1(s2, c_t1)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[542, 539, 447])).
% 0.66/0.71 tff(544,plain,
% 0.66/0.71 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node5(X))) <=> (m_main_v_state1(X, c_t1) | (~node5(X))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(545,plain,
% 0.66/0.71 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[544])).
% 0.66/0.71 tff(546,plain,
% 0.66/0.71 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(547,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_22')).
% 0.66/0.71 tff(548,plain,
% 0.66/0.71 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.66/0.71 tff(549,plain,(
% 0.66/0.71 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.66/0.71 inference(skolemize,[status(sab)],[548])).
% 0.66/0.71 tff(550,plain,
% 0.66/0.71 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[549, 545])).
% 0.66/0.71 tff(551,plain,
% 0.66/0.71 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s2, c_t1) | (~node5(s2)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s2, c_t1) | (~node5(s2)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(552,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s2, c_t1) | (~node5(s2)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(553,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s2, c_t1) | (~node5(s2))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.66/0.71 tff(554,plain,
% 0.66/0.71 (~node5(s2)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[553, 550, 543])).
% 0.66/0.71 tff(555,plain,
% 0.66/0.71 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s2, c_n2) | (~node4(s2)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s2, c_n2) | (~node4(s2)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(556,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s2, c_n2) | (~node4(s2)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(557,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s2, c_n2) | (~node4(s2))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.66/0.71 tff(558,plain,
% 0.66/0.71 (~node4(s2)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[557, 388, 318])).
% 0.66/0.71 tff(559,plain,
% 0.66/0.71 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s2, c_c2) | (~node3(s2)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s2, c_c2) | (~node3(s2)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(560,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s2, c_c2) | (~node3(s2)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(561,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s2, c_c2) | (~node3(s2))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.66/0.71 tff(562,plain,
% 0.66/0.71 (~node3(s2)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[561, 399, 473])).
% 0.66/0.71 tff(563,plain,
% 0.66/0.71 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s2, c_n2) | (~node2(s2)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s2, c_n2) | (~node2(s2)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(564,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s2, c_n2) | (~node2(s2)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(565,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s2, c_n2) | (~node2(s2))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.66/0.71 tff(566,plain,
% 0.66/0.71 (~node2(s2)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[565, 410, 318])).
% 0.66/0.71 tff(567,plain,
% 0.66/0.71 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s2, c_n1) | (~node1(s2)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s2, c_n1) | (~node1(s2)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(568,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s2, c_n1) | (~node1(s2)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(569,plain,
% 0.66/0.71 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s2, c_n1) | (~node1(s2))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.66/0.71 tff(570,plain,
% 0.66/0.71 (~node1(s2)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[569, 421, 458])).
% 0.66/0.71 tff(571,plain,
% 0.66/0.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s2, s3)) | node7(s2, s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s2, s3)) | node7(s2, s3))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(572,plain,
% 0.66/0.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s2, s3)) | node7(s2, s3))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(573,plain,
% 0.66/0.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s2, s3)) | node7(s2, s3)),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.66/0.71 tff(574,plain,
% 0.66/0.71 (node7(s2, s3)),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[573, 206, 484])).
% 0.66/0.71 tff(575,plain,
% 0.66/0.71 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1)) <=> ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1)))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(576,plain,
% 0.66/0.71 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[575])).
% 0.66/0.71 tff(577,plain,
% 0.66/0.71 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(578,plain,
% 0.66/0.71 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((node1(X) | node2(X)) | node3(X)) <=> (node1(X) | node2(X) | node3(X))), ((((node1(X) | node2(X)) | node3(X)) | node4(X)) <=> ((node1(X) | node2(X) | node3(X)) | node4(X)))), rewrite(((node1(X) | node2(X) | node3(X)) | node4(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X))), ((((node1(X) | node2(X)) | node3(X)) | node4(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X)))), (((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) <=> ((node1(X) | node2(X) | node3(X) | node4(X)) | node5(X)))), rewrite(((node1(X) | node2(X) | node3(X) | node4(X)) | node5(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X) | node5(X))), (((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X) | node5(X)))), ((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) <=> ((node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | (~m_main_v_state1(X, c_c1))))), rewrite(((node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | (~m_main_v_state1(X, c_c1))) <=> ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X))), ((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) <=> ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X)))), (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) | m_main_v_state1(Y, c_n1)) <=> (((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | m_main_v_state1(Y, c_n1)))), rewrite((((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | m_main_v_state1(Y, c_n1)) <=> ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | m_main_v_state1(Y, c_n1))), (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) | m_main_v_state1(Y, c_n1)) <=> ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | m_main_v_state1(Y, c_n1)))), ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) | m_main_v_state1(Y, c_n1)) | (~node7(X, Y))) <=> (((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | m_main_v_state1(Y, c_n1)) | (~node7(X, Y))))), rewrite((((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | m_main_v_state1(Y, c_n1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))), ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) | m_main_v_state1(Y, c_n1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(579,plain,
% 0.66/0.71 (![Y: $i, X: $i] : (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) | m_main_v_state1(Y, c_n1)) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[578])).
% 0.66/0.71 tff(580,axiom,(![Y: $i, X: $i] : (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | (~m_main_v_state1(X, c_c1))) | m_main_v_state1(Y, c_n1)) | (~node7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_32')).
% 0.66/0.71 tff(581,plain,
% 0.66/0.71 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.66/0.71 tff(582,plain,
% 0.66/0.71 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.66/0.71 tff(583,plain,(
% 0.66/0.71 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.66/0.71 inference(skolemize,[status(sab)],[582])).
% 0.66/0.71 tff(584,plain,
% 0.66/0.71 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[583, 576])).
% 0.66/0.71 tff(585,plain,
% 0.66/0.71 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(586,plain,
% 0.66/0.71 (((~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)) | m_main_v_state1(s3, c_n1)) <=> (m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(587,plain,
% 0.66/0.72 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)) | m_main_v_state1(s3, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3))))),
% 0.66/0.72 inference(monotonicity,[status(thm)],[586])).
% 0.66/0.72 tff(588,plain,
% 0.66/0.72 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)) | m_main_v_state1(s3, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)))),
% 0.66/0.72 inference(transitivity,[status(thm)],[587, 585])).
% 0.66/0.72 tff(589,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)) | m_main_v_state1(s3, c_n1))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(590,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.66/0.72 tff(591,plain,
% 0.66/0.72 (m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[590, 584, 574])).
% 0.66/0.72 tff(592,plain,
% 0.66/0.72 (m_main_v_state1(s3, c_n1)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[591, 570, 447, 566, 562, 558, 554])).
% 0.66/0.72 tff(593,plain,
% 0.66/0.72 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s3, c_n2) | (~node8(s3)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s3, c_n2) | (~node8(s3)))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(594,plain,
% 0.66/0.72 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s3, c_n2) | (~node8(s3)))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(595,plain,
% 0.66/0.72 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s3, c_n2) | (~node8(s3))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.66/0.72 tff(596,plain,
% 0.66/0.72 (~node8(s3)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[595, 271, 500])).
% 0.66/0.72 tff(597,plain,
% 0.66/0.72 (succ(s3, s4) <=> succ(s3, s4)),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(598,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 0.66/0.72 tff(599,plain,
% 0.66/0.72 (succ(s3, s4)),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.66/0.72 tff(600,plain,
% 0.66/0.72 (((~![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))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(601,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(602,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.66/0.72 tff(603,plain,
% 0.66/0.72 (trans(s3, s4)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[602, 599, 32])).
% 0.66/0.72 tff(604,plain,
% 0.66/0.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s3, s4)) | node14(s3, s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s3, s4)) | node14(s3, s4))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(605,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s3, s4)) | node14(s3, s4))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(606,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s3, s4)) | node14(s3, s4)),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.66/0.72 tff(607,plain,
% 0.66/0.72 (node14(s3, s4)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[606, 46, 603])).
% 0.66/0.72 tff(608,plain,
% 0.66/0.72 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2)))),
% 0.66/0.72 inference(bind,[status(th)],[])).
% 0.66/0.72 tff(609,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))),
% 0.66/0.72 inference(quant_intro,[status(thm)],[608])).
% 0.66/0.72 tff(610,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(611,plain,
% 0.66/0.72 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((node8(X) | node9(X)) | node10(X)) <=> (node9(X) | node8(X) | node10(X))), ((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) <=> ((node9(X) | node8(X) | node10(X)) | (~m_main_v_state2(X, c_t2))))), rewrite(((node9(X) | node8(X) | node10(X)) | (~m_main_v_state2(X, c_t2))) <=> ((~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X))), ((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) <=> ((~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X)))), (((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) <=> (((~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X)) | (~m_main_v_state1(X, c_n1))))), rewrite((((~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X)) | (~m_main_v_state1(X, c_n1))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X))), (((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X)))), ((((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_c2)) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X)) | m_main_v_state2(Y, c_c2)))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X)) | m_main_v_state2(Y, c_c2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | m_main_v_state2(Y, c_c2))), ((((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_c2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | m_main_v_state2(Y, c_c2)))), (((((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_c2)) | (~node14(X, Y))) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | m_main_v_state2(Y, c_c2)) | (~node14(X, Y))))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | m_main_v_state2(Y, c_c2)) | (~node14(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))), (((((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_c2)) | (~node14(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))))),
% 0.66/0.72 inference(bind,[status(th)],[])).
% 0.66/0.72 tff(612,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_c2)) | (~node14(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))),
% 0.66/0.72 inference(quant_intro,[status(thm)],[611])).
% 0.66/0.72 tff(613,axiom,(![Y: $i, X: $i] : ((((((node8(X) | node9(X)) | node10(X)) | (~m_main_v_state2(X, c_t2))) | (~m_main_v_state1(X, c_n1))) | m_main_v_state2(Y, c_c2)) | (~node14(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_51')).
% 0.66/0.72 tff(614,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.66/0.72 tff(615,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[614, 610])).
% 0.66/0.72 tff(616,plain,(
% 0.66/0.72 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))),
% 0.66/0.72 inference(skolemize,[status(sab)],[615])).
% 0.66/0.72 tff(617,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[616, 609])).
% 0.66/0.72 tff(618,plain,
% 0.66/0.72 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | node9(s3) | node8(s3) | node10(s3) | (~node14(s3, s4)) | m_main_v_state2(s4, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | node9(s3) | node8(s3) | node10(s3) | (~node14(s3, s4)) | m_main_v_state2(s4, c_c2))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(619,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | node9(s3) | node8(s3) | node10(s3) | (~node14(s3, s4)) | m_main_v_state2(s4, c_c2))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(620,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | node9(s3) | node8(s3) | node10(s3) | (~node14(s3, s4)) | m_main_v_state2(s4, c_c2)),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.66/0.72 tff(621,plain,
% 0.66/0.72 ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | node9(s3) | node8(s3) | node10(s3) | m_main_v_state2(s4, c_c2)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[620, 617, 607])).
% 0.66/0.72 tff(622,plain,
% 0.66/0.72 (m_main_v_state2(s4, c_c2)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[621, 596, 592, 532, 508, 504])).
% 0.66/0.72 tff(623,plain,
% 0.66/0.72 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s4, c_t2)) | (~m_main_v_state2(s4, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s4, c_t2)) | (~m_main_v_state2(s4, c_c2)))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(624,plain,
% 0.66/0.72 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s4, c_t2)) | (~m_main_v_state2(s4, c_c2)))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(625,plain,
% 0.66/0.72 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s4, c_t2)) | (~m_main_v_state2(s4, c_c2))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.66/0.72 tff(626,plain,
% 0.66/0.72 (~m_main_v_state2(s4, c_t2)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[625, 260, 622])).
% 0.66/0.72 tff(627,plain,
% 0.66/0.72 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node12(X))) <=> (m_main_v_state2(X, c_t2) | (~node12(X))))),
% 0.66/0.72 inference(bind,[status(th)],[])).
% 0.66/0.72 tff(628,plain,
% 0.66/0.72 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.66/0.72 inference(quant_intro,[status(thm)],[627])).
% 0.66/0.72 tff(629,plain,
% 0.66/0.72 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(630,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_43')).
% 0.66/0.72 tff(631,plain,
% 0.66/0.72 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.66/0.72 tff(632,plain,(
% 0.66/0.72 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.66/0.72 inference(skolemize,[status(sab)],[631])).
% 0.66/0.72 tff(633,plain,
% 0.66/0.72 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[632, 628])).
% 0.66/0.72 tff(634,plain,
% 0.66/0.72 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s4, c_t2) | (~node12(s4)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s4, c_t2) | (~node12(s4)))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(635,plain,
% 0.66/0.72 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s4, c_t2) | (~node12(s4)))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(636,plain,
% 0.66/0.72 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s4, c_t2) | (~node12(s4))),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.66/0.72 tff(637,plain,
% 0.66/0.72 (~node12(s4)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[636, 633, 626])).
% 0.66/0.72 tff(638,plain,
% 0.66/0.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s3, s4)) | node7(s3, s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s3, s4)) | node7(s3, s4))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(639,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s3, s4)) | node7(s3, s4))),
% 0.66/0.72 inference(quant_inst,[status(thm)],[])).
% 0.66/0.72 tff(640,plain,
% 0.66/0.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s3, s4)) | node7(s3, s4)),
% 0.66/0.72 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.66/0.72 tff(641,plain,
% 0.66/0.72 (node7(s3, s4)),
% 0.66/0.72 inference(unit_resolution,[status(thm)],[640, 206, 603])).
% 0.66/0.72 tff(642,plain,
% 0.66/0.72 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)))),
% 0.66/0.72 inference(bind,[status(th)],[])).
% 0.66/0.72 tff(643,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.66/0.72 inference(quant_intro,[status(thm)],[642])).
% 0.66/0.72 tff(644,plain,
% 0.66/0.72 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(645,plain,
% 0.66/0.73 (^[Y: $i, X: $i] : trans(monotonicity(rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_state1(Y, c_t1)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | m_main_v_state1(Y, c_t1))), (((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))), (((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))))),
% 0.66/0.73 inference(bind,[status(th)],[])).
% 0.66/0.73 tff(646,plain,
% 0.66/0.73 (![Y: $i, X: $i] : ((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.66/0.73 inference(quant_intro,[status(thm)],[645])).
% 0.66/0.73 tff(647,axiom,(![Y: $i, X: $i] : ((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_state1(Y, c_t1)) | (~node7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_27')).
% 0.66/0.73 tff(648,plain,
% 0.66/0.73 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.66/0.73 tff(649,plain,
% 0.66/0.73 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[648, 644])).
% 0.66/0.73 tff(650,plain,(
% 0.66/0.73 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.66/0.73 inference(skolemize,[status(sab)],[649])).
% 0.66/0.73 tff(651,plain,
% 0.66/0.73 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[650, 643])).
% 0.66/0.73 tff(652,plain,
% 0.66/0.73 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node7(s3, s4)) | m_main_v_state1(s4, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node7(s3, s4)) | m_main_v_state1(s4, c_t1))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(653,plain,
% 0.66/0.73 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node7(s3, s4)) | m_main_v_state1(s4, c_t1))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(654,plain,
% 0.66/0.73 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node7(s3, s4)) | m_main_v_state1(s4, c_t1)),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.66/0.73 tff(655,plain,
% 0.66/0.73 ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | m_main_v_state1(s4, c_t1)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[654, 651, 641])).
% 0.66/0.73 tff(656,plain,
% 0.66/0.73 (m_main_v_state1(s4, c_t1)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[655, 532, 592])).
% 0.66/0.73 tff(657,plain,
% 0.66/0.73 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s4, c_n1)) | (~m_main_v_state1(s4, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s4, c_n1)) | (~m_main_v_state1(s4, c_t1)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(658,plain,
% 0.66/0.73 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s4, c_n1)) | (~m_main_v_state1(s4, c_t1)))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(659,plain,
% 0.66/0.73 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s4, c_n1)) | (~m_main_v_state1(s4, c_t1))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.66/0.73 tff(660,plain,
% 0.66/0.73 (~m_main_v_state1(s4, c_n1)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[659, 10, 656])).
% 0.66/0.73 tff(661,plain,
% 0.66/0.73 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s4, c_n1) | (~node11(s4)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s4, c_n1) | (~node11(s4)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(662,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s4, c_n1) | (~node11(s4)))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(663,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s4, c_n1) | (~node11(s4))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.66/0.73 tff(664,plain,
% 0.66/0.73 (~node11(s4)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[663, 238, 660])).
% 0.66/0.73 tff(665,plain,
% 0.66/0.73 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s4, c_t1)) | (~m_main_v_state1(s4, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s4, c_t1)) | (~m_main_v_state1(s4, c_c1)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(666,plain,
% 0.66/0.73 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s4, c_t1)) | (~m_main_v_state1(s4, c_c1)))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(667,plain,
% 0.66/0.73 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s4, c_t1)) | (~m_main_v_state1(s4, c_c1))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.66/0.73 tff(668,plain,
% 0.66/0.73 (~m_main_v_state1(s4, c_c1)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[667, 539, 656])).
% 0.66/0.73 tff(669,plain,
% 0.66/0.73 (^[X: $i] : refl((m_main_v_state1(X, c_c1) | (~node10(X))) <=> (m_main_v_state1(X, c_c1) | (~node10(X))))),
% 0.66/0.73 inference(bind,[status(th)],[])).
% 0.66/0.73 tff(670,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X))) <=> ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.66/0.73 inference(quant_intro,[status(thm)],[669])).
% 0.66/0.73 tff(671,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X))) <=> ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(672,axiom,(![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_40')).
% 0.66/0.73 tff(673,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.66/0.73 tff(674,plain,(
% 0.66/0.73 ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.66/0.73 inference(skolemize,[status(sab)],[673])).
% 0.66/0.73 tff(675,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[674, 670])).
% 0.66/0.73 tff(676,plain,
% 0.66/0.73 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s4, c_c1) | (~node10(s4)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s4, c_c1) | (~node10(s4)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(677,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s4, c_c1) | (~node10(s4)))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(678,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s4, c_c1) | (~node10(s4))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.66/0.73 tff(679,plain,
% 0.66/0.73 (~node10(s4)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[678, 675, 668])).
% 0.66/0.73 tff(680,plain,
% 0.66/0.73 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node9(X))) <=> (m_main_v_state1(X, c_n1) | (~node9(X))))),
% 0.66/0.73 inference(bind,[status(th)],[])).
% 0.66/0.73 tff(681,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.66/0.73 inference(quant_intro,[status(thm)],[680])).
% 0.66/0.73 tff(682,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(683,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_38')).
% 0.66/0.73 tff(684,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.66/0.73 tff(685,plain,(
% 0.66/0.73 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.66/0.73 inference(skolemize,[status(sab)],[684])).
% 0.66/0.73 tff(686,plain,
% 0.66/0.73 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[685, 681])).
% 0.66/0.73 tff(687,plain,
% 0.66/0.73 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s4, c_n1) | (~node9(s4)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s4, c_n1) | (~node9(s4)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(688,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s4, c_n1) | (~node9(s4)))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(689,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s4, c_n1) | (~node9(s4))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[688, 687])).
% 0.66/0.73 tff(690,plain,
% 0.66/0.73 (~node9(s4)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[689, 686, 660])).
% 0.66/0.73 tff(691,plain,
% 0.66/0.73 (^[X: $i] : refl(((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2))) <=> ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2))))),
% 0.66/0.73 inference(bind,[status(th)],[])).
% 0.66/0.73 tff(692,plain,
% 0.66/0.73 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2))) <=> ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.66/0.73 inference(quant_intro,[status(thm)],[691])).
% 0.66/0.73 tff(693,plain,
% 0.66/0.73 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2))) <=> ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(694,axiom,(![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_7')).
% 0.66/0.73 tff(695,plain,
% 0.66/0.73 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.66/0.73 tff(696,plain,(
% 0.66/0.73 ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.66/0.73 inference(skolemize,[status(sab)],[695])).
% 0.66/0.73 tff(697,plain,
% 0.66/0.73 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[696, 692])).
% 0.66/0.73 tff(698,plain,
% 0.66/0.73 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s4, c_n2)) | (~m_main_v_state2(s4, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s4, c_n2)) | (~m_main_v_state2(s4, c_c2)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(699,plain,
% 0.66/0.73 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s4, c_n2)) | (~m_main_v_state2(s4, c_c2)))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(700,plain,
% 0.66/0.73 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s4, c_n2)) | (~m_main_v_state2(s4, c_c2))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.66/0.73 tff(701,plain,
% 0.66/0.73 (~m_main_v_state2(s4, c_n2)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[700, 697, 622])).
% 0.66/0.73 tff(702,plain,
% 0.66/0.73 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s4, c_n2) | (~node8(s4)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s4, c_n2) | (~node8(s4)))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(703,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s4, c_n2) | (~node8(s4)))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(704,plain,
% 0.66/0.73 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s4, c_n2) | (~node8(s4))),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.66/0.73 tff(705,plain,
% 0.66/0.73 (~node8(s4)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[704, 271, 701])).
% 0.66/0.73 tff(706,plain,
% 0.66/0.73 (succ(s4, s5) <=> succ(s4, s5)),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(707,axiom,(succ(s4, s5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 0.66/0.73 tff(708,plain,
% 0.66/0.73 (succ(s4, s5)),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.66/0.73 tff(709,plain,
% 0.66/0.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(710,plain,
% 0.66/0.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(711,plain,
% 0.66/0.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.66/0.73 tff(712,plain,
% 0.66/0.73 (trans(s4, s5)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[711, 708, 32])).
% 0.66/0.73 tff(713,plain,
% 0.66/0.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s4, s5)) | node14(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s4, s5)) | node14(s4, s5))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(714,plain,
% 0.66/0.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s4, s5)) | node14(s4, s5))),
% 0.66/0.73 inference(quant_inst,[status(thm)],[])).
% 0.66/0.73 tff(715,plain,
% 0.66/0.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s4, s5)) | node14(s4, s5)),
% 0.66/0.73 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.66/0.73 tff(716,plain,
% 0.66/0.73 (node14(s4, s5)),
% 0.66/0.73 inference(unit_resolution,[status(thm)],[715, 46, 712])).
% 0.66/0.73 tff(717,plain,
% 0.66/0.73 (^[Y: $i, X: $i] : refl(((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2)) <=> ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2)))),
% 0.66/0.73 inference(bind,[status(th)],[])).
% 0.66/0.73 tff(718,plain,
% 0.66/0.73 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.66/0.73 inference(quant_intro,[status(thm)],[717])).
% 0.66/0.73 tff(719,plain,
% 0.66/0.73 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.66/0.73 inference(rewrite,[status(thm)],[])).
% 0.66/0.73 tff(720,plain,
% 0.66/0.73 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((node8(X) | node9(X)) | node10(X)) <=> (node9(X) | node8(X) | node10(X))), ((((node8(X) | node9(X)) | node10(X)) | node11(X)) <=> ((node9(X) | node8(X) | node10(X)) | node11(X)))), rewrite(((node9(X) | node8(X) | node10(X)) | node11(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X))), ((((node8(X) | node9(X)) | node10(X)) | node11(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X)))), (((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) <=> ((node9(X) | node8(X) | node10(X) | node11(X)) | node12(X)))), rewrite(((node9(X) | node8(X) | node10(X) | node11(X)) | node12(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X) | node12(X))), (((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) <=> (node9(X) | node8(X) | node10(X) | node11(X) | node12(X)))), ((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) <=> ((node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | (~m_main_v_state2(X, c_c2))))), rewrite(((node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | (~m_main_v_state2(X, c_c2))) <=> ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X))), ((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) <=> ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X)))), (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) | m_main_v_state2(Y, c_n2)) <=> (((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | m_main_v_state2(Y, c_n2)))), rewrite((((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X)) | m_main_v_state2(Y, c_n2)) <=> ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | m_main_v_state2(Y, c_n2))), (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) | m_main_v_state2(Y, c_n2)) <=> ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | m_main_v_state2(Y, c_n2)))), ((((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) | m_main_v_state2(Y, c_n2)) | (~node14(X, Y))) <=> (((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | m_main_v_state2(Y, c_n2)) | (~node14(X, Y))))), rewrite((((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | m_main_v_state2(Y, c_n2)) | (~node14(X, Y))) <=> ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))), ((((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) | m_main_v_state2(Y, c_n2)) | (~node14(X, Y))) <=> ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))))),
% 0.66/0.74 inference(bind,[status(th)],[])).
% 0.66/0.74 tff(721,plain,
% 0.66/0.74 (![Y: $i, X: $i] : (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) | m_main_v_state2(Y, c_n2)) | (~node14(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.66/0.74 inference(quant_intro,[status(thm)],[720])).
% 0.66/0.74 tff(722,axiom,(![Y: $i, X: $i] : (((((((node8(X) | node9(X)) | node10(X)) | node11(X)) | node12(X)) | (~m_main_v_state2(X, c_c2))) | m_main_v_state2(Y, c_n2)) | (~node14(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_53')).
% 0.66/0.74 tff(723,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.66/0.74 tff(724,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[723, 719])).
% 0.66/0.74 tff(725,plain,(
% 0.66/0.74 ![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.66/0.74 inference(skolemize,[status(sab)],[724])).
% 0.66/0.74 tff(726,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[725, 718])).
% 0.66/0.74 tff(727,plain,
% 0.66/0.74 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | (~m_main_v_state2(s4, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | (~m_main_v_state2(s4, c_c2)))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(728,plain,
% 0.66/0.74 (((~m_main_v_state2(s4, c_c2)) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | m_main_v_state2(s5, c_n2)) <=> (m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | (~m_main_v_state2(s4, c_c2)))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(729,plain,
% 0.66/0.74 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s4, c_c2)) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | m_main_v_state2(s5, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | (~m_main_v_state2(s4, c_c2))))),
% 0.66/0.74 inference(monotonicity,[status(thm)],[728])).
% 0.66/0.74 tff(730,plain,
% 0.66/0.74 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s4, c_c2)) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | m_main_v_state2(s5, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | (~m_main_v_state2(s4, c_c2)))),
% 0.66/0.74 inference(transitivity,[status(thm)],[729, 727])).
% 0.66/0.74 tff(731,plain,
% 0.66/0.74 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s4, c_c2)) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | m_main_v_state2(s5, c_n2))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(732,plain,
% 0.66/0.74 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~node14(s4, s5)) | (~m_main_v_state2(s4, c_c2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.66/0.74 tff(733,plain,
% 0.66/0.74 (m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~m_main_v_state2(s4, c_c2))),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[732, 726, 716])).
% 0.66/0.74 tff(734,plain,
% 0.66/0.74 (m_main_v_state2(s5, c_n2)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[733, 705, 622, 690, 679, 664, 637])).
% 0.66/0.74 tff(735,plain,
% 0.66/0.74 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_c2)))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(736,plain,
% 0.66/0.74 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_c2)))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(737,plain,
% 0.66/0.74 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_c2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.66/0.74 tff(738,plain,
% 0.66/0.74 (~m_main_v_state2(s5, c_c2)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[737, 697, 734])).
% 0.66/0.74 tff(739,plain,
% 0.66/0.74 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s5, c_c2) | (~node3(s5)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s5, c_c2) | (~node3(s5)))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(740,plain,
% 0.66/0.74 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s5, c_c2) | (~node3(s5)))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(741,plain,
% 0.66/0.74 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s5, c_c2) | (~node3(s5))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.66/0.74 tff(742,plain,
% 0.66/0.74 (~node3(s5)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[741, 399, 738])).
% 0.66/0.74 tff(743,plain,
% 0.66/0.74 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s4, c_n1) | (~node1(s4)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s4, c_n1) | (~node1(s4)))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(744,plain,
% 0.66/0.74 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s4, c_n1) | (~node1(s4)))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(745,plain,
% 0.66/0.74 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s4, c_n1) | (~node1(s4))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.66/0.74 tff(746,plain,
% 0.66/0.74 (~node1(s4)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[745, 421, 660])).
% 0.66/0.74 tff(747,plain,
% 0.66/0.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s3, s4)) | node18(s3, s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s3, s4)) | node18(s3, s4))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(748,plain,
% 0.66/0.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s3, s4)) | node18(s3, s4))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(749,plain,
% 0.66/0.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s3, s4)) | node18(s3, s4)),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.66/0.74 tff(750,plain,
% 0.66/0.74 (node18(s3, s4)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[749, 125, 603])).
% 0.66/0.74 tff(751,plain,
% 0.66/0.74 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2)))),
% 0.66/0.74 inference(bind,[status(th)],[])).
% 0.66/0.74 tff(752,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))),
% 0.66/0.74 inference(quant_intro,[status(thm)],[751])).
% 0.66/0.74 tff(753,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(754,plain,
% 0.66/0.74 (^[Y: $i, X: $i] : trans(monotonicity(rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_turn(Y, c_2)) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | m_main_v_turn(Y, c_2))), (((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_turn(Y, c_2)) | (~node18(X, Y))) <=> (((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | m_main_v_turn(Y, c_2)) | (~node18(X, Y))))), rewrite((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | m_main_v_turn(Y, c_2)) | (~node18(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))), (((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_turn(Y, c_2)) | (~node18(X, Y))) <=> ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))))),
% 0.66/0.74 inference(bind,[status(th)],[])).
% 0.66/0.74 tff(755,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_turn(Y, c_2)) | (~node18(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))),
% 0.66/0.74 inference(quant_intro,[status(thm)],[754])).
% 0.66/0.74 tff(756,axiom,(![Y: $i, X: $i] : ((((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2))) | m_main_v_turn(Y, c_2)) | (~node18(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_62')).
% 0.66/0.74 tff(757,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.66/0.74 tff(758,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[757, 753])).
% 0.66/0.74 tff(759,plain,(
% 0.66/0.74 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))),
% 0.66/0.74 inference(skolemize,[status(sab)],[758])).
% 0.66/0.74 tff(760,plain,
% 0.66/0.74 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[759, 752])).
% 0.66/0.74 tff(761,plain,
% 0.66/0.74 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node18(s3, s4)) | m_main_v_turn(s4, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node18(s3, s4)) | m_main_v_turn(s4, c_2))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(762,plain,
% 0.66/0.74 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node18(s3, s4)) | m_main_v_turn(s4, c_2))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(763,plain,
% 0.66/0.74 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | (~node18(s3, s4)) | m_main_v_turn(s4, c_2)),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.66/0.74 tff(764,plain,
% 0.66/0.74 ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | m_main_v_turn(s4, c_2)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[763, 760, 750])).
% 0.66/0.74 tff(765,plain,
% 0.66/0.74 (m_main_v_turn(s4, c_2)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[764, 532, 592])).
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% 0.66/0.74 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s4, c_1)) | (~m_main_v_turn(s4, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s4, c_1)) | (~m_main_v_turn(s4, c_2)))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(767,plain,
% 0.66/0.74 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s4, c_1)) | (~m_main_v_turn(s4, c_2)))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(768,plain,
% 0.66/0.74 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s4, c_1)) | (~m_main_v_turn(s4, c_2))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.66/0.74 tff(769,plain,
% 0.66/0.74 (~m_main_v_turn(s4, c_1)),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[768, 156, 765])).
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% 0.66/0.74 (^[X: $i] : refl((m_main_v_turn(X, c_1) | (~node5(X))) <=> (m_main_v_turn(X, c_1) | (~node5(X))))),
% 0.66/0.74 inference(bind,[status(th)],[])).
% 0.66/0.74 tff(771,plain,
% 0.66/0.74 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X))) <=> ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.66/0.74 inference(quant_intro,[status(thm)],[770])).
% 0.66/0.74 tff(772,plain,
% 0.66/0.74 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X))) <=> ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.66/0.74 inference(rewrite,[status(thm)],[])).
% 0.66/0.74 tff(773,axiom,(![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_24')).
% 0.66/0.74 tff(774,plain,
% 0.66/0.74 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.66/0.74 tff(775,plain,(
% 0.66/0.74 ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.66/0.74 inference(skolemize,[status(sab)],[774])).
% 0.66/0.74 tff(776,plain,
% 0.66/0.74 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.66/0.75 inference(modus_ponens,[status(thm)],[775, 771])).
% 0.66/0.75 tff(777,plain,
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% 0.66/0.75 inference(rewrite,[status(thm)],[])).
% 0.66/0.75 tff(778,plain,
% 0.66/0.75 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s4, c_1) | (~node5(s4)))),
% 0.66/0.75 inference(quant_inst,[status(thm)],[])).
% 0.66/0.75 tff(779,plain,
% 0.66/0.75 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s4, c_1) | (~node5(s4))),
% 0.66/0.75 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.66/0.75 tff(780,plain,
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% 0.66/0.75 inference(unit_resolution,[status(thm)],[779, 776, 769])).
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% 0.66/0.75 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node2(X))) <=> (m_main_v_state1(X, c_n1) | (~node2(X))))),
% 0.66/0.75 inference(bind,[status(th)],[])).
% 0.66/0.75 tff(782,plain,
% 0.66/0.75 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.66/0.75 inference(quant_intro,[status(thm)],[781])).
% 0.66/0.75 tff(783,plain,
% 0.66/0.75 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.66/0.75 inference(rewrite,[status(thm)],[])).
% 0.66/0.75 tff(784,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_16')).
% 0.66/0.75 tff(785,plain,
% 0.66/0.75 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.66/0.75 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.66/0.75 tff(786,plain,(
% 0.66/0.75 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.66/0.75 inference(skolemize,[status(sab)],[785])).
% 0.66/0.75 tff(787,plain,
% 0.66/0.75 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.66/0.75 inference(modus_ponens,[status(thm)],[786, 782])).
% 0.66/0.75 tff(788,plain,
% 0.66/0.75 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s4, c_n1) | (~node2(s4)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s4, c_n1) | (~node2(s4)))),
% 0.66/0.75 inference(rewrite,[status(thm)],[])).
% 0.66/0.75 tff(789,plain,
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% 0.66/0.75 inference(quant_inst,[status(thm)],[])).
% 0.66/0.75 tff(790,plain,
% 0.66/0.75 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s4, c_n1) | (~node2(s4))),
% 0.66/0.75 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.66/0.75 tff(791,plain,
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% 0.66/0.75 inference(unit_resolution,[status(thm)],[790, 787, 660])).
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% 0.66/0.75 inference(bind,[status(th)],[])).
% 0.66/0.75 tff(793,plain,
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% 0.66/0.75 inference(quant_intro,[status(thm)],[792])).
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% 0.66/0.75 inference(rewrite,[status(thm)],[])).
% 0.66/0.75 tff(795,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_18')).
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% 0.66/0.75 tff(797,plain,(
% 0.66/0.75 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.66/0.75 inference(skolemize,[status(sab)],[796])).
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% 0.66/0.75 inference(rewrite,[status(thm)],[])).
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% 0.66/0.75 inference(quant_inst,[status(thm)],[])).
% 0.66/0.75 tff(801,plain,
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% 0.66/0.75 inference(modus_ponens,[status(thm)],[800, 799])).
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% 0.66/0.75 inference(rewrite,[status(thm)],[])).
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% 0.66/0.75 inference(quant_inst,[status(thm)],[])).
% 0.66/0.75 tff(805,plain,
% 0.66/0.75 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s4, c_n2) | (~node4(s4))),
% 0.66/0.75 inference(modus_ponens,[status(thm)],[804, 803])).
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% 0.66/0.75 inference(unit_resolution,[status(thm)],[805, 388, 701])).
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% 0.66/0.75 inference(rewrite,[status(thm)],[])).
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% 0.66/0.75 inference(quant_inst,[status(thm)],[])).
% 0.66/0.75 tff(809,plain,
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% 0.66/0.75 tff(810,plain,
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% 0.66/0.75 tff(811,plain,
% 0.66/0.75 (^[Y: $i, X: $i] : refl((m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y))) <=> (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y))))),
% 0.66/0.75 inference(bind,[status(th)],[])).
% 0.66/0.75 tff(812,plain,
% 0.66/0.75 (![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))),
% 0.66/0.75 inference(quant_intro,[status(thm)],[811])).
% 0.66/0.75 tff(813,plain,
% 0.66/0.75 (![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))),
% 0.66/0.75 inference(rewrite,[status(thm)],[])).
% 0.66/0.75 tff(814,plain,
% 0.66/0.75 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((node1(X) | node2(X)) | node3(X)) <=> (node1(X) | node2(X) | node3(X))), ((((node1(X) | node2(X)) | node3(X)) | node4(X)) <=> ((node1(X) | node2(X) | node3(X)) | node4(X)))), rewrite(((node1(X) | node2(X) | node3(X)) | node4(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X))), ((((node1(X) | node2(X)) | node3(X)) | node4(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X)))), (((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) <=> ((node1(X) | node2(X) | node3(X) | node4(X)) | node5(X)))), rewrite(((node1(X) | node2(X) | node3(X) | node4(X)) | node5(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X) | node5(X))), (((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) <=> (node1(X) | node2(X) | node3(X) | node4(X) | node5(X)))), ((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) <=> ((node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | m_main_v_state1(X, c_c1)))), rewrite(((node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | m_main_v_state1(X, c_c1)) <=> (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X))), ((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) <=> (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X)))), (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) | node6(X, Y)) <=> ((m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | node6(X, Y)))), rewrite(((m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X)) | node6(X, Y)) <=> (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y))), (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) | node6(X, Y)) <=> (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y)))), ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) | node6(X, Y)) | (~node7(X, Y))) <=> ((m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y)) | (~node7(X, Y))))), rewrite(((m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y)) | (~node7(X, Y))) <=> (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))), ((((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) | node6(X, Y)) | (~node7(X, Y))) <=> (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(815,plain,
% 0.73/0.75 (![Y: $i, X: $i] : (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) | node6(X, Y)) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[814])).
% 0.73/0.75 tff(816,axiom,(![Y: $i, X: $i] : (((((((node1(X) | node2(X)) | node3(X)) | node4(X)) | node5(X)) | m_main_v_state1(X, c_c1)) | node6(X, Y)) | (~node7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_33')).
% 0.73/0.75 tff(817,plain,
% 0.73/0.75 (![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.73/0.75 tff(818,plain,
% 0.73/0.75 (![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[817, 813])).
% 0.73/0.75 tff(819,plain,(
% 0.73/0.75 ![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))),
% 0.73/0.75 inference(skolemize,[status(sab)],[818])).
% 0.73/0.75 tff(820,plain,
% 0.73/0.75 (![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[819, 812])).
% 0.73/0.75 tff(821,plain,
% 0.73/0.75 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s4, c_c1) | node1(s4) | node2(s4) | node3(s4) | node4(s4) | node5(s4) | node6(s4, s5) | (~node7(s4, s5)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s4, c_c1) | node1(s4) | node2(s4) | node3(s4) | node4(s4) | node5(s4) | node6(s4, s5) | (~node7(s4, s5)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(822,plain,
% 0.73/0.75 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s4, c_c1) | node1(s4) | node2(s4) | node3(s4) | node4(s4) | node5(s4) | node6(s4, s5) | (~node7(s4, s5)))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(823,plain,
% 0.73/0.75 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s4, c_c1) | node1(s4) | node2(s4) | node3(s4) | node4(s4) | node5(s4) | node6(s4, s5) | (~node7(s4, s5))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.73/0.75 tff(824,plain,
% 0.73/0.75 (m_main_v_state1(s4, c_c1) | node1(s4) | node2(s4) | node3(s4) | node4(s4) | node5(s4) | node6(s4, s5)),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[823, 820, 810])).
% 0.73/0.75 tff(825,plain,
% 0.73/0.75 (node6(s4, s5)),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[824, 806, 668, 802, 791, 780, 746])).
% 0.73/0.75 tff(826,plain,
% 0.73/0.75 (^[V: $i, Y: $i, X: $i] : refl(((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V))) <=> ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(827,plain,
% 0.73/0.75 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V))) <=> ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[826])).
% 0.73/0.75 tff(828,plain,
% 0.73/0.75 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V))) <=> ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(829,plain,
% 0.73/0.75 (^[V: $i, Y: $i, X: $i] : rewrite((((~m_main_v_state1(Y, V)) | m_main_v_state1(X, V)) | (~node6(X, Y))) <=> ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(830,plain,
% 0.73/0.75 (![V: $i, Y: $i, X: $i] : (((~m_main_v_state1(Y, V)) | m_main_v_state1(X, V)) | (~node6(X, Y))) <=> ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[829])).
% 0.73/0.75 tff(831,axiom,(![V: $i, Y: $i, X: $i] : (((~m_main_v_state1(Y, V)) | m_main_v_state1(X, V)) | (~node6(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_26')).
% 0.73/0.75 tff(832,plain,
% 0.73/0.75 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.73/0.75 tff(833,plain,
% 0.73/0.75 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[832, 828])).
% 0.73/0.75 tff(834,plain,(
% 0.73/0.75 ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.73/0.75 inference(skolemize,[status(sab)],[833])).
% 0.73/0.75 tff(835,plain,
% 0.73/0.75 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[834, 827])).
% 0.73/0.75 tff(836,plain,
% 0.73/0.75 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)) | (~node6(s4, s5)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)) | (~node6(s4, s5)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(837,plain,
% 0.73/0.75 (((~node6(s4, s5)) | m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1))) <=> (m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)) | (~node6(s4, s5)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(838,plain,
% 0.73/0.75 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s4, s5)) | m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)) | (~node6(s4, s5))))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[837])).
% 0.73/0.75 tff(839,plain,
% 0.73/0.75 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s4, s5)) | m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)) | (~node6(s4, s5)))),
% 0.73/0.75 inference(transitivity,[status(thm)],[838, 836])).
% 0.73/0.75 tff(840,plain,
% 0.73/0.75 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s4, s5)) | m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(841,plain,
% 0.73/0.75 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s4, c_n1) | (~m_main_v_state1(s5, c_n1)) | (~node6(s4, s5))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.73/0.76 tff(842,plain,
% 0.73/0.76 (~m_main_v_state1(s5, c_n1)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[841, 835, 660, 825])).
% 0.73/0.76 tff(843,plain,
% 0.73/0.76 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s5, c_n1) | (~node2(s5)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s5, c_n1) | (~node2(s5)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(844,plain,
% 0.73/0.76 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s5, c_n1) | (~node2(s5)))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(845,plain,
% 0.73/0.76 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s5, c_n1) | (~node2(s5))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.73/0.76 tff(846,plain,
% 0.73/0.76 (~node2(s5)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[845, 787, 842])).
% 0.73/0.76 tff(847,plain,
% 0.73/0.76 (^[V: $i, Y: $i, X: $i] : refl(((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V)) <=> ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V)))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(848,plain,
% 0.73/0.76 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V)) <=> ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[847])).
% 0.73/0.76 tff(849,plain,
% 0.73/0.76 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V)) <=> ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(850,plain,
% 0.73/0.76 (^[V: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((m_main_v_state1(Y, V) | (~m_main_v_state1(X, V))) <=> ((~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))), (((m_main_v_state1(Y, V) | (~m_main_v_state1(X, V))) | (~node6(X, Y))) <=> (((~m_main_v_state1(X, V)) | m_main_v_state1(Y, V)) | (~node6(X, Y))))), rewrite((((~m_main_v_state1(X, V)) | m_main_v_state1(Y, V)) | (~node6(X, Y))) <=> ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))), (((m_main_v_state1(Y, V) | (~m_main_v_state1(X, V))) | (~node6(X, Y))) <=> ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(851,plain,
% 0.73/0.76 (![V: $i, Y: $i, X: $i] : ((m_main_v_state1(Y, V) | (~m_main_v_state1(X, V))) | (~node6(X, Y))) <=> ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[850])).
% 0.73/0.76 tff(852,axiom,(![V: $i, Y: $i, X: $i] : ((m_main_v_state1(Y, V) | (~m_main_v_state1(X, V))) | (~node6(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_25')).
% 0.73/0.76 tff(853,plain,
% 0.73/0.76 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.73/0.76 tff(854,plain,
% 0.73/0.76 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[853, 849])).
% 0.73/0.76 tff(855,plain,(
% 0.73/0.76 ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.73/0.76 inference(skolemize,[status(sab)],[854])).
% 0.73/0.76 tff(856,plain,
% 0.73/0.76 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[855, 848])).
% 0.73/0.76 tff(857,plain,
% 0.73/0.76 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1) | (~node6(s4, s5)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1) | (~node6(s4, s5)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(858,plain,
% 0.73/0.76 (((~node6(s4, s5)) | (~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1)) <=> ((~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1) | (~node6(s4, s5)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(859,plain,
% 0.73/0.76 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s4, s5)) | (~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1) | (~node6(s4, s5))))),
% 0.73/0.76 inference(monotonicity,[status(thm)],[858])).
% 0.73/0.76 tff(860,plain,
% 0.73/0.76 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s4, s5)) | (~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1) | (~node6(s4, s5)))),
% 0.73/0.76 inference(transitivity,[status(thm)],[859, 857])).
% 0.73/0.76 tff(861,plain,
% 0.73/0.76 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s4, s5)) | (~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(862,plain,
% 0.73/0.76 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s4, c_t1)) | m_main_v_state1(s5, c_t1) | (~node6(s4, s5))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.73/0.76 tff(863,plain,
% 0.73/0.76 (m_main_v_state1(s5, c_t1)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[862, 856, 656, 825])).
% 0.73/0.76 tff(864,plain,
% 0.73/0.76 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_t2)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(865,plain,
% 0.73/0.76 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_t2)))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(866,plain,
% 0.73/0.76 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s5, c_n2)) | (~m_main_v_state2(s5, c_t2))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.73/0.76 tff(867,plain,
% 0.73/0.76 (~m_main_v_state2(s5, c_t2)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[866, 77, 734])).
% 0.73/0.76 tff(868,plain,
% 0.73/0.76 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s5, c_t2) | (~node1(s5)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s5, c_t2) | (~node1(s5)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(869,plain,
% 0.73/0.76 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s5, c_t2) | (~node1(s5)))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(870,plain,
% 0.73/0.76 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s5, c_t2) | (~node1(s5))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.73/0.76 tff(871,plain,
% 0.73/0.76 (~node1(s5)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[870, 195, 867])).
% 0.73/0.76 tff(872,plain,
% 0.73/0.76 (succ(s5, s6) <=> succ(s5, s6)),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(873,axiom,(succ(s5, s6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 0.73/0.76 tff(874,plain,
% 0.73/0.76 (succ(s5, s6)),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.73/0.76 tff(875,plain,
% 0.73/0.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(876,plain,
% 0.73/0.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(877,plain,
% 0.73/0.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.73/0.76 tff(878,plain,
% 0.73/0.76 (trans(s5, s6)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[877, 874, 32])).
% 0.73/0.76 tff(879,plain,
% 0.73/0.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s5, s6)) | node7(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s5, s6)) | node7(s5, s6))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(880,plain,
% 0.73/0.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s5, s6)) | node7(s5, s6))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(881,plain,
% 0.73/0.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s5, s6)) | node7(s5, s6)),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.73/0.76 tff(882,plain,
% 0.73/0.76 (node7(s5, s6)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[881, 206, 878])).
% 0.73/0.76 tff(883,plain,
% 0.73/0.76 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(884,plain,
% 0.73/0.76 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[883])).
% 0.73/0.76 tff(885,plain,
% 0.73/0.76 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(886,plain,
% 0.73/0.76 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((node1(X) | node2(X)) | node3(X)) <=> (node1(X) | node2(X) | node3(X))), ((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) <=> ((node1(X) | node2(X) | node3(X)) | (~m_main_v_state1(X, c_t1))))), rewrite(((node1(X) | node2(X) | node3(X)) | (~m_main_v_state1(X, c_t1))) <=> ((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X))), ((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) <=> ((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X)))), (((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) <=> (((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X)) | (~m_main_v_state2(X, c_n2))))), rewrite((((~m_main_v_state1(X, c_t1)) | node1(X) | node2(X) | node3(X)) | (~m_main_v_state2(X, c_n2))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X))), (((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X)))), ((((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_c1)) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X)) | m_main_v_state1(Y, c_c1)))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X)) | m_main_v_state1(Y, c_c1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | m_main_v_state1(Y, c_c1))), ((((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_c1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | m_main_v_state1(Y, c_c1)))), (((((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))), (((((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(887,plain,
% 0.73/0.76 (![Y: $i, X: $i] : ((((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[886])).
% 0.73/0.76 tff(888,axiom,(![Y: $i, X: $i] : ((((((node1(X) | node2(X)) | node3(X)) | (~m_main_v_state1(X, c_t1))) | (~m_main_v_state2(X, c_n2))) | m_main_v_state1(Y, c_c1)) | (~node7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_30')).
% 0.73/0.76 tff(889,plain,
% 0.73/0.76 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.73/0.76 tff(890,plain,
% 0.73/0.76 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[889, 885])).
% 0.73/0.76 tff(891,plain,(
% 0.73/0.76 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.73/0.76 inference(skolemize,[status(sab)],[890])).
% 0.73/0.76 tff(892,plain,
% 0.73/0.76 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.73/0.76 tff(893,plain,
% 0.73/0.76 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state1(s6, c_c1) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state1(s6, c_c1) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(894,plain,
% 0.73/0.76 (((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)) | m_main_v_state1(s6, c_c1)) <=> ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state1(s6, c_c1) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(895,plain,
% 0.73/0.76 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)) | m_main_v_state1(s6, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state1(s6, c_c1) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6))))),
% 0.73/0.76 inference(monotonicity,[status(thm)],[894])).
% 0.73/0.76 tff(896,plain,
% 0.73/0.76 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)) | m_main_v_state1(s6, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state1(s6, c_c1) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)))),
% 0.75/0.77 inference(transitivity,[status(thm)],[895, 893])).
% 0.75/0.77 tff(897,plain,
% 0.75/0.77 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6)) | m_main_v_state1(s6, c_c1))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(898,plain,
% 0.75/0.77 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state1(s6, c_c1) | node1(s5) | node2(s5) | node3(s5) | (~node7(s5, s6))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.75/0.77 tff(899,plain,
% 0.75/0.77 ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state1(s6, c_c1) | node1(s5) | node2(s5) | node3(s5)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[898, 892, 882])).
% 0.75/0.77 tff(900,plain,
% 0.75/0.77 (m_main_v_state1(s6, c_c1)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[899, 871, 734, 863, 846, 742])).
% 0.75/0.77 tff(901,plain,
% 0.75/0.77 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s6, c_t1)) | (~m_main_v_state1(s6, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s6, c_t1)) | (~m_main_v_state1(s6, c_c1)))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(902,plain,
% 0.75/0.77 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s6, c_t1)) | (~m_main_v_state1(s6, c_c1)))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(903,plain,
% 0.75/0.77 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s6, c_t1)) | (~m_main_v_state1(s6, c_c1))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.75/0.77 tff(904,plain,
% 0.75/0.77 (~m_main_v_state1(s6, c_t1)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[903, 539, 900])).
% 0.75/0.77 tff(905,plain,
% 0.75/0.77 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s6, c_t1) | (~node5(s6)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s6, c_t1) | (~node5(s6)))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(906,plain,
% 0.75/0.77 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s6, c_t1) | (~node5(s6)))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(907,plain,
% 0.75/0.77 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s6, c_t1) | (~node5(s6))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.75/0.77 tff(908,plain,
% 0.75/0.77 (~node5(s6)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[907, 550, 904])).
% 0.75/0.77 tff(909,plain,
% 0.75/0.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s5, s6)) | node14(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s5, s6)) | node14(s5, s6))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(910,plain,
% 0.75/0.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s5, s6)) | node14(s5, s6))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(911,plain,
% 0.75/0.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s5, s6)) | node14(s5, s6)),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.75/0.77 tff(912,plain,
% 0.75/0.77 (node14(s5, s6)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[911, 46, 878])).
% 0.75/0.77 tff(913,plain,
% 0.75/0.77 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)))),
% 0.75/0.77 inference(bind,[status(th)],[])).
% 0.75/0.77 tff(914,plain,
% 0.75/0.77 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.75/0.77 inference(quant_intro,[status(thm)],[913])).
% 0.75/0.77 tff(915,plain,
% 0.75/0.77 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(916,plain,
% 0.75/0.77 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~m_main_v_state2(X, c_n2)) | (~m_main_v_state1(X, c_t1))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)))), ((((~m_main_v_state2(X, c_n2)) | (~m_main_v_state1(X, c_t1))) | m_main_v_state2(Y, c_t2)) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2))) | m_main_v_state2(Y, c_t2)))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2))) | m_main_v_state2(Y, c_t2)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | m_main_v_state2(Y, c_t2))), ((((~m_main_v_state2(X, c_n2)) | (~m_main_v_state1(X, c_t1))) | m_main_v_state2(Y, c_t2)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | m_main_v_state2(Y, c_t2)))), (((((~m_main_v_state2(X, c_n2)) | (~m_main_v_state1(X, c_t1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))), (((((~m_main_v_state2(X, c_n2)) | (~m_main_v_state1(X, c_t1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))))),
% 0.75/0.77 inference(bind,[status(th)],[])).
% 0.75/0.77 tff(917,plain,
% 0.75/0.77 (![Y: $i, X: $i] : ((((~m_main_v_state2(X, c_n2)) | (~m_main_v_state1(X, c_t1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.75/0.77 inference(quant_intro,[status(thm)],[916])).
% 0.75/0.77 tff(918,axiom,(![Y: $i, X: $i] : ((((~m_main_v_state2(X, c_n2)) | (~m_main_v_state1(X, c_t1))) | m_main_v_state2(Y, c_t2)) | (~node14(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_48')).
% 0.75/0.77 tff(919,plain,
% 0.75/0.77 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.75/0.77 tff(920,plain,
% 0.75/0.77 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[919, 915])).
% 0.75/0.77 tff(921,plain,(
% 0.75/0.77 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.75/0.77 inference(skolemize,[status(sab)],[920])).
% 0.75/0.77 tff(922,plain,
% 0.75/0.77 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[921, 914])).
% 0.75/0.77 tff(923,plain,
% 0.75/0.77 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | (~node14(s5, s6)) | m_main_v_state2(s6, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | (~node14(s5, s6)) | m_main_v_state2(s6, c_t2))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(924,plain,
% 0.75/0.77 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | (~node14(s5, s6)) | m_main_v_state2(s6, c_t2))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(925,plain,
% 0.75/0.77 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | (~node14(s5, s6)) | m_main_v_state2(s6, c_t2)),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.75/0.77 tff(926,plain,
% 0.75/0.77 ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state2(s6, c_t2)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[925, 922, 912])).
% 0.75/0.77 tff(927,plain,
% 0.75/0.77 (m_main_v_state2(s6, c_t2)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[926, 863, 734])).
% 0.75/0.77 tff(928,plain,
% 0.75/0.77 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s6, c_n2)) | (~m_main_v_state2(s6, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s6, c_n2)) | (~m_main_v_state2(s6, c_t2)))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(929,plain,
% 0.75/0.77 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s6, c_n2)) | (~m_main_v_state2(s6, c_t2)))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(930,plain,
% 0.75/0.77 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s6, c_n2)) | (~m_main_v_state2(s6, c_t2))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.75/0.77 tff(931,plain,
% 0.75/0.77 (~m_main_v_state2(s6, c_n2)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[930, 77, 927])).
% 0.75/0.77 tff(932,plain,
% 0.75/0.77 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s6, c_n2) | (~node4(s6)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s6, c_n2) | (~node4(s6)))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(933,plain,
% 0.75/0.77 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s6, c_n2) | (~node4(s6)))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(934,plain,
% 0.75/0.77 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s6, c_n2) | (~node4(s6))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.75/0.77 tff(935,plain,
% 0.75/0.77 (~node4(s6)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[934, 388, 931])).
% 0.75/0.77 tff(936,plain,
% 0.75/0.77 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s6, c_t2)) | (~m_main_v_state2(s6, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s6, c_t2)) | (~m_main_v_state2(s6, c_c2)))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(937,plain,
% 0.75/0.77 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s6, c_t2)) | (~m_main_v_state2(s6, c_c2)))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(938,plain,
% 0.75/0.77 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s6, c_t2)) | (~m_main_v_state2(s6, c_c2))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.75/0.77 tff(939,plain,
% 0.75/0.77 (~m_main_v_state2(s6, c_c2)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[938, 260, 927])).
% 0.75/0.77 tff(940,plain,
% 0.75/0.77 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s6, c_c2) | (~node3(s6)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s6, c_c2) | (~node3(s6)))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(941,plain,
% 0.75/0.77 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s6, c_c2) | (~node3(s6)))),
% 0.75/0.77 inference(quant_inst,[status(thm)],[])).
% 0.75/0.77 tff(942,plain,
% 0.75/0.77 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s6, c_c2) | (~node3(s6))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.75/0.77 tff(943,plain,
% 0.75/0.77 (~node3(s6)),
% 0.75/0.77 inference(unit_resolution,[status(thm)],[942, 399, 939])).
% 0.75/0.77 tff(944,plain,
% 0.75/0.77 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s6, c_n2) | (~node2(s6)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s6, c_n2) | (~node2(s6)))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(945,plain,
% 0.75/0.78 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s6, c_n2) | (~node2(s6)))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(946,plain,
% 0.75/0.78 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s6, c_n2) | (~node2(s6))),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.75/0.78 tff(947,plain,
% 0.75/0.78 (~node2(s6)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[946, 410, 931])).
% 0.75/0.78 tff(948,plain,
% 0.75/0.78 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s6, c_n1)) | (~m_main_v_state1(s6, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s6, c_n1)) | (~m_main_v_state1(s6, c_c1)))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(949,plain,
% 0.75/0.78 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s6, c_n1)) | (~m_main_v_state1(s6, c_c1)))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(950,plain,
% 0.75/0.78 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s6, c_n1)) | (~m_main_v_state1(s6, c_c1))),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.75/0.78 tff(951,plain,
% 0.75/0.78 (~m_main_v_state1(s6, c_n1)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[950, 454, 900])).
% 0.75/0.78 tff(952,plain,
% 0.75/0.78 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s6, c_n1) | (~node1(s6)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s6, c_n1) | (~node1(s6)))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(953,plain,
% 0.75/0.78 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s6, c_n1) | (~node1(s6)))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(954,plain,
% 0.75/0.78 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s6, c_n1) | (~node1(s6))),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.75/0.78 tff(955,plain,
% 0.75/0.78 (~node1(s6)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[954, 421, 951])).
% 0.75/0.78 tff(956,plain,
% 0.75/0.78 (succ(s6, s7) <=> succ(s6, s7)),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(957,axiom,(succ(s6, s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 0.75/0.78 tff(958,plain,
% 0.75/0.78 (succ(s6, s7)),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.75/0.78 tff(959,plain,
% 0.75/0.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(960,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(961,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.75/0.78 tff(962,plain,
% 0.75/0.78 (trans(s6, s7)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[961, 958, 32])).
% 0.75/0.78 tff(963,plain,
% 0.75/0.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s6, s7)) | node7(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s6, s7)) | node7(s6, s7))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(964,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s6, s7)) | node7(s6, s7))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(965,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s6, s7)) | node7(s6, s7)),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.75/0.78 tff(966,plain,
% 0.75/0.78 (node7(s6, s7)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[965, 206, 962])).
% 0.75/0.78 tff(967,plain,
% 0.75/0.78 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(968,plain,
% 0.75/0.78 (((~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)) | m_main_v_state1(s7, c_n1)) <=> (m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(969,plain,
% 0.75/0.78 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)) | m_main_v_state1(s7, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7))))),
% 0.75/0.78 inference(monotonicity,[status(thm)],[968])).
% 0.75/0.78 tff(970,plain,
% 0.75/0.78 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)) | m_main_v_state1(s7, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)))),
% 0.75/0.78 inference(transitivity,[status(thm)],[969, 967])).
% 0.75/0.78 tff(971,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)) | m_main_v_state1(s7, c_n1))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(972,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7))),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.75/0.78 tff(973,plain,
% 0.75/0.78 (m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[972, 584, 966])).
% 0.75/0.78 tff(974,plain,
% 0.75/0.78 (m_main_v_state1(s7, c_n1)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[973, 955, 900, 947, 943, 935, 908])).
% 0.75/0.78 tff(975,plain,
% 0.75/0.78 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s5, c_t2) | (~node15(s5)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s5, c_t2) | (~node15(s5)))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(976,plain,
% 0.75/0.78 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s5, c_t2) | (~node15(s5)))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(977,plain,
% 0.75/0.78 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s5, c_t2) | (~node15(s5))),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.75/0.78 tff(978,plain,
% 0.75/0.78 (~node15(s5)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[977, 103, 867])).
% 0.75/0.78 tff(979,plain,
% 0.75/0.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s5, s6)) | node18(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s5, s6)) | node18(s5, s6))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(980,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s5, s6)) | node18(s5, s6))),
% 0.75/0.78 inference(quant_inst,[status(thm)],[])).
% 0.75/0.78 tff(981,plain,
% 0.75/0.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s5, s6)) | node18(s5, s6)),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.75/0.78 tff(982,plain,
% 0.75/0.78 (node18(s5, s6)),
% 0.75/0.78 inference(unit_resolution,[status(thm)],[981, 125, 878])).
% 0.75/0.78 tff(983,plain,
% 0.75/0.78 (^[Y: $i, X: $i] : refl(((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1)))),
% 0.75/0.78 inference(bind,[status(th)],[])).
% 0.75/0.78 tff(984,plain,
% 0.75/0.78 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.75/0.78 inference(quant_intro,[status(thm)],[983])).
% 0.75/0.78 tff(985,plain,
% 0.75/0.78 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(986,plain,
% 0.75/0.78 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((node15(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_t1))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X))), ((((node15(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_t1))) | m_main_v_turn(Y, c_1)) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X)) | m_main_v_turn(Y, c_1)))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X)) | m_main_v_turn(Y, c_1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | m_main_v_turn(Y, c_1))), ((((node15(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_t1))) | m_main_v_turn(Y, c_1)) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | m_main_v_turn(Y, c_1)))), (((((node15(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_t1))) | m_main_v_turn(Y, c_1)) | (~node18(X, Y))) <=> (((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | m_main_v_turn(Y, c_1)) | (~node18(X, Y))))), rewrite((((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | m_main_v_turn(Y, c_1)) | (~node18(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))), (((((node15(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_t1))) | m_main_v_turn(Y, c_1)) | (~node18(X, Y))) <=> ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))))),
% 0.75/0.78 inference(bind,[status(th)],[])).
% 0.75/0.78 tff(987,plain,
% 0.75/0.78 (![Y: $i, X: $i] : ((((node15(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_t1))) | m_main_v_turn(Y, c_1)) | (~node18(X, Y))) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.75/0.78 inference(quant_intro,[status(thm)],[986])).
% 0.75/0.78 tff(988,axiom,(![Y: $i, X: $i] : ((((node15(X) | (~m_main_v_state2(X, c_n2))) | (~m_main_v_state1(X, c_t1))) | m_main_v_turn(Y, c_1)) | (~node18(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_63')).
% 0.75/0.78 tff(989,plain,
% 0.75/0.78 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.75/0.78 tff(990,plain,
% 0.75/0.78 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.75/0.78 inference(modus_ponens,[status(thm)],[989, 985])).
% 0.75/0.78 tff(991,plain,(
% 0.75/0.78 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.75/0.78 inference(skolemize,[status(sab)],[990])).
% 0.75/0.79 tff(992,plain,
% 0.75/0.79 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[991, 984])).
% 0.75/0.79 tff(993,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s5) | (~node18(s5, s6)) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s5) | (~node18(s5, s6)) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(994,plain,
% 0.75/0.79 (((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node15(s5) | (~node18(s5, s6)) | m_main_v_turn(s6, c_1)) <=> (node15(s5) | (~node18(s5, s6)) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(995,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node15(s5) | (~node18(s5, s6)) | m_main_v_turn(s6, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s5) | (~node18(s5, s6)) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1)))),
% 0.75/0.79 inference(monotonicity,[status(thm)],[994])).
% 0.75/0.79 tff(996,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node15(s5) | (~node18(s5, s6)) | m_main_v_turn(s6, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s5) | (~node18(s5, s6)) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1))),
% 0.75/0.79 inference(transitivity,[status(thm)],[995, 993])).
% 0.75/0.79 tff(997,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | node15(s5) | (~node18(s5, s6)) | m_main_v_turn(s6, c_1))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(998,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s5) | (~node18(s5, s6)) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1)),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.75/0.79 tff(999,plain,
% 0.75/0.79 (node15(s5) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[998, 992, 982])).
% 0.75/0.79 tff(1000,plain,
% 0.75/0.79 (m_main_v_turn(s6, c_1)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[999, 978, 734, 863])).
% 0.75/0.79 tff(1001,plain,
% 0.75/0.79 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s6, c_1)) | (~m_main_v_turn(s6, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s6, c_1)) | (~m_main_v_turn(s6, c_2)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1002,plain,
% 0.75/0.79 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s6, c_1)) | (~m_main_v_turn(s6, c_2)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1003,plain,
% 0.75/0.79 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s6, c_1)) | (~m_main_v_turn(s6, c_2))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.75/0.79 tff(1004,plain,
% 0.75/0.79 (~m_main_v_turn(s6, c_2)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1003, 156, 1000])).
% 0.75/0.79 tff(1005,plain,
% 0.75/0.79 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s6, c_2) | (~node12(s6)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s6, c_2) | (~node12(s6)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1006,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s6, c_2) | (~node12(s6)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1007,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s6, c_2) | (~node12(s6))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.75/0.79 tff(1008,plain,
% 0.75/0.79 (~node12(s6)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1007, 184, 1004])).
% 0.75/0.79 tff(1009,plain,
% 0.75/0.79 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s6, c_n2) | (~node8(s6)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s6, c_n2) | (~node8(s6)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1010,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s6, c_n2) | (~node8(s6)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1011,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s6, c_n2) | (~node8(s6))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.75/0.79 tff(1012,plain,
% 0.75/0.79 (~node8(s6)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1011, 271, 931])).
% 0.75/0.79 tff(1013,plain,
% 0.75/0.79 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s6, c_n2) | (~node9(s6)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s6, c_n2) | (~node9(s6)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1014,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s6, c_n2) | (~node9(s6)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1015,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s6, c_n2) | (~node9(s6))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.75/0.79 tff(1016,plain,
% 0.75/0.79 (~node9(s6)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1015, 88, 931])).
% 0.75/0.79 tff(1017,plain,
% 0.75/0.79 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s6, c_n2) | (~node10(s6)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s6, c_n2) | (~node10(s6)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1018,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s6, c_n2) | (~node10(s6)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1019,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s6, c_n2) | (~node10(s6))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.75/0.79 tff(1020,plain,
% 0.75/0.79 (~node10(s6)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1019, 249, 931])).
% 0.75/0.79 tff(1021,plain,
% 0.75/0.79 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s6, c_n1) | (~node11(s6)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s6, c_n1) | (~node11(s6)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1022,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s6, c_n1) | (~node11(s6)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1023,plain,
% 0.75/0.79 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s6, c_n1) | (~node11(s6))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.75/0.79 tff(1024,plain,
% 0.75/0.79 (~node11(s6)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1023, 238, 951])).
% 0.75/0.79 tff(1025,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s6, s7)) | node14(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s6, s7)) | node14(s6, s7))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1026,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s6, s7)) | node14(s6, s7))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1027,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s6, s7)) | node14(s6, s7)),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 0.75/0.79 tff(1028,plain,
% 0.75/0.79 (node14(s6, s7)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1027, 46, 962])).
% 0.75/0.79 tff(1029,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7) | (~node14(s6, s7)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7) | (~node14(s6, s7)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1030,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7) | (~node14(s6, s7)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1031,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7) | (~node14(s6, s7))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.75/0.79 tff(1032,plain,
% 0.75/0.79 (m_main_v_state2(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1031, 296, 1028])).
% 0.75/0.79 tff(1033,plain,
% 0.75/0.79 (node13(s6, s7)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1032, 1024, 939, 1020, 1016, 1012, 1008])).
% 0.75/0.79 tff(1034,plain,
% 0.75/0.79 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2) | (~node13(s6, s7)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2) | (~node13(s6, s7)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1035,plain,
% 0.75/0.79 (((~node13(s6, s7)) | (~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2)) <=> ((~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2) | (~node13(s6, s7)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1036,plain,
% 0.75/0.79 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s6, s7)) | (~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2) | (~node13(s6, s7))))),
% 0.75/0.79 inference(monotonicity,[status(thm)],[1035])).
% 0.75/0.79 tff(1037,plain,
% 0.75/0.79 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s6, s7)) | (~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2) | (~node13(s6, s7)))),
% 0.75/0.79 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.75/0.79 tff(1038,plain,
% 0.75/0.79 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s6, s7)) | (~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1039,plain,
% 0.75/0.79 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s6, c_t2)) | m_main_v_state2(s7, c_t2) | (~node13(s6, s7))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.75/0.79 tff(1040,plain,
% 0.75/0.79 (m_main_v_state2(s7, c_t2)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1039, 518, 927, 1033])).
% 0.75/0.79 tff(1041,plain,
% 0.75/0.79 (succ(s7, s8) <=> succ(s7, s8)),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1042,axiom,(succ(s7, s8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound8')).
% 0.75/0.79 tff(1043,plain,
% 0.75/0.79 (succ(s7, s8)),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.75/0.79 tff(1044,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1045,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1046,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.75/0.79 tff(1047,plain,
% 0.75/0.79 (trans(s7, s8)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1046, 1043, 32])).
% 0.75/0.79 tff(1048,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s7, s8)) | node7(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s7, s8)) | node7(s7, s8))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1049,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s7, s8)) | node7(s7, s8))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1050,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s7, s8)) | node7(s7, s8)),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.75/0.79 tff(1051,plain,
% 0.75/0.79 (node7(s7, s8)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1050, 206, 1047])).
% 0.75/0.79 tff(1052,plain,
% 0.75/0.79 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node7(s7, s8)) | m_main_v_state1(s8, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node7(s7, s8)) | m_main_v_state1(s8, c_t1))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1053,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node7(s7, s8)) | m_main_v_state1(s8, c_t1))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1054,plain,
% 0.75/0.79 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node7(s7, s8)) | m_main_v_state1(s8, c_t1)),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.75/0.79 tff(1055,plain,
% 0.75/0.79 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | m_main_v_state1(s8, c_t1)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1054, 651, 1051])).
% 0.75/0.79 tff(1056,plain,
% 0.75/0.79 (m_main_v_state1(s8, c_t1)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1055, 1040, 974])).
% 0.75/0.79 tff(1057,plain,
% 0.75/0.79 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s8, c_n1)) | (~m_main_v_state1(s8, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s8, c_n1)) | (~m_main_v_state1(s8, c_t1)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1058,plain,
% 0.75/0.79 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s8, c_n1)) | (~m_main_v_state1(s8, c_t1)))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(1059,plain,
% 0.75/0.79 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s8, c_n1)) | (~m_main_v_state1(s8, c_t1))),
% 0.75/0.79 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.75/0.79 tff(1060,plain,
% 0.75/0.79 (~m_main_v_state1(s8, c_n1)),
% 0.75/0.79 inference(unit_resolution,[status(thm)],[1059, 10, 1056])).
% 0.75/0.79 tff(1061,plain,
% 0.75/0.79 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s8, c_n1) | (~node1(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s8, c_n1) | (~node1(s8)))),
% 0.75/0.79 inference(rewrite,[status(thm)],[])).
% 0.75/0.79 tff(1062,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s8, c_n1) | (~node1(s8)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1063,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s8, c_n1) | (~node1(s8))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 0.75/0.80 tff(1064,plain,
% 0.75/0.80 (~node1(s8)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1063, 421, 1060])).
% 0.75/0.80 tff(1065,plain,
% 0.75/0.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s7, s8)) | node18(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s7, s8)) | node18(s7, s8))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1066,plain,
% 0.75/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s7, s8)) | node18(s7, s8))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1067,plain,
% 0.75/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s7, s8)) | node18(s7, s8)),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.75/0.80 tff(1068,plain,
% 0.75/0.80 (node18(s7, s8)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1067, 125, 1047])).
% 0.75/0.80 tff(1069,plain,
% 0.75/0.80 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1070,plain,
% 0.75/0.80 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1071,plain,
% 0.75/0.80 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2)),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 0.75/0.80 tff(1072,plain,
% 0.75/0.80 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | m_main_v_turn(s8, c_2)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1071, 760, 1068])).
% 0.75/0.80 tff(1073,plain,
% 0.75/0.80 (m_main_v_turn(s8, c_2)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1072, 1040, 974])).
% 0.75/0.80 tff(1074,plain,
% 0.75/0.80 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1075,plain,
% 0.75/0.80 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1076,plain,
% 0.75/0.80 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 0.75/0.80 tff(1077,plain,
% 0.75/0.80 (~m_main_v_turn(s8, c_1)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1076, 156, 1073])).
% 0.75/0.80 tff(1078,plain,
% 0.75/0.80 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s8, c_1) | (~node5(s8)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s8, c_1) | (~node5(s8)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1079,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s8, c_1) | (~node5(s8)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1080,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s8, c_1) | (~node5(s8))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 0.75/0.80 tff(1081,plain,
% 0.75/0.80 (~node5(s8)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1080, 776, 1077])).
% 0.75/0.80 tff(1082,plain,
% 0.75/0.80 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s8, c_n1) | (~node2(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s8, c_n1) | (~node2(s8)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1083,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s8, c_n1) | (~node2(s8)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1084,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s8, c_n1) | (~node2(s8))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 0.75/0.80 tff(1085,plain,
% 0.75/0.80 (~node2(s8)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1084, 787, 1060])).
% 0.75/0.80 tff(1086,plain,
% 0.75/0.80 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s8, c_n1) | (~node3(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s8, c_n1) | (~node3(s8)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1087,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s8, c_n1) | (~node3(s8)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1088,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s8, c_n1) | (~node3(s8))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 0.75/0.80 tff(1089,plain,
% 0.75/0.80 (~node3(s8)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1088, 798, 1060])).
% 0.75/0.80 tff(1090,plain,
% 0.75/0.80 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1091,plain,
% 0.75/0.80 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1092,plain,
% 0.75/0.80 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.75/0.80 tff(1093,plain,
% 0.75/0.80 (~m_main_v_state1(s8, c_c1)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1092, 539, 1056])).
% 0.75/0.80 tff(1094,plain,
% 0.75/0.80 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1095,plain,
% 0.75/0.80 (((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2))) <=> (m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1096,plain,
% 0.75/0.80 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7))))),
% 0.75/0.80 inference(monotonicity,[status(thm)],[1095])).
% 0.75/0.80 tff(1097,plain,
% 0.75/0.80 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))),
% 0.75/0.80 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.75/0.80 tff(1098,plain,
% 0.75/0.80 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1099,plain,
% 0.75/0.80 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.75/0.80 tff(1100,plain,
% 0.75/0.80 (~m_main_v_state2(s7, c_n2)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1099, 311, 931, 1033])).
% 0.75/0.80 tff(1101,plain,
% 0.75/0.80 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s7, c_n2) | (~node9(s7)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s7, c_n2) | (~node9(s7)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1102,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s7, c_n2) | (~node9(s7)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1103,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s7, c_n2) | (~node9(s7))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.75/0.80 tff(1104,plain,
% 0.75/0.80 (~node9(s7)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1103, 88, 1100])).
% 0.75/0.80 tff(1105,plain,
% 0.75/0.80 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s7, c_n2) | (~node10(s7)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s7, c_n2) | (~node10(s7)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1106,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s7, c_n2) | (~node10(s7)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1107,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s7, c_n2) | (~node10(s7))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.75/0.80 tff(1108,plain,
% 0.75/0.80 (~node10(s7)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1107, 249, 1100])).
% 0.75/0.80 tff(1109,plain,
% 0.75/0.80 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s7, c_n2) | (~node8(s7)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s7, c_n2) | (~node8(s7)))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1110,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s7, c_n2) | (~node8(s7)))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1111,plain,
% 0.75/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s7, c_n2) | (~node8(s7))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.75/0.80 tff(1112,plain,
% 0.75/0.80 (~node8(s7)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1111, 271, 1100])).
% 0.75/0.80 tff(1113,plain,
% 0.75/0.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s7, s8)) | node14(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s7, s8)) | node14(s7, s8))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1114,plain,
% 0.75/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s7, s8)) | node14(s7, s8))),
% 0.75/0.80 inference(quant_inst,[status(thm)],[])).
% 0.75/0.80 tff(1115,plain,
% 0.75/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s7, s8)) | node14(s7, s8)),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.75/0.80 tff(1116,plain,
% 0.75/0.80 (node14(s7, s8)),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[1115, 46, 1047])).
% 0.75/0.80 tff(1117,plain,
% 0.75/0.80 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2))),
% 0.75/0.80 inference(rewrite,[status(thm)],[])).
% 0.75/0.80 tff(1118,plain,
% 0.75/0.80 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2))),
% 0.75/0.81 inference(quant_inst,[status(thm)],[])).
% 0.75/0.81 tff(1119,plain,
% 0.75/0.81 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2)),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.75/0.81 tff(1120,plain,
% 0.75/0.81 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | m_main_v_state2(s8, c_c2)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1119, 617, 1116])).
% 0.75/0.81 tff(1121,plain,
% 0.75/0.81 (m_main_v_state2(s8, c_c2)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1120, 1112, 974, 1040, 1108, 1104])).
% 0.75/0.81 tff(1122,plain,
% 0.75/0.81 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1123,plain,
% 0.75/0.81 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.75/0.81 inference(quant_inst,[status(thm)],[])).
% 0.75/0.81 tff(1124,plain,
% 0.75/0.81 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2))),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 0.75/0.81 tff(1125,plain,
% 0.75/0.81 (~m_main_v_state2(s8, c_n2)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1124, 697, 1121])).
% 0.75/0.81 tff(1126,plain,
% 0.75/0.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s8, c_n2) | (~node4(s8)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s8, c_n2) | (~node4(s8)))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1127,plain,
% 0.75/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s8, c_n2) | (~node4(s8)))),
% 0.75/0.81 inference(quant_inst,[status(thm)],[])).
% 0.75/0.81 tff(1128,plain,
% 0.75/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s8, c_n2) | (~node4(s8))),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 0.75/0.81 tff(1129,plain,
% 0.75/0.81 (~node4(s8)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1128, 388, 1125])).
% 0.75/0.81 tff(1130,plain,
% 0.75/0.81 (succ(s8, s9) <=> succ(s8, s9)),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1131,axiom,(succ(s8, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound9')).
% 0.75/0.81 tff(1132,plain,
% 0.75/0.81 (succ(s8, s9)),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.75/0.81 tff(1133,plain,
% 0.75/0.81 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1134,plain,
% 0.75/0.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 0.75/0.81 inference(quant_inst,[status(thm)],[])).
% 0.75/0.81 tff(1135,plain,
% 0.75/0.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.75/0.81 tff(1136,plain,
% 0.75/0.81 (trans(s8, s9)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1135, 1132, 32])).
% 0.75/0.81 tff(1137,plain,
% 0.75/0.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s8, s9)) | node7(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s8, s9)) | node7(s8, s9))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1138,plain,
% 0.75/0.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s8, s9)) | node7(s8, s9))),
% 0.75/0.81 inference(quant_inst,[status(thm)],[])).
% 0.75/0.81 tff(1139,plain,
% 0.75/0.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s8, s9)) | node7(s8, s9)),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 0.75/0.81 tff(1140,plain,
% 0.75/0.81 (node7(s8, s9)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1139, 206, 1136])).
% 0.75/0.81 tff(1141,plain,
% 0.75/0.81 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9)))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1142,plain,
% 0.75/0.81 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9)))),
% 0.75/0.81 inference(quant_inst,[status(thm)],[])).
% 0.75/0.81 tff(1143,plain,
% 0.75/0.81 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9))),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 0.75/0.81 tff(1144,plain,
% 0.75/0.81 (m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1143, 820, 1140])).
% 0.75/0.81 tff(1145,plain,
% 0.75/0.81 (node6(s8, s9)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1144, 1129, 1093, 1089, 1085, 1081, 1064])).
% 0.75/0.81 tff(1146,plain,
% 0.75/0.81 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1147,plain,
% 0.75/0.81 (((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1)) <=> ((~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1148,plain,
% 0.75/0.81 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9))))),
% 0.75/0.81 inference(monotonicity,[status(thm)],[1147])).
% 0.75/0.81 tff(1149,plain,
% 0.75/0.81 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))),
% 0.75/0.81 inference(transitivity,[status(thm)],[1148, 1146])).
% 0.75/0.81 tff(1150,plain,
% 0.75/0.81 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1))),
% 0.75/0.81 inference(quant_inst,[status(thm)],[])).
% 0.75/0.81 tff(1151,plain,
% 0.75/0.81 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9))),
% 0.75/0.81 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.75/0.81 tff(1152,plain,
% 0.75/0.81 (m_main_v_state1(s9, c_t1)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[1151, 856, 1056, 1145])).
% 0.75/0.81 tff(1153,plain,
% 0.75/0.81 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.75/0.81 inference(rewrite,[status(thm)],[])).
% 0.75/0.81 tff(1154,plain,
% 0.79/0.81 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1155,plain,
% 0.79/0.81 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 0.79/0.81 tff(1156,plain,
% 0.79/0.81 (~m_main_v_state2(s8, c_t2)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1155, 260, 1121])).
% 0.79/0.81 tff(1157,plain,
% 0.79/0.81 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s8, c_t2) | (~node12(s8)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s8, c_t2) | (~node12(s8)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1158,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s8, c_t2) | (~node12(s8)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1159,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s8, c_t2) | (~node12(s8))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 0.79/0.81 tff(1160,plain,
% 0.79/0.81 (~node12(s8)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1159, 633, 1156])).
% 0.79/0.81 tff(1161,plain,
% 0.79/0.81 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s8, c_n1) | (~node11(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s8, c_n1) | (~node11(s8)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1162,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s8, c_n1) | (~node11(s8)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1163,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s8, c_n1) | (~node11(s8))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.79/0.81 tff(1164,plain,
% 0.79/0.81 (~node11(s8)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1163, 238, 1060])).
% 0.79/0.81 tff(1165,plain,
% 0.79/0.81 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s8, c_c1) | (~node10(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s8, c_c1) | (~node10(s8)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1166,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s8, c_c1) | (~node10(s8)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1167,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s8, c_c1) | (~node10(s8))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.79/0.81 tff(1168,plain,
% 0.79/0.81 (~node10(s8)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1167, 675, 1093])).
% 0.79/0.81 tff(1169,plain,
% 0.79/0.81 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s8, c_n1) | (~node9(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s8, c_n1) | (~node9(s8)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1170,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s8, c_n1) | (~node9(s8)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1171,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s8, c_n1) | (~node9(s8))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 0.79/0.81 tff(1172,plain,
% 0.79/0.81 (~node9(s8)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1171, 686, 1060])).
% 0.79/0.81 tff(1173,plain,
% 0.79/0.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s8, c_n2) | (~node8(s8)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s8, c_n2) | (~node8(s8)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1174,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s8, c_n2) | (~node8(s8)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1175,plain,
% 0.79/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s8, c_n2) | (~node8(s8))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 0.79/0.81 tff(1176,plain,
% 0.79/0.81 (~node8(s8)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1175, 271, 1125])).
% 0.79/0.81 tff(1177,plain,
% 0.79/0.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s8, s9)) | node14(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s8, s9)) | node14(s8, s9))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1178,plain,
% 0.79/0.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s8, s9)) | node14(s8, s9))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1179,plain,
% 0.79/0.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s8, s9)) | node14(s8, s9)),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 0.79/0.81 tff(1180,plain,
% 0.79/0.81 (node14(s8, s9)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1179, 46, 1136])).
% 0.79/0.81 tff(1181,plain,
% 0.79/0.81 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1182,plain,
% 0.79/0.82 (((~m_main_v_state2(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2)) <=> (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1183,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2))))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[1182])).
% 0.79/0.82 tff(1184,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))),
% 0.79/0.82 inference(transitivity,[status(thm)],[1183, 1181])).
% 0.79/0.82 tff(1185,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1186,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.79/0.82 tff(1187,plain,
% 0.79/0.82 (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~m_main_v_state2(s8, c_c2))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1186, 726, 1180])).
% 0.79/0.82 tff(1188,plain,
% 0.79/0.82 (m_main_v_state2(s9, c_n2)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1187, 1176, 1121, 1172, 1168, 1164, 1160])).
% 0.79/0.82 tff(1189,plain,
% 0.79/0.82 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1190,plain,
% 0.79/0.82 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1191,plain,
% 0.79/0.82 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.79/0.82 tff(1192,plain,
% 0.79/0.82 (~m_main_v_state2(s9, c_t2)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1191, 77, 1188])).
% 0.79/0.82 tff(1193,plain,
% 0.79/0.82 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s9, c_t2) | (~node15(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s9, c_t2) | (~node15(s9)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1194,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s9, c_t2) | (~node15(s9)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1195,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s9, c_t2) | (~node15(s9))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 0.79/0.82 tff(1196,plain,
% 0.79/0.82 (~node15(s9)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1195, 103, 1192])).
% 0.79/0.82 tff(1197,plain,
% 0.79/0.82 (succ(s9, s10) <=> succ(s9, s10)),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1198,axiom,(succ(s9, s10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound10')).
% 0.79/0.82 tff(1199,plain,
% 0.79/0.82 (succ(s9, s10)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.79/0.82 tff(1200,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1201,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1202,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 0.79/0.82 tff(1203,plain,
% 0.79/0.82 (trans(s9, s10)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1202, 1199, 32])).
% 0.79/0.82 tff(1204,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s9, s10)) | node18(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s9, s10)) | node18(s9, s10))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1205,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s9, s10)) | node18(s9, s10))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1206,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s9, s10)) | node18(s9, s10)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 0.79/0.82 tff(1207,plain,
% 0.79/0.82 (node18(s9, s10)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1206, 125, 1203])).
% 0.79/0.82 tff(1208,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1209,plain,
% 0.79/0.82 (((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1)) <=> (node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1210,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1)))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[1209])).
% 0.79/0.82 tff(1211,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))),
% 0.79/0.82 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.79/0.82 tff(1212,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1213,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.79/0.82 tff(1214,plain,
% 0.79/0.82 (node15(s9) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1213, 992, 1207])).
% 0.79/0.82 tff(1215,plain,
% 0.79/0.82 (m_main_v_turn(s10, c_1)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1214, 1196, 1188, 1152])).
% 0.79/0.82 tff(1216,plain,
% 0.79/0.82 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1217,plain,
% 0.79/0.82 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1218,plain,
% 0.79/0.82 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 0.79/0.82 tff(1219,plain,
% 0.79/0.82 (~m_main_v_turn(s10, c_2)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1218, 156, 1215])).
% 0.79/0.82 tff(1220,plain,
% 0.79/0.82 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s10, c_2) | (~node12(s10)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s10, c_2) | (~node12(s10)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1221,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s10, c_2) | (~node12(s10)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1222,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s10, c_2) | (~node12(s10))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 0.79/0.82 tff(1223,plain,
% 0.79/0.82 (~node12(s10)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1222, 184, 1219])).
% 0.79/0.82 tff(1224,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s9, s10)) | node14(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s9, s10)) | node14(s9, s10))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1225,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s9, s10)) | node14(s9, s10))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1226,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s9, s10)) | node14(s9, s10)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 0.79/0.82 tff(1227,plain,
% 0.79/0.82 (node14(s9, s10)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1226, 46, 1203])).
% 0.79/0.82 tff(1228,plain,
% 0.79/0.82 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1229,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1230,plain,
% 0.79/0.82 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 0.79/0.82 tff(1231,plain,
% 0.79/0.82 ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state2(s10, c_t2)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1230, 922, 1227])).
% 0.79/0.82 tff(1232,plain,
% 0.79/0.82 (m_main_v_state2(s10, c_t2)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1231, 1152, 1188])).
% 0.79/0.82 tff(1233,plain,
% 0.79/0.82 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1234,plain,
% 0.79/0.82 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1235,plain,
% 0.79/0.82 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 0.79/0.82 tff(1236,plain,
% 0.79/0.82 (~m_main_v_state2(s10, c_n2)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1235, 77, 1232])).
% 0.79/0.82 tff(1237,plain,
% 0.79/0.82 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s10, c_n2) | (~node8(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s10, c_n2) | (~node8(s10)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1238,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s10, c_n2) | (~node8(s10)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1239,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s10, c_n2) | (~node8(s10))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.79/0.82 tff(1240,plain,
% 0.79/0.82 (~node8(s10)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1239, 271, 1236])).
% 0.79/0.82 tff(1241,plain,
% 0.79/0.82 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s10, c_n2) | (~node9(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s10, c_n2) | (~node9(s10)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1242,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s10, c_n2) | (~node9(s10)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1243,plain,
% 0.79/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s10, c_n2) | (~node9(s10))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.79/0.83 tff(1244,plain,
% 0.79/0.83 (~node9(s10)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1243, 88, 1236])).
% 0.79/0.83 tff(1245,plain,
% 0.79/0.83 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s10, c_n2) | (~node10(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s10, c_n2) | (~node10(s10)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1246,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s10, c_n2) | (~node10(s10)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1247,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s10, c_n2) | (~node10(s10))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 0.79/0.83 tff(1248,plain,
% 0.79/0.83 (~node10(s10)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1247, 249, 1236])).
% 0.79/0.83 tff(1249,plain,
% 0.79/0.83 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1250,plain,
% 0.79/0.83 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1251,plain,
% 0.79/0.83 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.79/0.83 tff(1252,plain,
% 0.79/0.83 (~m_main_v_state2(s10, c_c2)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1251, 260, 1232])).
% 0.79/0.83 tff(1253,plain,
% 0.79/0.83 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1254,plain,
% 0.79/0.83 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1255,plain,
% 0.79/0.83 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 0.79/0.83 tff(1256,plain,
% 0.79/0.83 (~m_main_v_state2(s9, c_c2)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1255, 697, 1188])).
% 0.79/0.83 tff(1257,plain,
% 0.79/0.83 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s9, c_c2) | (~node3(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s9, c_c2) | (~node3(s9)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1258,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s9, c_c2) | (~node3(s9)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1259,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s9, c_c2) | (~node3(s9))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.79/0.83 tff(1260,plain,
% 0.79/0.83 (~node3(s9)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1259, 399, 1256])).
% 0.79/0.83 tff(1261,plain,
% 0.79/0.83 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1262,plain,
% 0.79/0.83 (((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1))) <=> (m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1263,plain,
% 0.79/0.83 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9))))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[1262])).
% 0.79/0.83 tff(1264,plain,
% 0.79/0.83 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))),
% 0.79/0.83 inference(transitivity,[status(thm)],[1263, 1261])).
% 0.79/0.83 tff(1265,plain,
% 0.79/0.83 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1266,plain,
% 0.79/0.83 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 0.79/0.83 tff(1267,plain,
% 0.79/0.83 (~m_main_v_state1(s9, c_n1)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1266, 835, 1060, 1145])).
% 0.79/0.83 tff(1268,plain,
% 0.79/0.83 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s9, c_n1) | (~node2(s9)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s9, c_n1) | (~node2(s9)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1269,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s9, c_n1) | (~node2(s9)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1270,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s9, c_n1) | (~node2(s9))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.79/0.83 tff(1271,plain,
% 0.79/0.83 (~node2(s9)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1270, 787, 1267])).
% 0.79/0.83 tff(1272,plain,
% 0.79/0.83 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s9, c_t2) | (~node1(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s9, c_t2) | (~node1(s9)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1273,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s9, c_t2) | (~node1(s9)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1274,plain,
% 0.79/0.83 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s9, c_t2) | (~node1(s9))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.79/0.83 tff(1275,plain,
% 0.79/0.83 (~node1(s9)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1274, 195, 1192])).
% 0.79/0.83 tff(1276,plain,
% 0.79/0.83 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s9, s10)) | node7(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s9, s10)) | node7(s9, s10))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1277,plain,
% 0.79/0.83 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s9, s10)) | node7(s9, s10))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1278,plain,
% 0.79/0.83 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s9, s10)) | node7(s9, s10)),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 0.79/0.83 tff(1279,plain,
% 0.79/0.83 (node7(s9, s10)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1278, 206, 1203])).
% 0.79/0.83 tff(1280,plain,
% 0.79/0.83 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1281,plain,
% 0.79/0.83 (((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1)) <=> ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1282,plain,
% 0.79/0.83 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10))))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[1281])).
% 0.79/0.83 tff(1283,plain,
% 0.79/0.83 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))),
% 0.79/0.83 inference(transitivity,[status(thm)],[1282, 1280])).
% 0.79/0.83 tff(1284,plain,
% 0.79/0.83 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1285,plain,
% 0.79/0.83 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.79/0.83 tff(1286,plain,
% 0.79/0.83 ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1285, 892, 1279])).
% 0.79/0.83 tff(1287,plain,
% 0.79/0.83 (m_main_v_state1(s10, c_c1)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1286, 1275, 1188, 1152, 1271, 1260])).
% 0.79/0.83 tff(1288,plain,
% 0.79/0.83 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1289,plain,
% 0.79/0.83 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1290,plain,
% 0.79/0.83 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 0.79/0.83 tff(1291,plain,
% 0.79/0.83 (~m_main_v_state1(s10, c_n1)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1290, 454, 1287])).
% 0.79/0.83 tff(1292,plain,
% 0.79/0.83 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s10, c_n1) | (~node11(s10)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s10, c_n1) | (~node11(s10)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1293,plain,
% 0.79/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s10, c_n1) | (~node11(s10)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1294,plain,
% 0.79/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s10, c_n1) | (~node11(s10))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.79/0.84 tff(1295,plain,
% 0.79/0.84 (~node11(s10)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1294, 238, 1291])).
% 0.79/0.84 tff(1296,plain,
% 0.79/0.84 (succ(s10, s11) <=> succ(s10, s11)),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1297,axiom,(succ(s10, s11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound11')).
% 0.79/0.84 tff(1298,plain,
% 0.79/0.84 (succ(s10, s11)),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 0.79/0.84 tff(1299,plain,
% 0.79/0.84 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1300,plain,
% 0.79/0.84 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1301,plain,
% 0.79/0.84 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.79/0.84 tff(1302,plain,
% 0.79/0.84 (trans(s10, s11)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1301, 1298, 32])).
% 0.79/0.84 tff(1303,plain,
% 0.79/0.84 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s10, s11)) | node14(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s10, s11)) | node14(s10, s11))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1304,plain,
% 0.79/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s10, s11)) | node14(s10, s11))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1305,plain,
% 0.79/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s10, s11)) | node14(s10, s11)),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 0.79/0.84 tff(1306,plain,
% 0.79/0.84 (node14(s10, s11)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1305, 46, 1302])).
% 0.79/0.84 tff(1307,plain,
% 0.79/0.84 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1308,plain,
% 0.79/0.84 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1309,plain,
% 0.79/0.84 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 0.79/0.84 tff(1310,plain,
% 0.79/0.84 (m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1309, 296, 1306])).
% 0.79/0.84 tff(1311,plain,
% 0.79/0.84 (node13(s10, s11)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1310, 1295, 1252, 1248, 1244, 1240, 1223])).
% 0.79/0.84 tff(1312,plain,
% 0.79/0.84 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1313,plain,
% 0.79/0.84 (((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2))) <=> (m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1314,plain,
% 0.79/0.84 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[1313])).
% 0.79/0.84 tff(1315,plain,
% 0.79/0.84 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))),
% 0.79/0.84 inference(transitivity,[status(thm)],[1314, 1312])).
% 0.79/0.84 tff(1316,plain,
% 0.79/0.84 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1317,plain,
% 0.79/0.84 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.79/0.84 tff(1318,plain,
% 0.79/0.84 (~m_main_v_state2(s11, c_n2)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1317, 311, 1236, 1311])).
% 0.79/0.84 tff(1319,plain,
% 0.79/0.84 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s11, c_n2) | (~node9(s11)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s11, c_n2) | (~node9(s11)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1320,plain,
% 0.79/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s11, c_n2) | (~node9(s11)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1321,plain,
% 0.79/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s11, c_n2) | (~node9(s11))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.79/0.84 tff(1322,plain,
% 0.79/0.84 (~node9(s11)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1321, 88, 1318])).
% 0.79/0.84 tff(1323,plain,
% 0.79/0.84 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s11, c_n2) | (~node10(s11)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s11, c_n2) | (~node10(s11)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1324,plain,
% 0.79/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s11, c_n2) | (~node10(s11)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1325,plain,
% 0.79/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s11, c_n2) | (~node10(s11))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.79/0.84 tff(1326,plain,
% 0.79/0.84 (~node10(s11)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1325, 249, 1318])).
% 0.79/0.84 tff(1327,plain,
% 0.79/0.84 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1328,plain,
% 0.79/0.84 (((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2)) <=> ((~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1329,plain,
% 0.82/0.84 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11))))),
% 0.82/0.84 inference(monotonicity,[status(thm)],[1328])).
% 0.82/0.84 tff(1330,plain,
% 0.82/0.84 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))),
% 0.82/0.84 inference(transitivity,[status(thm)],[1329, 1327])).
% 0.82/0.84 tff(1331,plain,
% 0.82/0.84 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1332,plain,
% 0.82/0.84 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.82/0.84 tff(1333,plain,
% 0.82/0.84 (m_main_v_state2(s11, c_t2)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1332, 518, 1232, 1311])).
% 0.82/0.84 tff(1334,plain,
% 0.82/0.84 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1335,plain,
% 0.82/0.84 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1336,plain,
% 0.82/0.84 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.82/0.84 tff(1337,plain,
% 0.82/0.84 (~m_main_v_state1(s10, c_t1)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1336, 539, 1287])).
% 0.82/0.84 tff(1338,plain,
% 0.82/0.84 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s10, c_t1) | (~node5(s10)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s10, c_t1) | (~node5(s10)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1339,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s10, c_t1) | (~node5(s10)))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1340,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s10, c_t1) | (~node5(s10))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 0.82/0.84 tff(1341,plain,
% 0.82/0.84 (~node5(s10)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1340, 550, 1337])).
% 0.82/0.84 tff(1342,plain,
% 0.82/0.84 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s10, c_n2) | (~node4(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s10, c_n2) | (~node4(s10)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1343,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s10, c_n2) | (~node4(s10)))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1344,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s10, c_n2) | (~node4(s10))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.82/0.84 tff(1345,plain,
% 0.82/0.84 (~node4(s10)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1344, 388, 1236])).
% 0.82/0.84 tff(1346,plain,
% 0.82/0.84 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s10, c_c2) | (~node3(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s10, c_c2) | (~node3(s10)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1347,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s10, c_c2) | (~node3(s10)))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1348,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s10, c_c2) | (~node3(s10))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 0.82/0.84 tff(1349,plain,
% 0.82/0.84 (~node3(s10)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1348, 399, 1252])).
% 0.82/0.84 tff(1350,plain,
% 0.82/0.84 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s10, c_n2) | (~node2(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s10, c_n2) | (~node2(s10)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1351,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s10, c_n2) | (~node2(s10)))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1352,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s10, c_n2) | (~node2(s10))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 0.82/0.84 tff(1353,plain,
% 0.82/0.84 (~node2(s10)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1352, 410, 1236])).
% 0.82/0.84 tff(1354,plain,
% 0.82/0.84 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s10, c_n1) | (~node1(s10)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s10, c_n1) | (~node1(s10)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1355,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s10, c_n1) | (~node1(s10)))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1356,plain,
% 0.82/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s10, c_n1) | (~node1(s10))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 0.82/0.84 tff(1357,plain,
% 0.82/0.84 (~node1(s10)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1356, 421, 1291])).
% 0.82/0.84 tff(1358,plain,
% 0.82/0.84 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s10, s11)) | node7(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s10, s11)) | node7(s10, s11))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1359,plain,
% 0.82/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s10, s11)) | node7(s10, s11))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(1360,plain,
% 0.82/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s10, s11)) | node7(s10, s11)),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 0.82/0.84 tff(1361,plain,
% 0.82/0.84 (node7(s10, s11)),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[1360, 206, 1302])).
% 0.82/0.84 tff(1362,plain,
% 0.82/0.84 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1363,plain,
% 0.82/0.84 (((~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1)) <=> (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(1364,plain,
% 0.82/0.84 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11))))),
% 0.82/0.85 inference(monotonicity,[status(thm)],[1363])).
% 0.82/0.85 tff(1365,plain,
% 0.82/0.85 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))),
% 0.82/0.85 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.82/0.85 tff(1366,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1367,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.82/0.85 tff(1368,plain,
% 0.82/0.85 (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1367, 584, 1361])).
% 0.82/0.85 tff(1369,plain,
% 0.82/0.85 (m_main_v_state1(s11, c_n1)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1368, 1357, 1287, 1353, 1349, 1345, 1341])).
% 0.82/0.85 tff(1370,plain,
% 0.82/0.85 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s11, c_n2) | (~node8(s11)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s11, c_n2) | (~node8(s11)))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1371,plain,
% 0.82/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s11, c_n2) | (~node8(s11)))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1372,plain,
% 0.82/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s11, c_n2) | (~node8(s11))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.82/0.85 tff(1373,plain,
% 0.82/0.85 (~node8(s11)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1372, 271, 1318])).
% 0.82/0.85 tff(1374,plain,
% 0.82/0.85 (succ(s11, s12) <=> succ(s11, s12)),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1375,axiom,(succ(s11, s12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound12')).
% 0.82/0.85 tff(1376,plain,
% 0.82/0.85 (succ(s11, s12)),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 0.82/0.85 tff(1377,plain,
% 0.82/0.85 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1378,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1379,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.82/0.85 tff(1380,plain,
% 0.82/0.85 (trans(s11, s12)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1379, 1376, 32])).
% 0.82/0.85 tff(1381,plain,
% 0.82/0.85 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s11, s12)) | node14(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s11, s12)) | node14(s11, s12))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1382,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s11, s12)) | node14(s11, s12))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1383,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s11, s12)) | node14(s11, s12)),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 0.82/0.85 tff(1384,plain,
% 0.82/0.85 (node14(s11, s12)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1383, 46, 1380])).
% 0.82/0.85 tff(1385,plain,
% 0.82/0.85 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1386,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1387,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2)),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 0.82/0.85 tff(1388,plain,
% 0.82/0.85 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | m_main_v_state2(s12, c_c2)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1387, 617, 1384])).
% 0.82/0.85 tff(1389,plain,
% 0.82/0.85 (m_main_v_state2(s12, c_c2)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1388, 1373, 1369, 1333, 1326, 1322])).
% 0.82/0.85 tff(1390,plain,
% 0.82/0.85 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1391,plain,
% 0.82/0.85 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1392,plain,
% 0.82/0.85 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.82/0.85 tff(1393,plain,
% 0.82/0.85 (~m_main_v_state2(s12, c_t2)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1392, 260, 1389])).
% 0.82/0.85 tff(1394,plain,
% 0.82/0.85 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s12, c_t2) | (~node12(s12)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s12, c_t2) | (~node12(s12)))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1395,plain,
% 0.82/0.85 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s12, c_t2) | (~node12(s12)))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1396,plain,
% 0.82/0.85 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s12, c_t2) | (~node12(s12))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 0.82/0.85 tff(1397,plain,
% 0.82/0.85 (~node12(s12)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1396, 633, 1393])).
% 0.82/0.85 tff(1398,plain,
% 0.82/0.85 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s11, s12)) | node7(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s11, s12)) | node7(s11, s12))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1399,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s11, s12)) | node7(s11, s12))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1400,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s11, s12)) | node7(s11, s12)),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 0.82/0.85 tff(1401,plain,
% 0.82/0.85 (node7(s11, s12)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1400, 206, 1380])).
% 0.82/0.85 tff(1402,plain,
% 0.82/0.85 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1403,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1404,plain,
% 0.82/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1)),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 0.82/0.85 tff(1405,plain,
% 0.82/0.85 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | m_main_v_state1(s12, c_t1)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1404, 651, 1401])).
% 0.82/0.85 tff(1406,plain,
% 0.82/0.85 (m_main_v_state1(s12, c_t1)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1405, 1333, 1369])).
% 0.82/0.85 tff(1407,plain,
% 0.82/0.85 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1)))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1408,plain,
% 0.82/0.85 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1)))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1409,plain,
% 0.82/0.85 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.82/0.85 tff(1410,plain,
% 0.82/0.85 (~m_main_v_state1(s12, c_n1)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1409, 10, 1406])).
% 0.82/0.85 tff(1411,plain,
% 0.82/0.85 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s12, c_n1) | (~node11(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s12, c_n1) | (~node11(s12)))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1412,plain,
% 0.82/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s12, c_n1) | (~node11(s12)))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(1413,plain,
% 0.82/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s12, c_n1) | (~node11(s12))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 0.82/0.85 tff(1414,plain,
% 0.82/0.85 (~node11(s12)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[1413, 238, 1410])).
% 0.82/0.85 tff(1415,plain,
% 0.82/0.85 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1)))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(1416,plain,
% 0.82/0.85 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1)))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1417,plain,
% 0.82/0.86 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.82/0.86 tff(1418,plain,
% 0.82/0.86 (~m_main_v_state1(s12, c_c1)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1417, 539, 1406])).
% 0.82/0.86 tff(1419,plain,
% 0.82/0.86 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s12, c_c1) | (~node10(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s12, c_c1) | (~node10(s12)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1420,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s12, c_c1) | (~node10(s12)))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1421,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s12, c_c1) | (~node10(s12))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.82/0.86 tff(1422,plain,
% 0.82/0.86 (~node10(s12)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1421, 675, 1418])).
% 0.82/0.86 tff(1423,plain,
% 0.82/0.86 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s12, c_n1) | (~node9(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s12, c_n1) | (~node9(s12)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1424,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s12, c_n1) | (~node9(s12)))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1425,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s12, c_n1) | (~node9(s12))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 0.82/0.86 tff(1426,plain,
% 0.82/0.86 (~node9(s12)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1425, 686, 1410])).
% 0.82/0.86 tff(1427,plain,
% 0.82/0.86 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1428,plain,
% 0.82/0.86 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1429,plain,
% 0.82/0.86 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.82/0.86 tff(1430,plain,
% 0.82/0.86 (~m_main_v_state2(s12, c_n2)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1429, 697, 1389])).
% 0.82/0.86 tff(1431,plain,
% 0.82/0.86 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s12, c_n2) | (~node8(s12)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s12, c_n2) | (~node8(s12)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1432,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s12, c_n2) | (~node8(s12)))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1433,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s12, c_n2) | (~node8(s12))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.82/0.86 tff(1434,plain,
% 0.82/0.86 (~node8(s12)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1433, 271, 1430])).
% 0.82/0.86 tff(1435,plain,
% 0.82/0.86 (succ(s12, s13) <=> succ(s12, s13)),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1436,axiom,(succ(s12, s13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound13')).
% 0.82/0.86 tff(1437,plain,
% 0.82/0.86 (succ(s12, s13)),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 0.82/0.86 tff(1438,plain,
% 0.82/0.86 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1439,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1440,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 0.82/0.86 tff(1441,plain,
% 0.82/0.86 (trans(s12, s13)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1440, 1437, 32])).
% 0.82/0.86 tff(1442,plain,
% 0.82/0.86 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s12, s13)) | node14(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s12, s13)) | node14(s12, s13))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1443,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s12, s13)) | node14(s12, s13))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1444,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s12, s13)) | node14(s12, s13)),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.82/0.86 tff(1445,plain,
% 0.82/0.86 (node14(s12, s13)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1444, 46, 1441])).
% 0.82/0.86 tff(1446,plain,
% 0.82/0.86 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1447,plain,
% 0.82/0.86 (((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2)) <=> (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1448,plain,
% 0.82/0.86 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2))))),
% 0.82/0.86 inference(monotonicity,[status(thm)],[1447])).
% 0.82/0.86 tff(1449,plain,
% 0.82/0.86 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))),
% 0.82/0.86 inference(transitivity,[status(thm)],[1448, 1446])).
% 0.82/0.86 tff(1450,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1451,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 0.82/0.86 tff(1452,plain,
% 0.82/0.86 (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~m_main_v_state2(s12, c_c2))),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1451, 726, 1445])).
% 0.82/0.86 tff(1453,plain,
% 0.82/0.86 (m_main_v_state2(s13, c_n2)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1452, 1434, 1389, 1426, 1422, 1414, 1397])).
% 0.82/0.86 tff(1454,plain,
% 0.82/0.86 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1455,plain,
% 0.82/0.86 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2)))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1456,plain,
% 0.82/0.86 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 0.82/0.86 tff(1457,plain,
% 0.82/0.86 (~m_main_v_state2(s13, c_c2)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1456, 697, 1453])).
% 0.82/0.86 tff(1458,plain,
% 0.82/0.86 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s13, c_c2) | (~node3(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s13, c_c2) | (~node3(s13)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1459,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s13, c_c2) | (~node3(s13)))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1460,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s13, c_c2) | (~node3(s13))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 0.82/0.86 tff(1461,plain,
% 0.82/0.86 (~node3(s13)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1460, 399, 1457])).
% 0.82/0.86 tff(1462,plain,
% 0.82/0.86 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s12, c_n1) | (~node1(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s12, c_n1) | (~node1(s12)))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1463,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s12, c_n1) | (~node1(s12)))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1464,plain,
% 0.82/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s12, c_n1) | (~node1(s12))),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 0.82/0.86 tff(1465,plain,
% 0.82/0.86 (~node1(s12)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1464, 421, 1410])).
% 0.82/0.86 tff(1466,plain,
% 0.82/0.86 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s11, s12)) | node18(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s11, s12)) | node18(s11, s12))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(1467,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s11, s12)) | node18(s11, s12))),
% 0.82/0.86 inference(quant_inst,[status(thm)],[])).
% 0.82/0.86 tff(1468,plain,
% 0.82/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s11, s12)) | node18(s11, s12)),
% 0.82/0.86 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 0.82/0.86 tff(1469,plain,
% 0.82/0.86 (node18(s11, s12)),
% 0.82/0.86 inference(unit_resolution,[status(thm)],[1468, 125, 1380])).
% 0.82/0.86 tff(1470,plain,
% 0.82/0.86 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1471,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1472,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2)),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.82/0.87 tff(1473,plain,
% 0.82/0.87 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | m_main_v_turn(s12, c_2)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1472, 760, 1469])).
% 0.82/0.87 tff(1474,plain,
% 0.82/0.87 (m_main_v_turn(s12, c_2)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1473, 1333, 1369])).
% 0.82/0.87 tff(1475,plain,
% 0.82/0.87 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1476,plain,
% 0.82/0.87 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1477,plain,
% 0.82/0.87 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 0.82/0.87 tff(1478,plain,
% 0.82/0.87 (~m_main_v_turn(s12, c_1)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1477, 156, 1474])).
% 0.82/0.87 tff(1479,plain,
% 0.82/0.87 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s12, c_1) | (~node5(s12)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s12, c_1) | (~node5(s12)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1480,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s12, c_1) | (~node5(s12)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1481,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s12, c_1) | (~node5(s12))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 0.82/0.87 tff(1482,plain,
% 0.82/0.87 (~node5(s12)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1481, 776, 1478])).
% 0.82/0.87 tff(1483,plain,
% 0.82/0.87 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s12, c_n1) | (~node2(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s12, c_n1) | (~node2(s12)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1484,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s12, c_n1) | (~node2(s12)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1485,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s12, c_n1) | (~node2(s12))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 0.82/0.87 tff(1486,plain,
% 0.82/0.87 (~node2(s12)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1485, 787, 1410])).
% 0.82/0.87 tff(1487,plain,
% 0.82/0.87 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s12, c_n1) | (~node3(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s12, c_n1) | (~node3(s12)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1488,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s12, c_n1) | (~node3(s12)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1489,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s12, c_n1) | (~node3(s12))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 0.82/0.87 tff(1490,plain,
% 0.82/0.87 (~node3(s12)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1489, 798, 1410])).
% 0.82/0.87 tff(1491,plain,
% 0.82/0.87 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s12, c_n2) | (~node4(s12)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s12, c_n2) | (~node4(s12)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1492,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s12, c_n2) | (~node4(s12)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1493,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s12, c_n2) | (~node4(s12))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.82/0.87 tff(1494,plain,
% 0.82/0.87 (~node4(s12)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1493, 388, 1430])).
% 0.82/0.87 tff(1495,plain,
% 0.82/0.87 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s12, s13)) | node7(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s12, s13)) | node7(s12, s13))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1496,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s12, s13)) | node7(s12, s13))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1497,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s12, s13)) | node7(s12, s13)),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 0.82/0.87 tff(1498,plain,
% 0.82/0.87 (node7(s12, s13)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1497, 206, 1441])).
% 0.82/0.87 tff(1499,plain,
% 0.82/0.87 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1500,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1501,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 0.82/0.87 tff(1502,plain,
% 0.82/0.87 (m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1501, 820, 1498])).
% 0.82/0.87 tff(1503,plain,
% 0.82/0.87 (node6(s12, s13)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1502, 1494, 1418, 1490, 1486, 1482, 1465])).
% 0.82/0.87 tff(1504,plain,
% 0.82/0.87 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1505,plain,
% 0.82/0.87 (((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1))) <=> (m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1506,plain,
% 0.82/0.87 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13))))),
% 0.82/0.87 inference(monotonicity,[status(thm)],[1505])).
% 0.82/0.87 tff(1507,plain,
% 0.82/0.87 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))),
% 0.82/0.87 inference(transitivity,[status(thm)],[1506, 1504])).
% 0.82/0.87 tff(1508,plain,
% 0.82/0.87 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1509,plain,
% 0.82/0.87 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 0.82/0.87 tff(1510,plain,
% 0.82/0.87 (~m_main_v_state1(s13, c_n1)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1509, 835, 1410, 1503])).
% 0.82/0.87 tff(1511,plain,
% 0.82/0.87 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s13, c_n1) | (~node2(s13)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s13, c_n1) | (~node2(s13)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1512,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s13, c_n1) | (~node2(s13)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1513,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s13, c_n1) | (~node2(s13))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 0.82/0.87 tff(1514,plain,
% 0.82/0.87 (~node2(s13)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1513, 787, 1510])).
% 0.82/0.87 tff(1515,plain,
% 0.82/0.87 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1516,plain,
% 0.82/0.87 (((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1)) <=> ((~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1517,plain,
% 0.82/0.87 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13))))),
% 0.82/0.87 inference(monotonicity,[status(thm)],[1516])).
% 0.82/0.87 tff(1518,plain,
% 0.82/0.87 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))),
% 0.82/0.87 inference(transitivity,[status(thm)],[1517, 1515])).
% 0.82/0.87 tff(1519,plain,
% 0.82/0.87 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1520,plain,
% 0.82/0.87 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 0.82/0.87 tff(1521,plain,
% 0.82/0.87 (m_main_v_state1(s13, c_t1)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1520, 856, 1406, 1503])).
% 0.82/0.87 tff(1522,plain,
% 0.82/0.87 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1523,plain,
% 0.82/0.87 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1524,plain,
% 0.82/0.87 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.82/0.87 tff(1525,plain,
% 0.82/0.87 (~m_main_v_state2(s13, c_t2)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1524, 77, 1453])).
% 0.82/0.87 tff(1526,plain,
% 0.82/0.87 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s13, c_t2) | (~node1(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s13, c_t2) | (~node1(s13)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1527,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s13, c_t2) | (~node1(s13)))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1528,plain,
% 0.82/0.87 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s13, c_t2) | (~node1(s13))),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 0.82/0.87 tff(1529,plain,
% 0.82/0.87 (~node1(s13)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1528, 195, 1525])).
% 0.82/0.87 tff(1530,plain,
% 0.82/0.87 (succ(s13, s14) <=> succ(s13, s14)),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1531,axiom,(succ(s13, s14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound14')).
% 0.82/0.87 tff(1532,plain,
% 0.82/0.87 (succ(s13, s14)),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 0.82/0.87 tff(1533,plain,
% 0.82/0.87 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1534,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1535,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.82/0.87 tff(1536,plain,
% 0.82/0.87 (trans(s13, s14)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1535, 1532, 32])).
% 0.82/0.87 tff(1537,plain,
% 0.82/0.87 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s13, s14)) | node7(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s13, s14)) | node7(s13, s14))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1538,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s13, s14)) | node7(s13, s14))),
% 0.82/0.87 inference(quant_inst,[status(thm)],[])).
% 0.82/0.87 tff(1539,plain,
% 0.82/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s13, s14)) | node7(s13, s14)),
% 0.82/0.87 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.82/0.87 tff(1540,plain,
% 0.82/0.87 (node7(s13, s14)),
% 0.82/0.87 inference(unit_resolution,[status(thm)],[1539, 206, 1536])).
% 0.82/0.87 tff(1541,plain,
% 0.82/0.87 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.87 tff(1542,plain,
% 0.82/0.87 (((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1)) <=> ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))),
% 0.82/0.87 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1543,plain,
% 0.82/0.88 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14))))),
% 0.82/0.88 inference(monotonicity,[status(thm)],[1542])).
% 0.82/0.88 tff(1544,plain,
% 0.82/0.88 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))),
% 0.82/0.88 inference(transitivity,[status(thm)],[1543, 1541])).
% 0.82/0.88 tff(1545,plain,
% 0.82/0.88 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1546,plain,
% 0.82/0.88 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.82/0.88 tff(1547,plain,
% 0.82/0.88 ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1546, 892, 1540])).
% 0.82/0.88 tff(1548,plain,
% 0.82/0.88 (m_main_v_state1(s14, c_c1)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1547, 1529, 1453, 1521, 1514, 1461])).
% 0.82/0.88 tff(1549,plain,
% 0.82/0.88 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1550,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1551,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 0.82/0.88 tff(1552,plain,
% 0.82/0.88 (~m_main_v_state1(s14, c_t1)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1551, 539, 1548])).
% 0.82/0.88 tff(1553,plain,
% 0.82/0.88 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s14, c_t1) | (~node5(s14)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s14, c_t1) | (~node5(s14)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1554,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s14, c_t1) | (~node5(s14)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1555,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s14, c_t1) | (~node5(s14))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 0.82/0.88 tff(1556,plain,
% 0.82/0.88 (~node5(s14)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1555, 550, 1552])).
% 0.82/0.88 tff(1557,plain,
% 0.82/0.88 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s13, s14)) | node14(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s13, s14)) | node14(s13, s14))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1558,plain,
% 0.82/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s13, s14)) | node14(s13, s14))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1559,plain,
% 0.82/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s13, s14)) | node14(s13, s14)),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 0.82/0.88 tff(1560,plain,
% 0.82/0.88 (node14(s13, s14)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1559, 46, 1536])).
% 0.82/0.88 tff(1561,plain,
% 0.82/0.88 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1562,plain,
% 0.82/0.88 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1563,plain,
% 0.82/0.88 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2)),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 0.82/0.88 tff(1564,plain,
% 0.82/0.88 ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state2(s14, c_t2)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1563, 922, 1560])).
% 0.82/0.88 tff(1565,plain,
% 0.82/0.88 (m_main_v_state2(s14, c_t2)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1564, 1521, 1453])).
% 0.82/0.88 tff(1566,plain,
% 0.82/0.88 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1567,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1568,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 0.82/0.88 tff(1569,plain,
% 0.82/0.88 (~m_main_v_state2(s14, c_n2)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1568, 77, 1565])).
% 0.82/0.88 tff(1570,plain,
% 0.82/0.88 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s14, c_n2) | (~node4(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s14, c_n2) | (~node4(s14)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1571,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s14, c_n2) | (~node4(s14)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1572,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s14, c_n2) | (~node4(s14))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 0.82/0.88 tff(1573,plain,
% 0.82/0.88 (~node4(s14)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1572, 388, 1569])).
% 0.82/0.88 tff(1574,plain,
% 0.82/0.88 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1575,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1576,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 0.82/0.88 tff(1577,plain,
% 0.82/0.88 (~m_main_v_state2(s14, c_c2)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1576, 260, 1565])).
% 0.82/0.88 tff(1578,plain,
% 0.82/0.88 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s14, c_c2) | (~node3(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s14, c_c2) | (~node3(s14)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1579,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s14, c_c2) | (~node3(s14)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1580,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s14, c_c2) | (~node3(s14))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 0.82/0.88 tff(1581,plain,
% 0.82/0.88 (~node3(s14)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1580, 399, 1577])).
% 0.82/0.88 tff(1582,plain,
% 0.82/0.88 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s14, c_n2) | (~node2(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s14, c_n2) | (~node2(s14)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1583,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s14, c_n2) | (~node2(s14)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1584,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s14, c_n2) | (~node2(s14))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 0.82/0.88 tff(1585,plain,
% 0.82/0.88 (~node2(s14)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1584, 410, 1569])).
% 0.82/0.88 tff(1586,plain,
% 0.82/0.88 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1587,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1588,plain,
% 0.82/0.88 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 0.82/0.88 tff(1589,plain,
% 0.82/0.88 (~m_main_v_state1(s14, c_n1)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1588, 454, 1548])).
% 0.82/0.88 tff(1590,plain,
% 0.82/0.88 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s14, c_n1) | (~node1(s14)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s14, c_n1) | (~node1(s14)))),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1591,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s14, c_n1) | (~node1(s14)))),
% 0.82/0.88 inference(quant_inst,[status(thm)],[])).
% 0.82/0.88 tff(1592,plain,
% 0.82/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s14, c_n1) | (~node1(s14))),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 0.82/0.88 tff(1593,plain,
% 0.82/0.88 (~node1(s14)),
% 0.82/0.88 inference(unit_resolution,[status(thm)],[1592, 421, 1589])).
% 0.82/0.88 tff(1594,plain,
% 0.82/0.88 (succ(s14, s15) <=> succ(s14, s15)),
% 0.82/0.88 inference(rewrite,[status(thm)],[])).
% 0.82/0.88 tff(1595,axiom,(succ(s14, s15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound15')).
% 0.82/0.88 tff(1596,plain,
% 0.82/0.88 (succ(s14, s15)),
% 0.82/0.88 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 0.82/0.88 tff(1597,plain,
% 0.82/0.88 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1598,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1599,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.82/0.89 tff(1600,plain,
% 0.82/0.89 (trans(s14, s15)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1599, 1596, 32])).
% 0.82/0.89 tff(1601,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s14, s15)) | node7(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s14, s15)) | node7(s14, s15))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1602,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s14, s15)) | node7(s14, s15))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1603,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s14, s15)) | node7(s14, s15)),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 0.82/0.89 tff(1604,plain,
% 0.82/0.89 (node7(s14, s15)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1603, 206, 1600])).
% 0.82/0.89 tff(1605,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1606,plain,
% 0.82/0.89 (((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1)) <=> (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1607,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15))))),
% 0.82/0.89 inference(monotonicity,[status(thm)],[1606])).
% 0.82/0.89 tff(1608,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))),
% 0.82/0.89 inference(transitivity,[status(thm)],[1607, 1605])).
% 0.82/0.89 tff(1609,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1610,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15))),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 0.82/0.89 tff(1611,plain,
% 0.82/0.89 (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1610, 584, 1604])).
% 0.82/0.89 tff(1612,plain,
% 0.82/0.89 (m_main_v_state1(s15, c_n1)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1611, 1593, 1548, 1585, 1581, 1573, 1556])).
% 0.82/0.89 tff(1613,plain,
% 0.82/0.89 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s13, c_t2) | (~node15(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s13, c_t2) | (~node15(s13)))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1614,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s13, c_t2) | (~node15(s13)))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1615,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s13, c_t2) | (~node15(s13))),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 0.82/0.89 tff(1616,plain,
% 0.82/0.89 (~node15(s13)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1615, 103, 1525])).
% 0.82/0.89 tff(1617,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s13, s14)) | node18(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s13, s14)) | node18(s13, s14))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1618,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s13, s14)) | node18(s13, s14))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1619,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s13, s14)) | node18(s13, s14)),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 0.82/0.89 tff(1620,plain,
% 0.82/0.89 (node18(s13, s14)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1619, 125, 1536])).
% 0.82/0.89 tff(1621,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1622,plain,
% 0.82/0.89 (((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1)) <=> (node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1623,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1)))),
% 0.82/0.89 inference(monotonicity,[status(thm)],[1622])).
% 0.82/0.89 tff(1624,plain,
% 0.82/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))),
% 0.82/0.89 inference(transitivity,[status(thm)],[1623, 1621])).
% 0.82/0.89 tff(1625,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1626,plain,
% 0.82/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1)),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 0.82/0.89 tff(1627,plain,
% 0.82/0.89 (node15(s13) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1626, 992, 1620])).
% 0.82/0.89 tff(1628,plain,
% 0.82/0.89 (m_main_v_turn(s14, c_1)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1627, 1616, 1453, 1521])).
% 0.82/0.89 tff(1629,plain,
% 0.82/0.89 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2)))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1630,plain,
% 0.82/0.89 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2)))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1631,plain,
% 0.82/0.89 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2))),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 0.82/0.89 tff(1632,plain,
% 0.82/0.89 (~m_main_v_turn(s14, c_2)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1631, 156, 1628])).
% 0.82/0.89 tff(1633,plain,
% 0.82/0.89 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s14, c_2) | (~node12(s14)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s14, c_2) | (~node12(s14)))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1634,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s14, c_2) | (~node12(s14)))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1635,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s14, c_2) | (~node12(s14))),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 0.82/0.89 tff(1636,plain,
% 0.82/0.89 (~node12(s14)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1635, 184, 1632])).
% 0.82/0.89 tff(1637,plain,
% 0.82/0.89 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s14, c_n2) | (~node8(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s14, c_n2) | (~node8(s14)))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1638,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s14, c_n2) | (~node8(s14)))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1639,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s14, c_n2) | (~node8(s14))),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 0.82/0.89 tff(1640,plain,
% 0.82/0.89 (~node8(s14)),
% 0.82/0.89 inference(unit_resolution,[status(thm)],[1639, 271, 1569])).
% 0.82/0.89 tff(1641,plain,
% 0.82/0.89 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s14, c_n2) | (~node9(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s14, c_n2) | (~node9(s14)))),
% 0.82/0.89 inference(rewrite,[status(thm)],[])).
% 0.82/0.89 tff(1642,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s14, c_n2) | (~node9(s14)))),
% 0.82/0.89 inference(quant_inst,[status(thm)],[])).
% 0.82/0.89 tff(1643,plain,
% 0.82/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s14, c_n2) | (~node9(s14))),
% 0.82/0.89 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.82/0.89 tff(1644,plain,
% 0.82/0.89 (~node9(s14)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1643, 88, 1569])).
% 0.82/0.90 tff(1645,plain,
% 0.82/0.90 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s14, c_n2) | (~node10(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s14, c_n2) | (~node10(s14)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1646,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s14, c_n2) | (~node10(s14)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1647,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s14, c_n2) | (~node10(s14))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 0.82/0.90 tff(1648,plain,
% 0.82/0.90 (~node10(s14)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1647, 249, 1569])).
% 0.82/0.90 tff(1649,plain,
% 0.82/0.90 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s14, c_n1) | (~node11(s14)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s14, c_n1) | (~node11(s14)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1650,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s14, c_n1) | (~node11(s14)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1651,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s14, c_n1) | (~node11(s14))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.82/0.90 tff(1652,plain,
% 0.82/0.90 (~node11(s14)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1651, 238, 1589])).
% 0.82/0.90 tff(1653,plain,
% 0.82/0.90 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s14, s15)) | node14(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s14, s15)) | node14(s14, s15))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1654,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s14, s15)) | node14(s14, s15))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1655,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s14, s15)) | node14(s14, s15)),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 0.82/0.90 tff(1656,plain,
% 0.82/0.90 (node14(s14, s15)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1655, 46, 1600])).
% 0.82/0.90 tff(1657,plain,
% 0.82/0.90 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1658,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1659,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 0.82/0.90 tff(1660,plain,
% 0.82/0.90 (m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1659, 296, 1656])).
% 0.82/0.90 tff(1661,plain,
% 0.82/0.90 (node13(s14, s15)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1660, 1652, 1577, 1648, 1644, 1640, 1636])).
% 0.82/0.90 tff(1662,plain,
% 0.82/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1663,plain,
% 0.82/0.90 (((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2)) <=> ((~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1664,plain,
% 0.82/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15))))),
% 0.82/0.90 inference(monotonicity,[status(thm)],[1663])).
% 0.82/0.90 tff(1665,plain,
% 0.82/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))),
% 0.82/0.90 inference(transitivity,[status(thm)],[1664, 1662])).
% 0.82/0.90 tff(1666,plain,
% 0.82/0.90 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1667,plain,
% 0.82/0.90 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 0.82/0.90 tff(1668,plain,
% 0.82/0.90 (m_main_v_state2(s15, c_t2)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1667, 518, 1565, 1661])).
% 0.82/0.90 tff(1669,plain,
% 0.82/0.90 (succ(s15, s16) <=> succ(s15, s16)),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1670,axiom,(succ(s15, s16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound16')).
% 0.82/0.90 tff(1671,plain,
% 0.82/0.90 (succ(s15, s16)),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 0.82/0.90 tff(1672,plain,
% 0.82/0.90 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1673,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1674,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 0.82/0.90 tff(1675,plain,
% 0.82/0.90 (trans(s15, s16)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1674, 1671, 32])).
% 0.82/0.90 tff(1676,plain,
% 0.82/0.90 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s15, s16)) | node7(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s15, s16)) | node7(s15, s16))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1677,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s15, s16)) | node7(s15, s16))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1678,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s15, s16)) | node7(s15, s16)),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 0.82/0.90 tff(1679,plain,
% 0.82/0.90 (node7(s15, s16)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1678, 206, 1675])).
% 0.82/0.90 tff(1680,plain,
% 0.82/0.90 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1681,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1682,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1)),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 0.82/0.90 tff(1683,plain,
% 0.82/0.90 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | m_main_v_state1(s16, c_t1)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1682, 651, 1679])).
% 0.82/0.90 tff(1684,plain,
% 0.82/0.90 (m_main_v_state1(s16, c_t1)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1683, 1668, 1612])).
% 0.82/0.90 tff(1685,plain,
% 0.82/0.90 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1686,plain,
% 0.82/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1687,plain,
% 0.82/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 0.82/0.90 tff(1688,plain,
% 0.82/0.90 (~m_main_v_state1(s16, c_n1)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1687, 10, 1684])).
% 0.82/0.90 tff(1689,plain,
% 0.82/0.90 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s16, c_n1) | (~node1(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s16, c_n1) | (~node1(s16)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1690,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s16, c_n1) | (~node1(s16)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1691,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s16, c_n1) | (~node1(s16))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 0.82/0.90 tff(1692,plain,
% 0.82/0.90 (~node1(s16)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1691, 421, 1688])).
% 0.82/0.90 tff(1693,plain,
% 0.82/0.90 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s15, s16)) | node18(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s15, s16)) | node18(s15, s16))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1694,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s15, s16)) | node18(s15, s16))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1695,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s15, s16)) | node18(s15, s16)),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 0.82/0.90 tff(1696,plain,
% 0.82/0.90 (node18(s15, s16)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1695, 125, 1675])).
% 0.82/0.90 tff(1697,plain,
% 0.82/0.90 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1698,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1699,plain,
% 0.82/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2)),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.82/0.90 tff(1700,plain,
% 0.82/0.90 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | m_main_v_turn(s16, c_2)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1699, 760, 1696])).
% 0.82/0.90 tff(1701,plain,
% 0.82/0.90 (m_main_v_turn(s16, c_2)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1700, 1668, 1612])).
% 0.82/0.90 tff(1702,plain,
% 0.82/0.90 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1703,plain,
% 0.82/0.90 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1704,plain,
% 0.82/0.90 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 0.82/0.90 tff(1705,plain,
% 0.82/0.90 (~m_main_v_turn(s16, c_1)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1704, 156, 1701])).
% 0.82/0.90 tff(1706,plain,
% 0.82/0.90 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s16, c_1) | (~node5(s16)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s16, c_1) | (~node5(s16)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1707,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s16, c_1) | (~node5(s16)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1708,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s16, c_1) | (~node5(s16))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 0.82/0.90 tff(1709,plain,
% 0.82/0.90 (~node5(s16)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1708, 776, 1705])).
% 0.82/0.90 tff(1710,plain,
% 0.82/0.90 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s16, c_n1) | (~node2(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s16, c_n1) | (~node2(s16)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1711,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s16, c_n1) | (~node2(s16)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1712,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s16, c_n1) | (~node2(s16))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 0.82/0.90 tff(1713,plain,
% 0.82/0.90 (~node2(s16)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1712, 787, 1688])).
% 0.82/0.90 tff(1714,plain,
% 0.82/0.90 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s16, c_n1) | (~node3(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s16, c_n1) | (~node3(s16)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1715,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s16, c_n1) | (~node3(s16)))),
% 0.82/0.90 inference(quant_inst,[status(thm)],[])).
% 0.82/0.90 tff(1716,plain,
% 0.82/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s16, c_n1) | (~node3(s16))),
% 0.82/0.90 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 0.82/0.90 tff(1717,plain,
% 0.82/0.90 (~node3(s16)),
% 0.82/0.90 inference(unit_resolution,[status(thm)],[1716, 798, 1688])).
% 0.82/0.90 tff(1718,plain,
% 0.82/0.90 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1)))),
% 0.82/0.90 inference(rewrite,[status(thm)],[])).
% 0.82/0.90 tff(1719,plain,
% 0.82/0.91 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1720,plain,
% 0.82/0.91 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 0.82/0.91 tff(1721,plain,
% 0.82/0.91 (~m_main_v_state1(s16, c_c1)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1720, 539, 1684])).
% 0.82/0.91 tff(1722,plain,
% 0.82/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1723,plain,
% 0.82/0.91 (((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2))) <=> (m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1724,plain,
% 0.82/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15))))),
% 0.82/0.91 inference(monotonicity,[status(thm)],[1723])).
% 0.82/0.91 tff(1725,plain,
% 0.82/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))),
% 0.82/0.91 inference(transitivity,[status(thm)],[1724, 1722])).
% 0.82/0.91 tff(1726,plain,
% 0.82/0.91 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1727,plain,
% 0.82/0.91 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 0.82/0.91 tff(1728,plain,
% 0.82/0.91 (~m_main_v_state2(s15, c_n2)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1727, 311, 1569, 1661])).
% 0.82/0.91 tff(1729,plain,
% 0.82/0.91 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s15, c_n2) | (~node9(s15)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s15, c_n2) | (~node9(s15)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1730,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s15, c_n2) | (~node9(s15)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1731,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s15, c_n2) | (~node9(s15))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 0.82/0.91 tff(1732,plain,
% 0.82/0.91 (~node9(s15)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1731, 88, 1728])).
% 0.82/0.91 tff(1733,plain,
% 0.82/0.91 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s15, c_n2) | (~node10(s15)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s15, c_n2) | (~node10(s15)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1734,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s15, c_n2) | (~node10(s15)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1735,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s15, c_n2) | (~node10(s15))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 0.82/0.91 tff(1736,plain,
% 0.82/0.91 (~node10(s15)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1735, 249, 1728])).
% 0.82/0.91 tff(1737,plain,
% 0.82/0.91 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s15, c_n2) | (~node8(s15)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s15, c_n2) | (~node8(s15)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1738,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s15, c_n2) | (~node8(s15)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1739,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s15, c_n2) | (~node8(s15))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 0.82/0.91 tff(1740,plain,
% 0.82/0.91 (~node8(s15)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1739, 271, 1728])).
% 0.82/0.91 tff(1741,plain,
% 0.82/0.91 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s15, s16)) | node14(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s15, s16)) | node14(s15, s16))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1742,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s15, s16)) | node14(s15, s16))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1743,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s15, s16)) | node14(s15, s16)),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 0.82/0.91 tff(1744,plain,
% 0.82/0.91 (node14(s15, s16)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1743, 46, 1675])).
% 0.82/0.91 tff(1745,plain,
% 0.82/0.91 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1746,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1747,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2)),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 0.82/0.91 tff(1748,plain,
% 0.82/0.91 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | m_main_v_state2(s16, c_c2)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1747, 617, 1744])).
% 0.82/0.91 tff(1749,plain,
% 0.82/0.91 (m_main_v_state2(s16, c_c2)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1748, 1740, 1612, 1668, 1736, 1732])).
% 0.82/0.91 tff(1750,plain,
% 0.82/0.91 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1751,plain,
% 0.82/0.91 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1752,plain,
% 0.82/0.91 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 0.82/0.91 tff(1753,plain,
% 0.82/0.91 (~m_main_v_state2(s16, c_n2)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1752, 697, 1749])).
% 0.82/0.91 tff(1754,plain,
% 0.82/0.91 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s16, c_n2) | (~node4(s16)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s16, c_n2) | (~node4(s16)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1755,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s16, c_n2) | (~node4(s16)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1756,plain,
% 0.82/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s16, c_n2) | (~node4(s16))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 0.82/0.91 tff(1757,plain,
% 0.82/0.91 (~node4(s16)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1756, 388, 1753])).
% 0.82/0.91 tff(1758,plain,
% 0.82/0.91 (succ(s16, s17) <=> succ(s16, s17)),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1759,axiom,(succ(s16, s17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound17')).
% 0.82/0.91 tff(1760,plain,
% 0.82/0.91 (succ(s16, s17)),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 0.82/0.91 tff(1761,plain,
% 0.82/0.91 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1762,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1763,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 0.82/0.91 tff(1764,plain,
% 0.82/0.91 (trans(s16, s17)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1763, 1760, 32])).
% 0.82/0.91 tff(1765,plain,
% 0.82/0.91 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s16, s17)) | node7(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s16, s17)) | node7(s16, s17))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1766,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s16, s17)) | node7(s16, s17))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1767,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s16, s17)) | node7(s16, s17)),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 0.82/0.91 tff(1768,plain,
% 0.82/0.91 (node7(s16, s17)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1767, 206, 1764])).
% 0.82/0.91 tff(1769,plain,
% 0.82/0.91 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17)))),
% 0.82/0.91 inference(rewrite,[status(thm)],[])).
% 0.82/0.91 tff(1770,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17)))),
% 0.82/0.91 inference(quant_inst,[status(thm)],[])).
% 0.82/0.91 tff(1771,plain,
% 0.82/0.91 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17))),
% 0.82/0.91 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 0.82/0.91 tff(1772,plain,
% 0.82/0.91 (m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1771, 820, 1768])).
% 0.82/0.91 tff(1773,plain,
% 0.82/0.91 (node6(s16, s17)),
% 0.82/0.91 inference(unit_resolution,[status(thm)],[1772, 1757, 1721, 1717, 1713, 1709, 1692])).
% 0.82/0.92 tff(1774,plain,
% 0.82/0.92 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1775,plain,
% 0.82/0.92 (((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1)) <=> ((~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1776,plain,
% 0.82/0.92 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17))))),
% 0.82/0.92 inference(monotonicity,[status(thm)],[1775])).
% 0.82/0.92 tff(1777,plain,
% 0.82/0.92 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))),
% 0.82/0.92 inference(transitivity,[status(thm)],[1776, 1774])).
% 0.82/0.92 tff(1778,plain,
% 0.82/0.92 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1779,plain,
% 0.82/0.92 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 0.82/0.92 tff(1780,plain,
% 0.82/0.92 (m_main_v_state1(s17, c_t1)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1779, 856, 1684, 1773])).
% 0.82/0.92 tff(1781,plain,
% 0.82/0.92 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1782,plain,
% 0.82/0.92 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1783,plain,
% 0.82/0.92 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 0.82/0.92 tff(1784,plain,
% 0.82/0.92 (~m_main_v_state2(s16, c_t2)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1783, 260, 1749])).
% 0.82/0.92 tff(1785,plain,
% 0.82/0.92 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s16, c_t2) | (~node12(s16)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s16, c_t2) | (~node12(s16)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1786,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s16, c_t2) | (~node12(s16)))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1787,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s16, c_t2) | (~node12(s16))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 0.82/0.92 tff(1788,plain,
% 0.82/0.92 (~node12(s16)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1787, 633, 1784])).
% 0.82/0.92 tff(1789,plain,
% 0.82/0.92 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s16, c_n1) | (~node11(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s16, c_n1) | (~node11(s16)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1790,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s16, c_n1) | (~node11(s16)))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1791,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s16, c_n1) | (~node11(s16))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 0.82/0.92 tff(1792,plain,
% 0.82/0.92 (~node11(s16)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1791, 238, 1688])).
% 0.82/0.92 tff(1793,plain,
% 0.82/0.92 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s16, c_c1) | (~node10(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s16, c_c1) | (~node10(s16)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1794,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s16, c_c1) | (~node10(s16)))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1795,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s16, c_c1) | (~node10(s16))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 0.82/0.92 tff(1796,plain,
% 0.82/0.92 (~node10(s16)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1795, 675, 1721])).
% 0.82/0.92 tff(1797,plain,
% 0.82/0.92 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s16, c_n1) | (~node9(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s16, c_n1) | (~node9(s16)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1798,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s16, c_n1) | (~node9(s16)))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1799,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s16, c_n1) | (~node9(s16))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 0.82/0.92 tff(1800,plain,
% 0.82/0.92 (~node9(s16)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1799, 686, 1688])).
% 0.82/0.92 tff(1801,plain,
% 0.82/0.92 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s16, c_n2) | (~node8(s16)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s16, c_n2) | (~node8(s16)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1802,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s16, c_n2) | (~node8(s16)))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1803,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s16, c_n2) | (~node8(s16))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 0.82/0.92 tff(1804,plain,
% 0.82/0.92 (~node8(s16)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1803, 271, 1753])).
% 0.82/0.92 tff(1805,plain,
% 0.82/0.92 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s16, s17)) | node14(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s16, s17)) | node14(s16, s17))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1806,plain,
% 0.82/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s16, s17)) | node14(s16, s17))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1807,plain,
% 0.82/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s16, s17)) | node14(s16, s17)),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.82/0.92 tff(1808,plain,
% 0.82/0.92 (node14(s16, s17)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1807, 46, 1764])).
% 0.82/0.92 tff(1809,plain,
% 0.82/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1810,plain,
% 0.82/0.92 (((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2)) <=> (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1811,plain,
% 0.82/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2))))),
% 0.82/0.92 inference(monotonicity,[status(thm)],[1810])).
% 0.82/0.92 tff(1812,plain,
% 0.82/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))),
% 0.82/0.92 inference(transitivity,[status(thm)],[1811, 1809])).
% 0.82/0.92 tff(1813,plain,
% 0.82/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1814,plain,
% 0.82/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 0.82/0.92 tff(1815,plain,
% 0.82/0.92 (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~m_main_v_state2(s16, c_c2))),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1814, 726, 1808])).
% 0.82/0.92 tff(1816,plain,
% 0.82/0.92 (m_main_v_state2(s17, c_n2)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1815, 1804, 1749, 1800, 1796, 1792, 1788])).
% 0.82/0.92 tff(1817,plain,
% 0.82/0.92 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1818,plain,
% 0.82/0.92 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2)))),
% 0.82/0.92 inference(quant_inst,[status(thm)],[])).
% 0.82/0.92 tff(1819,plain,
% 0.82/0.92 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2))),
% 0.82/0.92 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 0.82/0.92 tff(1820,plain,
% 0.82/0.92 (~m_main_v_state2(s17, c_t2)),
% 0.82/0.92 inference(unit_resolution,[status(thm)],[1819, 77, 1816])).
% 0.82/0.92 tff(1821,plain,
% 0.82/0.92 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s17, c_t2) | (~node15(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s17, c_t2) | (~node15(s17)))),
% 0.82/0.92 inference(rewrite,[status(thm)],[])).
% 0.82/0.92 tff(1822,plain,
% 0.82/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s17, c_t2) | (~node15(s17)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1823,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s17, c_t2) | (~node15(s17))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 0.91/0.93 tff(1824,plain,
% 0.91/0.93 (~node15(s17)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1823, 103, 1820])).
% 0.91/0.93 tff(1825,plain,
% 0.91/0.93 (succ(s17, s18) <=> succ(s17, s18)),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1826,axiom,(succ(s17, s18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound18')).
% 0.91/0.93 tff(1827,plain,
% 0.91/0.93 (succ(s17, s18)),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 0.91/0.93 tff(1828,plain,
% 0.91/0.93 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1829,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1830,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 0.91/0.93 tff(1831,plain,
% 0.91/0.93 (trans(s17, s18)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1830, 1827, 32])).
% 0.91/0.93 tff(1832,plain,
% 0.91/0.93 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s17, s18)) | node18(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s17, s18)) | node18(s17, s18))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1833,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s17, s18)) | node18(s17, s18))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1834,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s17, s18)) | node18(s17, s18)),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 0.91/0.93 tff(1835,plain,
% 0.91/0.93 (node18(s17, s18)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1834, 125, 1831])).
% 0.91/0.93 tff(1836,plain,
% 0.91/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1837,plain,
% 0.91/0.93 (((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1)) <=> (node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1838,plain,
% 0.91/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1)))),
% 0.91/0.93 inference(monotonicity,[status(thm)],[1837])).
% 0.91/0.93 tff(1839,plain,
% 0.91/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))),
% 0.91/0.93 inference(transitivity,[status(thm)],[1838, 1836])).
% 0.91/0.93 tff(1840,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1841,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1)),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 0.91/0.93 tff(1842,plain,
% 0.91/0.93 (node15(s17) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1841, 992, 1835])).
% 0.91/0.93 tff(1843,plain,
% 0.91/0.93 (m_main_v_turn(s18, c_1)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1842, 1824, 1816, 1780])).
% 0.91/0.93 tff(1844,plain,
% 0.91/0.93 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1845,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1846,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 0.91/0.93 tff(1847,plain,
% 0.91/0.93 (~m_main_v_turn(s18, c_2)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1846, 156, 1843])).
% 0.91/0.93 tff(1848,plain,
% 0.91/0.93 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s18, c_2) | (~node12(s18)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s18, c_2) | (~node12(s18)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1849,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s18, c_2) | (~node12(s18)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1850,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s18, c_2) | (~node12(s18))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 0.91/0.93 tff(1851,plain,
% 0.91/0.93 (~node12(s18)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1850, 184, 1847])).
% 0.91/0.93 tff(1852,plain,
% 0.91/0.93 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s17, s18)) | node14(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s17, s18)) | node14(s17, s18))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1853,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s17, s18)) | node14(s17, s18))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1854,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s17, s18)) | node14(s17, s18)),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 0.91/0.93 tff(1855,plain,
% 0.91/0.93 (node14(s17, s18)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1854, 46, 1831])).
% 0.91/0.93 tff(1856,plain,
% 0.91/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1857,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1858,plain,
% 0.91/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2)),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 0.91/0.93 tff(1859,plain,
% 0.91/0.93 ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state2(s18, c_t2)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1858, 922, 1855])).
% 0.91/0.93 tff(1860,plain,
% 0.91/0.93 (m_main_v_state2(s18, c_t2)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1859, 1780, 1816])).
% 0.91/0.93 tff(1861,plain,
% 0.91/0.93 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1862,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1863,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 0.91/0.93 tff(1864,plain,
% 0.91/0.93 (~m_main_v_state2(s18, c_n2)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1863, 77, 1860])).
% 0.91/0.93 tff(1865,plain,
% 0.91/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s18, c_n2) | (~node8(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s18, c_n2) | (~node8(s18)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1866,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s18, c_n2) | (~node8(s18)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1867,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s18, c_n2) | (~node8(s18))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 0.91/0.93 tff(1868,plain,
% 0.91/0.93 (~node8(s18)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1867, 271, 1864])).
% 0.91/0.93 tff(1869,plain,
% 0.91/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s18, c_n2) | (~node9(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s18, c_n2) | (~node9(s18)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1870,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s18, c_n2) | (~node9(s18)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1871,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s18, c_n2) | (~node9(s18))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 0.91/0.93 tff(1872,plain,
% 0.91/0.93 (~node9(s18)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1871, 88, 1864])).
% 0.91/0.93 tff(1873,plain,
% 0.91/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s18, c_n2) | (~node10(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s18, c_n2) | (~node10(s18)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1874,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s18, c_n2) | (~node10(s18)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1875,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s18, c_n2) | (~node10(s18))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 0.91/0.93 tff(1876,plain,
% 0.91/0.93 (~node10(s18)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1875, 249, 1864])).
% 0.91/0.93 tff(1877,plain,
% 0.91/0.93 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1878,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1879,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 0.91/0.93 tff(1880,plain,
% 0.91/0.93 (~m_main_v_state2(s18, c_c2)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1879, 260, 1860])).
% 0.91/0.93 tff(1881,plain,
% 0.91/0.93 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1882,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1883,plain,
% 0.91/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 0.91/0.93 tff(1884,plain,
% 0.91/0.93 (~m_main_v_state2(s17, c_c2)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1883, 697, 1816])).
% 0.91/0.93 tff(1885,plain,
% 0.91/0.93 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s17, c_c2) | (~node3(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s17, c_c2) | (~node3(s17)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1886,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s17, c_c2) | (~node3(s17)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1887,plain,
% 0.91/0.93 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s17, c_c2) | (~node3(s17))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 0.91/0.93 tff(1888,plain,
% 0.91/0.93 (~node3(s17)),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[1887, 399, 1884])).
% 0.91/0.93 tff(1889,plain,
% 0.91/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1890,plain,
% 0.91/0.93 (((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1))) <=> (m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(1891,plain,
% 0.91/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17))))),
% 0.91/0.93 inference(monotonicity,[status(thm)],[1890])).
% 0.91/0.93 tff(1892,plain,
% 0.91/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))),
% 0.91/0.93 inference(transitivity,[status(thm)],[1891, 1889])).
% 0.91/0.93 tff(1893,plain,
% 0.91/0.93 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(1894,plain,
% 0.91/0.93 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 0.91/0.94 tff(1895,plain,
% 0.91/0.94 (~m_main_v_state1(s17, c_n1)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1894, 835, 1688, 1773])).
% 0.91/0.94 tff(1896,plain,
% 0.91/0.94 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s17, c_n1) | (~node2(s17)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s17, c_n1) | (~node2(s17)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1897,plain,
% 0.91/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s17, c_n1) | (~node2(s17)))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1898,plain,
% 0.91/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s17, c_n1) | (~node2(s17))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 0.91/0.94 tff(1899,plain,
% 0.91/0.94 (~node2(s17)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1898, 787, 1895])).
% 0.91/0.94 tff(1900,plain,
% 0.91/0.94 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s17, c_t2) | (~node1(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s17, c_t2) | (~node1(s17)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1901,plain,
% 0.91/0.94 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s17, c_t2) | (~node1(s17)))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1902,plain,
% 0.91/0.94 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s17, c_t2) | (~node1(s17))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 0.91/0.94 tff(1903,plain,
% 0.91/0.94 (~node1(s17)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1902, 195, 1820])).
% 0.91/0.94 tff(1904,plain,
% 0.91/0.94 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s17, s18)) | node7(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s17, s18)) | node7(s17, s18))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1905,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s17, s18)) | node7(s17, s18))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1906,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s17, s18)) | node7(s17, s18)),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 0.91/0.94 tff(1907,plain,
% 0.91/0.94 (node7(s17, s18)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1906, 206, 1831])).
% 0.91/0.94 tff(1908,plain,
% 0.91/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1909,plain,
% 0.91/0.94 (((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1)) <=> ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1910,plain,
% 0.91/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18))))),
% 0.91/0.94 inference(monotonicity,[status(thm)],[1909])).
% 0.91/0.94 tff(1911,plain,
% 0.91/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))),
% 0.91/0.94 inference(transitivity,[status(thm)],[1910, 1908])).
% 0.91/0.94 tff(1912,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1913,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 0.91/0.94 tff(1914,plain,
% 0.91/0.94 ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1913, 892, 1907])).
% 0.91/0.94 tff(1915,plain,
% 0.91/0.94 (m_main_v_state1(s18, c_c1)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1914, 1903, 1816, 1780, 1899, 1888])).
% 0.91/0.94 tff(1916,plain,
% 0.91/0.94 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1917,plain,
% 0.91/0.94 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1918,plain,
% 0.91/0.94 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 0.91/0.94 tff(1919,plain,
% 0.91/0.94 (~m_main_v_state1(s18, c_n1)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1918, 454, 1915])).
% 0.91/0.94 tff(1920,plain,
% 0.91/0.94 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s18, c_n1) | (~node11(s18)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s18, c_n1) | (~node11(s18)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1921,plain,
% 0.91/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s18, c_n1) | (~node11(s18)))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1922,plain,
% 0.91/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s18, c_n1) | (~node11(s18))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 0.91/0.94 tff(1923,plain,
% 0.91/0.94 (~node11(s18)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1922, 238, 1919])).
% 0.91/0.94 tff(1924,plain,
% 0.91/0.94 (succ(s18, s19) <=> succ(s18, s19)),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1925,axiom,(succ(s18, s19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound19')).
% 0.91/0.94 tff(1926,plain,
% 0.91/0.94 (succ(s18, s19)),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 0.91/0.94 tff(1927,plain,
% 0.91/0.94 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1928,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1929,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 0.91/0.94 tff(1930,plain,
% 0.91/0.94 (trans(s18, s19)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1929, 1926, 32])).
% 0.91/0.94 tff(1931,plain,
% 0.91/0.94 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s18, s19)) | node14(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s18, s19)) | node14(s18, s19))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1932,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s18, s19)) | node14(s18, s19))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1933,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s18, s19)) | node14(s18, s19)),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 0.91/0.94 tff(1934,plain,
% 0.91/0.94 (node14(s18, s19)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1933, 46, 1930])).
% 0.91/0.94 tff(1935,plain,
% 0.91/0.94 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1936,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19)))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(1937,plain,
% 0.91/0.94 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 0.91/0.94 tff(1938,plain,
% 0.91/0.94 (m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1937, 296, 1934])).
% 0.91/0.94 tff(1939,plain,
% 0.91/0.94 (node13(s18, s19)),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[1938, 1923, 1880, 1876, 1872, 1868, 1851])).
% 0.91/0.94 tff(1940,plain,
% 0.91/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1941,plain,
% 0.91/0.94 (((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2))) <=> (m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(1942,plain,
% 0.91/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19))))),
% 0.91/0.94 inference(monotonicity,[status(thm)],[1941])).
% 0.91/0.94 tff(1943,plain,
% 0.91/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))),
% 0.91/0.95 inference(transitivity,[status(thm)],[1942, 1940])).
% 0.91/0.95 tff(1944,plain,
% 0.91/0.95 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1945,plain,
% 0.91/0.95 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 0.91/0.95 tff(1946,plain,
% 0.91/0.95 (~m_main_v_state2(s19, c_n2)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1945, 311, 1864, 1939])).
% 0.91/0.95 tff(1947,plain,
% 0.91/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s19, c_n2) | (~node9(s19)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s19, c_n2) | (~node9(s19)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1948,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s19, c_n2) | (~node9(s19)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1949,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s19, c_n2) | (~node9(s19))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 0.91/0.95 tff(1950,plain,
% 0.91/0.95 (~node9(s19)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1949, 88, 1946])).
% 0.91/0.95 tff(1951,plain,
% 0.91/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s19, c_n2) | (~node10(s19)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s19, c_n2) | (~node10(s19)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1952,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s19, c_n2) | (~node10(s19)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1953,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s19, c_n2) | (~node10(s19))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 0.91/0.95 tff(1954,plain,
% 0.91/0.95 (~node10(s19)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1953, 249, 1946])).
% 0.91/0.95 tff(1955,plain,
% 0.91/0.95 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1956,plain,
% 0.91/0.95 (((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2)) <=> ((~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1957,plain,
% 0.91/0.95 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19))))),
% 0.91/0.95 inference(monotonicity,[status(thm)],[1956])).
% 0.91/0.95 tff(1958,plain,
% 0.91/0.95 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))),
% 0.91/0.95 inference(transitivity,[status(thm)],[1957, 1955])).
% 0.91/0.95 tff(1959,plain,
% 0.91/0.95 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1960,plain,
% 0.91/0.95 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 0.91/0.95 tff(1961,plain,
% 0.91/0.95 (m_main_v_state2(s19, c_t2)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1960, 518, 1860, 1939])).
% 0.91/0.95 tff(1962,plain,
% 0.91/0.95 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1963,plain,
% 0.91/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1964,plain,
% 0.91/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 0.91/0.95 tff(1965,plain,
% 0.91/0.95 (~m_main_v_state1(s18, c_t1)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1964, 539, 1915])).
% 0.91/0.95 tff(1966,plain,
% 0.91/0.95 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s18, c_t1) | (~node5(s18)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s18, c_t1) | (~node5(s18)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1967,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s18, c_t1) | (~node5(s18)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1968,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s18, c_t1) | (~node5(s18))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 0.91/0.95 tff(1969,plain,
% 0.91/0.95 (~node5(s18)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1968, 550, 1965])).
% 0.91/0.95 tff(1970,plain,
% 0.91/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s18, c_n2) | (~node4(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s18, c_n2) | (~node4(s18)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1971,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s18, c_n2) | (~node4(s18)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1972,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s18, c_n2) | (~node4(s18))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1971, 1970])).
% 0.91/0.95 tff(1973,plain,
% 0.91/0.95 (~node4(s18)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1972, 388, 1864])).
% 0.91/0.95 tff(1974,plain,
% 0.91/0.95 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s18, c_c2) | (~node3(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s18, c_c2) | (~node3(s18)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1975,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s18, c_c2) | (~node3(s18)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1976,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s18, c_c2) | (~node3(s18))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 0.91/0.95 tff(1977,plain,
% 0.91/0.95 (~node3(s18)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1976, 399, 1880])).
% 0.91/0.95 tff(1978,plain,
% 0.91/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s18, c_n2) | (~node2(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s18, c_n2) | (~node2(s18)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1979,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s18, c_n2) | (~node2(s18)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1980,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s18, c_n2) | (~node2(s18))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 0.91/0.95 tff(1981,plain,
% 0.91/0.95 (~node2(s18)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1980, 410, 1864])).
% 0.91/0.95 tff(1982,plain,
% 0.91/0.95 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s18, c_n1) | (~node1(s18)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s18, c_n1) | (~node1(s18)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1983,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s18, c_n1) | (~node1(s18)))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1984,plain,
% 0.91/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s18, c_n1) | (~node1(s18))),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 0.91/0.95 tff(1985,plain,
% 0.91/0.95 (~node1(s18)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1984, 421, 1919])).
% 0.91/0.95 tff(1986,plain,
% 0.91/0.95 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s18, s19)) | node7(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s18, s19)) | node7(s18, s19))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1987,plain,
% 0.91/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s18, s19)) | node7(s18, s19))),
% 0.91/0.95 inference(quant_inst,[status(thm)],[])).
% 0.91/0.95 tff(1988,plain,
% 0.91/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s18, s19)) | node7(s18, s19)),
% 0.91/0.95 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 0.91/0.95 tff(1989,plain,
% 0.91/0.95 (node7(s18, s19)),
% 0.91/0.95 inference(unit_resolution,[status(thm)],[1988, 206, 1930])).
% 0.91/0.95 tff(1990,plain,
% 0.91/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1991,plain,
% 0.91/0.95 (((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1)) <=> (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))),
% 0.91/0.95 inference(rewrite,[status(thm)],[])).
% 0.91/0.95 tff(1992,plain,
% 0.91/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19))))),
% 0.91/0.95 inference(monotonicity,[status(thm)],[1991])).
% 0.91/0.95 tff(1993,plain,
% 0.91/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))),
% 0.91/0.95 inference(transitivity,[status(thm)],[1992, 1990])).
% 0.91/0.95 tff(1994,plain,
% 0.91/0.95 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(1995,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 0.91/0.96 tff(1996,plain,
% 0.91/0.96 (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[1995, 584, 1989])).
% 0.91/0.96 tff(1997,plain,
% 0.91/0.96 (m_main_v_state1(s19, c_n1)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[1996, 1985, 1915, 1981, 1977, 1973, 1969])).
% 0.91/0.96 tff(1998,plain,
% 0.91/0.96 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s19, c_n2) | (~node8(s19)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s19, c_n2) | (~node8(s19)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(1999,plain,
% 0.91/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s19, c_n2) | (~node8(s19)))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2000,plain,
% 0.91/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s19, c_n2) | (~node8(s19))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 0.91/0.96 tff(2001,plain,
% 0.91/0.96 (~node8(s19)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2000, 271, 1946])).
% 0.91/0.96 tff(2002,plain,
% 0.91/0.96 (succ(s19, s20) <=> succ(s19, s20)),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2003,axiom,(succ(s19, s20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound20')).
% 0.91/0.96 tff(2004,plain,
% 0.91/0.96 (succ(s19, s20)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 0.91/0.96 tff(2005,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2006,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2007,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 0.91/0.96 tff(2008,plain,
% 0.91/0.96 (trans(s19, s20)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2007, 2004, 32])).
% 0.91/0.96 tff(2009,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s19, s20)) | node14(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s19, s20)) | node14(s19, s20))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2010,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s19, s20)) | node14(s19, s20))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2011,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s19, s20)) | node14(s19, s20)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 0.91/0.96 tff(2012,plain,
% 0.91/0.96 (node14(s19, s20)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2011, 46, 2008])).
% 0.91/0.96 tff(2013,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2014,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2015,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 0.91/0.96 tff(2016,plain,
% 0.91/0.96 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | m_main_v_state2(s20, c_c2)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2015, 617, 2012])).
% 0.91/0.96 tff(2017,plain,
% 0.91/0.96 (m_main_v_state2(s20, c_c2)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2016, 2001, 1997, 1961, 1954, 1950])).
% 0.91/0.96 tff(2018,plain,
% 0.91/0.96 (^[X: $i] : refl(((~m_main_v_state2(X, c_c2)) | (~always25(X))) <=> ((~m_main_v_state2(X, c_c2)) | (~always25(X))))),
% 0.91/0.96 inference(bind,[status(th)],[])).
% 0.91/0.96 tff(2019,plain,
% 0.91/0.96 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X))) <=> ![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/0.96 inference(quant_intro,[status(thm)],[2018])).
% 0.91/0.96 tff(2020,plain,
% 0.91/0.96 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X))) <=> ![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2021,axiom,(![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty14')).
% 0.91/0.96 tff(2022,plain,
% 0.91/0.96 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 0.91/0.96 tff(2023,plain,(
% 0.91/0.96 ![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/0.96 inference(skolemize,[status(sab)],[2022])).
% 0.91/0.96 tff(2024,plain,
% 0.91/0.96 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2023, 2019])).
% 0.91/0.96 tff(2025,plain,
% 0.91/0.96 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s20)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s20)) | (~m_main_v_state2(s20, c_c2)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2026,plain,
% 0.91/0.96 (((~m_main_v_state2(s20, c_c2)) | (~always25(s20))) <=> ((~always25(s20)) | (~m_main_v_state2(s20, c_c2)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2027,plain,
% 0.91/0.96 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s20, c_c2)) | (~always25(s20)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s20)) | (~m_main_v_state2(s20, c_c2))))),
% 0.91/0.96 inference(monotonicity,[status(thm)],[2026])).
% 0.91/0.96 tff(2028,plain,
% 0.91/0.96 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s20, c_c2)) | (~always25(s20)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s20)) | (~m_main_v_state2(s20, c_c2)))),
% 0.91/0.96 inference(transitivity,[status(thm)],[2027, 2025])).
% 0.91/0.96 tff(2029,plain,
% 0.91/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s20, c_c2)) | (~always25(s20)))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2030,plain,
% 0.91/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s20)) | (~m_main_v_state2(s20, c_c2))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 0.91/0.96 tff(2031,plain,
% 0.91/0.96 (~always25(s20)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2030, 2024, 2017])).
% 0.91/0.96 tff(2032,plain,
% 0.91/0.96 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | (~always25(X)) | always25(Y)) <=> ((~trans(X, Y)) | (~always25(X)) | always25(Y)))),
% 0.91/0.96 inference(bind,[status(th)],[])).
% 0.91/0.96 tff(2033,plain,
% 0.91/0.96 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/0.96 inference(quant_intro,[status(thm)],[2032])).
% 0.91/0.96 tff(2034,plain,
% 0.91/0.96 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2035,plain,
% 0.91/0.96 (^[Y: $i, X: $i] : rewrite(((always25(Y) | (~trans(X, Y))) | (~always25(X))) <=> ((~trans(X, Y)) | (~always25(X)) | always25(Y)))),
% 0.91/0.96 inference(bind,[status(th)],[])).
% 0.91/0.96 tff(2036,plain,
% 0.91/0.96 (![Y: $i, X: $i] : ((always25(Y) | (~trans(X, Y))) | (~always25(X))) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/0.96 inference(quant_intro,[status(thm)],[2035])).
% 0.91/0.96 tff(2037,axiom,(![Y: $i, X: $i] : ((always25(Y) | (~trans(X, Y))) | (~always25(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty15')).
% 0.91/0.96 tff(2038,plain,
% 0.91/0.96 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 0.91/0.96 tff(2039,plain,
% 0.91/0.96 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2038, 2034])).
% 0.91/0.96 tff(2040,plain,(
% 0.91/0.96 ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/0.96 inference(skolemize,[status(sab)],[2039])).
% 0.91/0.96 tff(2041,plain,
% 0.91/0.96 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2040, 2033])).
% 0.91/0.96 tff(2042,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s19, s20)) | (~always25(s19)) | always25(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s19, s20)) | (~always25(s19)) | always25(s20))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2043,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s19, s20)) | (~always25(s19)) | always25(s20))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2044,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s19, s20)) | (~always25(s19)) | always25(s20)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 0.91/0.96 tff(2045,plain,
% 0.91/0.96 ((~always25(s19)) | always25(s20)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2044, 2041, 2008])).
% 0.91/0.96 tff(2046,plain,
% 0.91/0.96 (~always25(s19)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2045, 2031])).
% 0.91/0.96 tff(2047,assumption,(~always25(s59)), introduced(assumption)).
% 0.91/0.96 tff(2048,plain,
% 0.91/0.96 (succ(s58, s59) <=> succ(s58, s59)),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2049,axiom,(succ(s58, s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound59')).
% 0.91/0.96 tff(2050,plain,
% 0.91/0.96 (succ(s58, s59)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 0.91/0.96 tff(2051,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2052,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2053,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 0.91/0.96 tff(2054,plain,
% 0.91/0.96 (trans(s58, s59)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2053, 2050, 32])).
% 0.91/0.96 tff(2055,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (always25(s59) | (~trans(s58, s59)) | (~always25(s58)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | always25(s59) | (~trans(s58, s59)) | (~always25(s58)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2056,plain,
% 0.91/0.96 (((~trans(s58, s59)) | (~always25(s58)) | always25(s59)) <=> (always25(s59) | (~trans(s58, s59)) | (~always25(s58)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2057,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s58, s59)) | (~always25(s58)) | always25(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (always25(s59) | (~trans(s58, s59)) | (~always25(s58))))),
% 0.91/0.96 inference(monotonicity,[status(thm)],[2056])).
% 0.91/0.96 tff(2058,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s58, s59)) | (~always25(s58)) | always25(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | always25(s59) | (~trans(s58, s59)) | (~always25(s58)))),
% 0.91/0.96 inference(transitivity,[status(thm)],[2057, 2055])).
% 0.91/0.96 tff(2059,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s58, s59)) | (~always25(s58)) | always25(s59))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2060,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | always25(s59) | (~trans(s58, s59)) | (~always25(s58))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 0.91/0.96 tff(2061,plain,
% 0.91/0.96 (always25(s59) | (~always25(s58))),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2060, 2041, 2054])).
% 0.91/0.96 tff(2062,plain,
% 0.91/0.96 (~always25(s58)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2061, 2047])).
% 0.91/0.96 tff(2063,plain,
% 0.91/0.96 (^[X: $i] : refl((always25(X) | (~node26(X))) <=> (always25(X) | (~node26(X))))),
% 0.91/0.96 inference(bind,[status(th)],[])).
% 0.91/0.96 tff(2064,plain,
% 0.91/0.96 (![X: $i] : (always25(X) | (~node26(X))) <=> ![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/0.96 inference(quant_intro,[status(thm)],[2063])).
% 0.91/0.96 tff(2065,plain,
% 0.91/0.96 (![X: $i] : (always25(X) | (~node26(X))) <=> ![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2066,axiom,(![X: $i] : (always25(X) | (~node26(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty18')).
% 0.91/0.96 tff(2067,plain,
% 0.91/0.96 (![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 0.91/0.96 tff(2068,plain,(
% 0.91/0.96 ![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/0.96 inference(skolemize,[status(sab)],[2067])).
% 0.91/0.96 tff(2069,plain,
% 0.91/0.96 (![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2068, 2064])).
% 0.91/0.96 tff(2070,plain,
% 0.91/0.96 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s58) | (~node26(s58)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s58) | (~node26(s58)))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2071,plain,
% 0.91/0.96 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s58) | (~node26(s58)))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2072,plain,
% 0.91/0.96 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s58) | (~node26(s58))),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 0.91/0.96 tff(2073,plain,
% 0.91/0.96 (~node26(s58)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2072, 2069, 2062])).
% 0.91/0.96 tff(2074,assumption,(~node26(s59)), introduced(assumption)).
% 0.91/0.96 tff(2075,assumption,(~node26(s58)), introduced(assumption)).
% 0.91/0.96 tff(2076,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s19, s20)) | node7(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s19, s20)) | node7(s19, s20))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.96 tff(2077,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s19, s20)) | node7(s19, s20))),
% 0.91/0.96 inference(quant_inst,[status(thm)],[])).
% 0.91/0.96 tff(2078,plain,
% 0.91/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s19, s20)) | node7(s19, s20)),
% 0.91/0.96 inference(modus_ponens,[status(thm)],[2077, 2076])).
% 0.91/0.96 tff(2079,plain,
% 0.91/0.96 (node7(s19, s20)),
% 0.91/0.96 inference(unit_resolution,[status(thm)],[2078, 206, 2008])).
% 0.91/0.96 tff(2080,plain,
% 0.91/0.96 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1))),
% 0.91/0.96 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2081,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2082,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1)),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 0.91/0.97 tff(2083,plain,
% 0.91/0.97 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | m_main_v_state1(s20, c_t1)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2082, 651, 2079])).
% 0.91/0.97 tff(2084,plain,
% 0.91/0.97 (m_main_v_state1(s20, c_t1)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2083, 1961, 1997])).
% 0.91/0.97 tff(2085,plain,
% 0.91/0.97 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2086,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2087,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 0.91/0.97 tff(2088,plain,
% 0.91/0.97 (~m_main_v_state1(s20, c_n1)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2087, 10, 2084])).
% 0.91/0.97 tff(2089,plain,
% 0.91/0.97 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s20, c_n1) | (~node1(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s20, c_n1) | (~node1(s20)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2090,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s20, c_n1) | (~node1(s20)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2091,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s20, c_n1) | (~node1(s20))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2090, 2089])).
% 0.91/0.97 tff(2092,plain,
% 0.91/0.97 (~node1(s20)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2091, 421, 2088])).
% 0.91/0.97 tff(2093,plain,
% 0.91/0.97 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s19, s20)) | node18(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s19, s20)) | node18(s19, s20))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2094,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s19, s20)) | node18(s19, s20))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2095,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s19, s20)) | node18(s19, s20)),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 0.91/0.97 tff(2096,plain,
% 0.91/0.97 (node18(s19, s20)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2095, 125, 2008])).
% 0.91/0.97 tff(2097,plain,
% 0.91/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2098,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2099,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2)),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 0.91/0.97 tff(2100,plain,
% 0.91/0.97 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | m_main_v_turn(s20, c_2)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2099, 760, 2096])).
% 0.91/0.97 tff(2101,plain,
% 0.91/0.97 (m_main_v_turn(s20, c_2)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2100, 1961, 1997])).
% 0.91/0.97 tff(2102,plain,
% 0.91/0.97 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2103,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2104,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 0.91/0.97 tff(2105,plain,
% 0.91/0.97 (~m_main_v_turn(s20, c_1)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2104, 156, 2101])).
% 0.91/0.97 tff(2106,plain,
% 0.91/0.97 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s20, c_1) | (~node5(s20)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s20, c_1) | (~node5(s20)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2107,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s20, c_1) | (~node5(s20)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2108,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s20, c_1) | (~node5(s20))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2107, 2106])).
% 0.91/0.97 tff(2109,plain,
% 0.91/0.97 (~node5(s20)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2108, 776, 2105])).
% 0.91/0.97 tff(2110,plain,
% 0.91/0.97 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s20, c_n1) | (~node2(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s20, c_n1) | (~node2(s20)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2111,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s20, c_n1) | (~node2(s20)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2112,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s20, c_n1) | (~node2(s20))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 0.91/0.97 tff(2113,plain,
% 0.91/0.97 (~node2(s20)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2112, 787, 2088])).
% 0.91/0.97 tff(2114,plain,
% 0.91/0.97 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s20, c_n1) | (~node3(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s20, c_n1) | (~node3(s20)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2115,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s20, c_n1) | (~node3(s20)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2116,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s20, c_n1) | (~node3(s20))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 0.91/0.97 tff(2117,plain,
% 0.91/0.97 (~node3(s20)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2116, 798, 2088])).
% 0.91/0.97 tff(2118,plain,
% 0.91/0.97 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2119,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2120,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 0.91/0.97 tff(2121,plain,
% 0.91/0.97 (~m_main_v_state1(s20, c_c1)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2120, 539, 2084])).
% 0.91/0.97 tff(2122,plain,
% 0.91/0.97 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2123,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2124,plain,
% 0.91/0.97 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 0.91/0.97 tff(2125,plain,
% 0.91/0.97 (~m_main_v_state2(s20, c_n2)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2124, 697, 2017])).
% 0.91/0.97 tff(2126,plain,
% 0.91/0.97 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s20, c_n2) | (~node4(s20)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s20, c_n2) | (~node4(s20)))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2127,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s20, c_n2) | (~node4(s20)))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2128,plain,
% 0.91/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s20, c_n2) | (~node4(s20))),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2127, 2126])).
% 0.91/0.97 tff(2129,plain,
% 0.91/0.97 (~node4(s20)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2128, 388, 2125])).
% 0.91/0.97 tff(2130,plain,
% 0.91/0.97 (succ(s20, s21) <=> succ(s20, s21)),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2131,axiom,(succ(s20, s21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound21')).
% 0.91/0.97 tff(2132,plain,
% 0.91/0.97 (succ(s20, s21)),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 0.91/0.97 tff(2133,plain,
% 0.91/0.97 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2134,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2135,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 0.91/0.97 tff(2136,plain,
% 0.91/0.97 (trans(s20, s21)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2135, 2132, 32])).
% 0.91/0.97 tff(2137,plain,
% 0.91/0.97 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s20, s21)) | node7(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s20, s21)) | node7(s20, s21))),
% 0.91/0.97 inference(rewrite,[status(thm)],[])).
% 0.91/0.97 tff(2138,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s20, s21)) | node7(s20, s21))),
% 0.91/0.97 inference(quant_inst,[status(thm)],[])).
% 0.91/0.97 tff(2139,plain,
% 0.91/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s20, s21)) | node7(s20, s21)),
% 0.91/0.97 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 0.91/0.97 tff(2140,plain,
% 0.91/0.97 (node7(s20, s21)),
% 0.91/0.97 inference(unit_resolution,[status(thm)],[2139, 206, 2136])).
% 0.91/0.97 tff(2141,plain,
% 0.91/0.97 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2142,plain,
% 0.91/0.98 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21)))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2143,plain,
% 0.91/0.98 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 0.91/0.98 tff(2144,plain,
% 0.91/0.98 (m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2143, 820, 2140])).
% 0.91/0.98 tff(2145,plain,
% 0.91/0.98 (node6(s20, s21)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2144, 2129, 2121, 2117, 2113, 2109, 2092])).
% 0.91/0.98 tff(2146,plain,
% 0.91/0.98 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2147,plain,
% 0.91/0.98 (((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1)) <=> ((~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2148,plain,
% 0.91/0.98 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21))))),
% 0.91/0.98 inference(monotonicity,[status(thm)],[2147])).
% 0.91/0.98 tff(2149,plain,
% 0.91/0.98 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))),
% 0.91/0.98 inference(transitivity,[status(thm)],[2148, 2146])).
% 0.91/0.98 tff(2150,plain,
% 0.91/0.98 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2151,plain,
% 0.91/0.98 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 0.91/0.98 tff(2152,plain,
% 0.91/0.98 (m_main_v_state1(s21, c_t1)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2151, 856, 2084, 2145])).
% 0.91/0.98 tff(2153,plain,
% 0.91/0.98 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2154,plain,
% 0.91/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2155,plain,
% 0.91/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 0.91/0.98 tff(2156,plain,
% 0.91/0.98 (~m_main_v_state2(s20, c_t2)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2155, 260, 2017])).
% 0.91/0.98 tff(2157,plain,
% 0.91/0.98 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s20, c_t2) | (~node12(s20)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s20, c_t2) | (~node12(s20)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2158,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s20, c_t2) | (~node12(s20)))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2159,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s20, c_t2) | (~node12(s20))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 0.91/0.98 tff(2160,plain,
% 0.91/0.98 (~node12(s20)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2159, 633, 2156])).
% 0.91/0.98 tff(2161,plain,
% 0.91/0.98 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s20, c_n1) | (~node11(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s20, c_n1) | (~node11(s20)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2162,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s20, c_n1) | (~node11(s20)))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2163,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s20, c_n1) | (~node11(s20))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 0.91/0.98 tff(2164,plain,
% 0.91/0.98 (~node11(s20)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2163, 238, 2088])).
% 0.91/0.98 tff(2165,plain,
% 0.91/0.98 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s20, c_c1) | (~node10(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s20, c_c1) | (~node10(s20)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2166,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s20, c_c1) | (~node10(s20)))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2167,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s20, c_c1) | (~node10(s20))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 0.91/0.98 tff(2168,plain,
% 0.91/0.98 (~node10(s20)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2167, 675, 2121])).
% 0.91/0.98 tff(2169,plain,
% 0.91/0.98 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s20, c_n1) | (~node9(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s20, c_n1) | (~node9(s20)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2170,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s20, c_n1) | (~node9(s20)))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2171,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s20, c_n1) | (~node9(s20))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2170, 2169])).
% 0.91/0.98 tff(2172,plain,
% 0.91/0.98 (~node9(s20)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2171, 686, 2088])).
% 0.91/0.98 tff(2173,plain,
% 0.91/0.98 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s20, c_n2) | (~node8(s20)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s20, c_n2) | (~node8(s20)))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.91/0.98 tff(2174,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s20, c_n2) | (~node8(s20)))),
% 0.91/0.98 inference(quant_inst,[status(thm)],[])).
% 0.91/0.98 tff(2175,plain,
% 0.91/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s20, c_n2) | (~node8(s20))),
% 0.91/0.98 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 0.91/0.98 tff(2176,plain,
% 0.91/0.98 (~node8(s20)),
% 0.91/0.98 inference(unit_resolution,[status(thm)],[2175, 271, 2125])).
% 0.91/0.98 tff(2177,plain,
% 0.91/0.98 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s20, s21)) | node14(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s20, s21)) | node14(s20, s21))),
% 0.91/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2178,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s20, s21)) | node14(s20, s21))),
% 0.96/0.98 inference(quant_inst,[status(thm)],[])).
% 0.96/0.98 tff(2179,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s20, s21)) | node14(s20, s21)),
% 0.96/0.98 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 0.96/0.98 tff(2180,plain,
% 0.96/0.98 (node14(s20, s21)),
% 0.96/0.98 inference(unit_resolution,[status(thm)],[2179, 46, 2136])).
% 0.96/0.98 tff(2181,plain,
% 0.96/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2182,plain,
% 0.96/0.98 (((~m_main_v_state2(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2)) <=> (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2183,plain,
% 0.96/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2))))),
% 0.96/0.98 inference(monotonicity,[status(thm)],[2182])).
% 0.96/0.98 tff(2184,plain,
% 0.96/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))),
% 0.96/0.98 inference(transitivity,[status(thm)],[2183, 2181])).
% 0.96/0.98 tff(2185,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2))),
% 0.96/0.98 inference(quant_inst,[status(thm)],[])).
% 0.96/0.98 tff(2186,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2))),
% 0.96/0.98 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 0.96/0.98 tff(2187,plain,
% 0.96/0.98 (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~m_main_v_state2(s20, c_c2))),
% 0.96/0.98 inference(unit_resolution,[status(thm)],[2186, 726, 2180])).
% 0.96/0.98 tff(2188,plain,
% 0.96/0.98 (m_main_v_state2(s21, c_n2)),
% 0.96/0.98 inference(unit_resolution,[status(thm)],[2187, 2176, 2017, 2172, 2168, 2164, 2160])).
% 0.96/0.98 tff(2189,plain,
% 0.96/0.98 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2)))),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2190,plain,
% 0.96/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2)))),
% 0.96/0.98 inference(quant_inst,[status(thm)],[])).
% 0.96/0.98 tff(2191,plain,
% 0.96/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2))),
% 0.96/0.98 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 0.96/0.98 tff(2192,plain,
% 0.96/0.98 (~m_main_v_state2(s21, c_t2)),
% 0.96/0.98 inference(unit_resolution,[status(thm)],[2191, 77, 2188])).
% 0.96/0.98 tff(2193,plain,
% 0.96/0.98 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s21, c_t2) | (~node15(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s21, c_t2) | (~node15(s21)))),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2194,plain,
% 0.96/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s21, c_t2) | (~node15(s21)))),
% 0.96/0.98 inference(quant_inst,[status(thm)],[])).
% 0.96/0.98 tff(2195,plain,
% 0.96/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s21, c_t2) | (~node15(s21))),
% 0.96/0.98 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 0.96/0.98 tff(2196,plain,
% 0.96/0.98 (~node15(s21)),
% 0.96/0.98 inference(unit_resolution,[status(thm)],[2195, 103, 2192])).
% 0.96/0.98 tff(2197,plain,
% 0.96/0.98 (succ(s21, s22) <=> succ(s21, s22)),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2198,axiom,(succ(s21, s22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound22')).
% 0.96/0.98 tff(2199,plain,
% 0.96/0.98 (succ(s21, s22)),
% 0.96/0.98 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 0.96/0.98 tff(2200,plain,
% 0.96/0.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22))),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2201,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 0.96/0.98 inference(quant_inst,[status(thm)],[])).
% 0.96/0.98 tff(2202,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 0.96/0.98 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 0.96/0.98 tff(2203,plain,
% 0.96/0.98 (trans(s21, s22)),
% 0.96/0.98 inference(unit_resolution,[status(thm)],[2202, 2199, 32])).
% 0.96/0.98 tff(2204,plain,
% 0.96/0.98 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s21, s22)) | node18(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s21, s22)) | node18(s21, s22))),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2205,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s21, s22)) | node18(s21, s22))),
% 0.96/0.98 inference(quant_inst,[status(thm)],[])).
% 0.96/0.98 tff(2206,plain,
% 0.96/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s21, s22)) | node18(s21, s22)),
% 0.96/0.98 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 0.96/0.98 tff(2207,plain,
% 0.96/0.98 (node18(s21, s22)),
% 0.96/0.98 inference(unit_resolution,[status(thm)],[2206, 125, 2203])).
% 0.96/0.98 tff(2208,plain,
% 0.96/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))),
% 0.96/0.98 inference(rewrite,[status(thm)],[])).
% 0.96/0.98 tff(2209,plain,
% 0.96/0.98 (((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1)) <=> (node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2210,plain,
% 0.96/0.99 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1)))),
% 0.96/0.99 inference(monotonicity,[status(thm)],[2209])).
% 0.96/0.99 tff(2211,plain,
% 0.96/0.99 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))),
% 0.96/0.99 inference(transitivity,[status(thm)],[2210, 2208])).
% 0.96/0.99 tff(2212,plain,
% 0.96/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2213,plain,
% 0.96/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1)),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 0.96/0.99 tff(2214,plain,
% 0.96/0.99 (node15(s21) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2213, 992, 2207])).
% 0.96/0.99 tff(2215,plain,
% 0.96/0.99 (m_main_v_turn(s22, c_1)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2214, 2196, 2188, 2152])).
% 0.96/0.99 tff(2216,plain,
% 0.96/0.99 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2217,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2218,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 0.96/0.99 tff(2219,plain,
% 0.96/0.99 (~m_main_v_turn(s22, c_2)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2218, 156, 2215])).
% 0.96/0.99 tff(2220,plain,
% 0.96/0.99 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s22, c_2) | (~node12(s22)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s22, c_2) | (~node12(s22)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2221,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s22, c_2) | (~node12(s22)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2222,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s22, c_2) | (~node12(s22))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 0.96/0.99 tff(2223,plain,
% 0.96/0.99 (~node12(s22)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2222, 184, 2219])).
% 0.96/0.99 tff(2224,plain,
% 0.96/0.99 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s21, s22)) | node14(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s21, s22)) | node14(s21, s22))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2225,plain,
% 0.96/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s21, s22)) | node14(s21, s22))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2226,plain,
% 0.96/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s21, s22)) | node14(s21, s22)),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 0.96/0.99 tff(2227,plain,
% 0.96/0.99 (node14(s21, s22)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2226, 46, 2203])).
% 0.96/0.99 tff(2228,plain,
% 0.96/0.99 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2229,plain,
% 0.96/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2230,plain,
% 0.96/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2)),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 0.96/0.99 tff(2231,plain,
% 0.96/0.99 ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state2(s22, c_t2)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2230, 922, 2227])).
% 0.96/0.99 tff(2232,plain,
% 0.96/0.99 (m_main_v_state2(s22, c_t2)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2231, 2152, 2188])).
% 0.96/0.99 tff(2233,plain,
% 0.96/0.99 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2234,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2235,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 0.96/0.99 tff(2236,plain,
% 0.96/0.99 (~m_main_v_state2(s22, c_n2)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2235, 77, 2232])).
% 0.96/0.99 tff(2237,plain,
% 0.96/0.99 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s22, c_n2) | (~node8(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s22, c_n2) | (~node8(s22)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2238,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s22, c_n2) | (~node8(s22)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2239,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s22, c_n2) | (~node8(s22))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 0.96/0.99 tff(2240,plain,
% 0.96/0.99 (~node8(s22)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2239, 271, 2236])).
% 0.96/0.99 tff(2241,plain,
% 0.96/0.99 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s22, c_n2) | (~node9(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s22, c_n2) | (~node9(s22)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2242,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s22, c_n2) | (~node9(s22)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2243,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s22, c_n2) | (~node9(s22))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 0.96/0.99 tff(2244,plain,
% 0.96/0.99 (~node9(s22)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2243, 88, 2236])).
% 0.96/0.99 tff(2245,plain,
% 0.96/0.99 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s22, c_n2) | (~node10(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s22, c_n2) | (~node10(s22)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2246,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s22, c_n2) | (~node10(s22)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2247,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s22, c_n2) | (~node10(s22))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 0.96/0.99 tff(2248,plain,
% 0.96/0.99 (~node10(s22)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2247, 249, 2236])).
% 0.96/0.99 tff(2249,plain,
% 0.96/0.99 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2250,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2251,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 0.96/0.99 tff(2252,plain,
% 0.96/0.99 (~m_main_v_state2(s22, c_c2)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2251, 260, 2232])).
% 0.96/0.99 tff(2253,plain,
% 0.96/0.99 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2254,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2255,plain,
% 0.96/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2254, 2253])).
% 0.96/0.99 tff(2256,plain,
% 0.96/0.99 (~m_main_v_state2(s21, c_c2)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2255, 697, 2188])).
% 0.96/0.99 tff(2257,plain,
% 0.96/0.99 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s21, c_c2) | (~node3(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s21, c_c2) | (~node3(s21)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2258,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s21, c_c2) | (~node3(s21)))),
% 0.96/0.99 inference(quant_inst,[status(thm)],[])).
% 0.96/0.99 tff(2259,plain,
% 0.96/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s21, c_c2) | (~node3(s21))),
% 0.96/0.99 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 0.96/0.99 tff(2260,plain,
% 0.96/0.99 (~node3(s21)),
% 0.96/0.99 inference(unit_resolution,[status(thm)],[2259, 399, 2256])).
% 0.96/0.99 tff(2261,plain,
% 0.96/0.99 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2262,plain,
% 0.96/0.99 (((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1))) <=> (m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))),
% 0.96/0.99 inference(rewrite,[status(thm)],[])).
% 0.96/0.99 tff(2263,plain,
% 0.96/0.99 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21))))),
% 0.96/1.00 inference(monotonicity,[status(thm)],[2262])).
% 0.96/1.00 tff(2264,plain,
% 0.96/1.00 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))),
% 0.96/1.00 inference(transitivity,[status(thm)],[2263, 2261])).
% 0.96/1.00 tff(2265,plain,
% 0.96/1.00 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2266,plain,
% 0.96/1.00 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21))),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 0.96/1.00 tff(2267,plain,
% 0.96/1.00 (~m_main_v_state1(s21, c_n1)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2266, 835, 2088, 2145])).
% 0.96/1.00 tff(2268,plain,
% 0.96/1.00 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s21, c_n1) | (~node2(s21)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s21, c_n1) | (~node2(s21)))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2269,plain,
% 0.96/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s21, c_n1) | (~node2(s21)))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2270,plain,
% 0.96/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s21, c_n1) | (~node2(s21))),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 0.96/1.00 tff(2271,plain,
% 0.96/1.00 (~node2(s21)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2270, 787, 2267])).
% 0.96/1.00 tff(2272,plain,
% 0.96/1.00 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s21, c_t2) | (~node1(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s21, c_t2) | (~node1(s21)))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2273,plain,
% 0.96/1.00 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s21, c_t2) | (~node1(s21)))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2274,plain,
% 0.96/1.00 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s21, c_t2) | (~node1(s21))),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2273, 2272])).
% 0.96/1.00 tff(2275,plain,
% 0.96/1.00 (~node1(s21)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2274, 195, 2192])).
% 0.96/1.00 tff(2276,plain,
% 0.96/1.00 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s21, s22)) | node7(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s21, s22)) | node7(s21, s22))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2277,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s21, s22)) | node7(s21, s22))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2278,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s21, s22)) | node7(s21, s22)),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 0.96/1.00 tff(2279,plain,
% 0.96/1.00 (node7(s21, s22)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2278, 206, 2203])).
% 0.96/1.00 tff(2280,plain,
% 0.96/1.00 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2281,plain,
% 0.96/1.00 (((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1)) <=> ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2282,plain,
% 0.96/1.00 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22))))),
% 0.96/1.00 inference(monotonicity,[status(thm)],[2281])).
% 0.96/1.00 tff(2283,plain,
% 0.96/1.00 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))),
% 0.96/1.00 inference(transitivity,[status(thm)],[2282, 2280])).
% 0.96/1.00 tff(2284,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2285,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22))),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 0.96/1.00 tff(2286,plain,
% 0.96/1.00 ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2285, 892, 2279])).
% 0.96/1.00 tff(2287,plain,
% 0.96/1.00 (m_main_v_state1(s22, c_c1)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2286, 2275, 2188, 2152, 2271, 2260])).
% 0.96/1.00 tff(2288,plain,
% 0.96/1.00 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2289,plain,
% 0.96/1.00 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2290,plain,
% 0.96/1.00 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1))),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 0.96/1.00 tff(2291,plain,
% 0.96/1.00 (~m_main_v_state1(s22, c_n1)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2290, 454, 2287])).
% 0.96/1.00 tff(2292,plain,
% 0.96/1.00 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s22, c_n1) | (~node11(s22)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s22, c_n1) | (~node11(s22)))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2293,plain,
% 0.96/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s22, c_n1) | (~node11(s22)))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2294,plain,
% 0.96/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s22, c_n1) | (~node11(s22))),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 0.96/1.00 tff(2295,plain,
% 0.96/1.00 (~node11(s22)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2294, 238, 2291])).
% 0.96/1.00 tff(2296,plain,
% 0.96/1.00 (succ(s22, s23) <=> succ(s22, s23)),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2297,axiom,(succ(s22, s23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound23')).
% 0.96/1.00 tff(2298,plain,
% 0.96/1.00 (succ(s22, s23)),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 0.96/1.00 tff(2299,plain,
% 0.96/1.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2300,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2301,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 0.96/1.00 tff(2302,plain,
% 0.96/1.00 (trans(s22, s23)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2301, 2298, 32])).
% 0.96/1.00 tff(2303,plain,
% 0.96/1.00 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s22, s23)) | node14(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s22, s23)) | node14(s22, s23))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2304,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s22, s23)) | node14(s22, s23))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2305,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s22, s23)) | node14(s22, s23)),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2304, 2303])).
% 0.96/1.00 tff(2306,plain,
% 0.96/1.00 (node14(s22, s23)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2305, 46, 2302])).
% 0.96/1.00 tff(2307,plain,
% 0.96/1.00 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23)))),
% 0.96/1.00 inference(rewrite,[status(thm)],[])).
% 0.96/1.00 tff(2308,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23)))),
% 0.96/1.00 inference(quant_inst,[status(thm)],[])).
% 0.96/1.00 tff(2309,plain,
% 0.96/1.00 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23))),
% 0.96/1.00 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 0.96/1.00 tff(2310,plain,
% 0.96/1.00 (m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2309, 296, 2306])).
% 0.96/1.00 tff(2311,plain,
% 0.96/1.00 (node13(s22, s23)),
% 0.96/1.00 inference(unit_resolution,[status(thm)],[2310, 2295, 2252, 2248, 2244, 2240, 2223])).
% 0.96/1.00 tff(2312,plain,
% 0.96/1.00 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2313,plain,
% 0.96/1.01 (((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2))) <=> (m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2314,plain,
% 0.96/1.01 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23))))),
% 0.96/1.01 inference(monotonicity,[status(thm)],[2313])).
% 0.96/1.01 tff(2315,plain,
% 0.96/1.01 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))),
% 0.96/1.01 inference(transitivity,[status(thm)],[2314, 2312])).
% 0.96/1.01 tff(2316,plain,
% 0.96/1.01 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2317,plain,
% 0.96/1.01 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 0.96/1.01 tff(2318,plain,
% 0.96/1.01 (~m_main_v_state2(s23, c_n2)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2317, 311, 2236, 2311])).
% 0.96/1.01 tff(2319,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s23, c_n2) | (~node9(s23)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s23, c_n2) | (~node9(s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2320,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s23, c_n2) | (~node9(s23)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2321,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s23, c_n2) | (~node9(s23))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 0.96/1.01 tff(2322,plain,
% 0.96/1.01 (~node9(s23)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2321, 88, 2318])).
% 0.96/1.01 tff(2323,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s23, c_n2) | (~node10(s23)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s23, c_n2) | (~node10(s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2324,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s23, c_n2) | (~node10(s23)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2325,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s23, c_n2) | (~node10(s23))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 0.96/1.01 tff(2326,plain,
% 0.96/1.01 (~node10(s23)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2325, 249, 2318])).
% 0.96/1.01 tff(2327,plain,
% 0.96/1.01 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2328,plain,
% 0.96/1.01 (((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2)) <=> ((~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2329,plain,
% 0.96/1.01 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23))))),
% 0.96/1.01 inference(monotonicity,[status(thm)],[2328])).
% 0.96/1.01 tff(2330,plain,
% 0.96/1.01 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))),
% 0.96/1.01 inference(transitivity,[status(thm)],[2329, 2327])).
% 0.96/1.01 tff(2331,plain,
% 0.96/1.01 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2332,plain,
% 0.96/1.01 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 0.96/1.01 tff(2333,plain,
% 0.96/1.01 (m_main_v_state2(s23, c_t2)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2332, 518, 2232, 2311])).
% 0.96/1.01 tff(2334,plain,
% 0.96/1.01 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2335,plain,
% 0.96/1.01 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2336,plain,
% 0.96/1.01 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 0.96/1.01 tff(2337,plain,
% 0.96/1.01 (~m_main_v_state1(s22, c_t1)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2336, 539, 2287])).
% 0.96/1.01 tff(2338,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s22, c_t1) | (~node5(s22)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s22, c_t1) | (~node5(s22)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2339,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s22, c_t1) | (~node5(s22)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2340,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s22, c_t1) | (~node5(s22))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 0.96/1.01 tff(2341,plain,
% 0.96/1.01 (~node5(s22)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2340, 550, 2337])).
% 0.96/1.01 tff(2342,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s22, c_n2) | (~node4(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s22, c_n2) | (~node4(s22)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2343,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s22, c_n2) | (~node4(s22)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2344,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s22, c_n2) | (~node4(s22))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 0.96/1.01 tff(2345,plain,
% 0.96/1.01 (~node4(s22)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2344, 388, 2236])).
% 0.96/1.01 tff(2346,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s22, c_c2) | (~node3(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s22, c_c2) | (~node3(s22)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2347,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s22, c_c2) | (~node3(s22)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2348,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s22, c_c2) | (~node3(s22))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 0.96/1.01 tff(2349,plain,
% 0.96/1.01 (~node3(s22)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2348, 399, 2252])).
% 0.96/1.01 tff(2350,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s22, c_n2) | (~node2(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s22, c_n2) | (~node2(s22)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2351,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s22, c_n2) | (~node2(s22)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2352,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s22, c_n2) | (~node2(s22))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 0.96/1.01 tff(2353,plain,
% 0.96/1.01 (~node2(s22)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2352, 410, 2236])).
% 0.96/1.01 tff(2354,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s22, c_n1) | (~node1(s22)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s22, c_n1) | (~node1(s22)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2355,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s22, c_n1) | (~node1(s22)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2356,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s22, c_n1) | (~node1(s22))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2355, 2354])).
% 0.96/1.01 tff(2357,plain,
% 0.96/1.01 (~node1(s22)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2356, 421, 2291])).
% 0.96/1.01 tff(2358,plain,
% 0.96/1.01 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s22, s23)) | node7(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s22, s23)) | node7(s22, s23))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2359,plain,
% 0.96/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s22, s23)) | node7(s22, s23))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2360,plain,
% 0.96/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s22, s23)) | node7(s22, s23)),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2359, 2358])).
% 0.96/1.01 tff(2361,plain,
% 0.96/1.01 (node7(s22, s23)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2360, 206, 2302])).
% 0.96/1.01 tff(2362,plain,
% 0.96/1.01 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2363,plain,
% 0.96/1.01 (((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1)) <=> (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2364,plain,
% 0.96/1.01 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23))))),
% 0.96/1.01 inference(monotonicity,[status(thm)],[2363])).
% 0.96/1.01 tff(2365,plain,
% 0.96/1.01 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))),
% 0.96/1.01 inference(transitivity,[status(thm)],[2364, 2362])).
% 0.96/1.01 tff(2366,plain,
% 0.96/1.01 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2367,plain,
% 0.96/1.01 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 0.96/1.01 tff(2368,plain,
% 0.96/1.01 (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2367, 584, 2361])).
% 0.96/1.01 tff(2369,plain,
% 0.96/1.01 (m_main_v_state1(s23, c_n1)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2368, 2357, 2287, 2353, 2349, 2345, 2341])).
% 0.96/1.01 tff(2370,plain,
% 0.96/1.01 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s23, c_n2) | (~node8(s23)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s23, c_n2) | (~node8(s23)))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2371,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s23, c_n2) | (~node8(s23)))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2372,plain,
% 0.96/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s23, c_n2) | (~node8(s23))),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 0.96/1.01 tff(2373,plain,
% 0.96/1.01 (~node8(s23)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2372, 271, 2318])).
% 0.96/1.01 tff(2374,plain,
% 0.96/1.01 (succ(s23, s24) <=> succ(s23, s24)),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2375,axiom,(succ(s23, s24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound24')).
% 0.96/1.01 tff(2376,plain,
% 0.96/1.01 (succ(s23, s24)),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 0.96/1.01 tff(2377,plain,
% 0.96/1.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24))),
% 0.96/1.01 inference(rewrite,[status(thm)],[])).
% 0.96/1.01 tff(2378,plain,
% 0.96/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 0.96/1.01 inference(quant_inst,[status(thm)],[])).
% 0.96/1.01 tff(2379,plain,
% 0.96/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 0.96/1.01 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 0.96/1.01 tff(2380,plain,
% 0.96/1.01 (trans(s23, s24)),
% 0.96/1.01 inference(unit_resolution,[status(thm)],[2379, 2376, 32])).
% 0.96/1.01 tff(2381,plain,
% 0.96/1.01 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s23, s24)) | node14(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s23, s24)) | node14(s23, s24))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2382,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s23, s24)) | node14(s23, s24))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2383,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s23, s24)) | node14(s23, s24)),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2382, 2381])).
% 0.96/1.02 tff(2384,plain,
% 0.96/1.02 (node14(s23, s24)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2383, 46, 2380])).
% 0.96/1.02 tff(2385,plain,
% 0.96/1.02 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2386,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2387,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2)),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 0.96/1.02 tff(2388,plain,
% 0.96/1.02 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | m_main_v_state2(s24, c_c2)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2387, 617, 2384])).
% 0.96/1.02 tff(2389,plain,
% 0.96/1.02 (m_main_v_state2(s24, c_c2)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2388, 2373, 2369, 2333, 2326, 2322])).
% 0.96/1.02 tff(2390,plain,
% 0.96/1.02 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2391,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2392,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 0.96/1.02 tff(2393,plain,
% 0.96/1.02 (~m_main_v_state2(s24, c_t2)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2392, 260, 2389])).
% 0.96/1.02 tff(2394,plain,
% 0.96/1.02 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s24, c_t2) | (~node12(s24)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s24, c_t2) | (~node12(s24)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2395,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s24, c_t2) | (~node12(s24)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2396,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s24, c_t2) | (~node12(s24))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 0.96/1.02 tff(2397,plain,
% 0.96/1.02 (~node12(s24)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2396, 633, 2393])).
% 0.96/1.02 tff(2398,plain,
% 0.96/1.02 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s23, s24)) | node7(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s23, s24)) | node7(s23, s24))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2399,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s23, s24)) | node7(s23, s24))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2400,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s23, s24)) | node7(s23, s24)),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2399, 2398])).
% 0.96/1.02 tff(2401,plain,
% 0.96/1.02 (node7(s23, s24)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2400, 206, 2380])).
% 0.96/1.02 tff(2402,plain,
% 0.96/1.02 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2403,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2404,plain,
% 0.96/1.02 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1)),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 0.96/1.02 tff(2405,plain,
% 0.96/1.02 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | m_main_v_state1(s24, c_t1)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2404, 651, 2401])).
% 0.96/1.02 tff(2406,plain,
% 0.96/1.02 (m_main_v_state1(s24, c_t1)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2405, 2333, 2369])).
% 0.96/1.02 tff(2407,plain,
% 0.96/1.02 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2408,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2409,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 0.96/1.02 tff(2410,plain,
% 0.96/1.02 (~m_main_v_state1(s24, c_n1)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2409, 10, 2406])).
% 0.96/1.02 tff(2411,plain,
% 0.96/1.02 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s24, c_n1) | (~node11(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s24, c_n1) | (~node11(s24)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2412,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s24, c_n1) | (~node11(s24)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2413,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s24, c_n1) | (~node11(s24))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2412, 2411])).
% 0.96/1.02 tff(2414,plain,
% 0.96/1.02 (~node11(s24)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2413, 238, 2410])).
% 0.96/1.02 tff(2415,plain,
% 0.96/1.02 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2416,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2417,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 0.96/1.02 tff(2418,plain,
% 0.96/1.02 (~m_main_v_state1(s24, c_c1)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2417, 539, 2406])).
% 0.96/1.02 tff(2419,plain,
% 0.96/1.02 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s24, c_c1) | (~node10(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s24, c_c1) | (~node10(s24)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2420,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s24, c_c1) | (~node10(s24)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2421,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s24, c_c1) | (~node10(s24))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 0.96/1.02 tff(2422,plain,
% 0.96/1.02 (~node10(s24)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2421, 675, 2418])).
% 0.96/1.02 tff(2423,plain,
% 0.96/1.02 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s24, c_n1) | (~node9(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s24, c_n1) | (~node9(s24)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2424,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s24, c_n1) | (~node9(s24)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2425,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s24, c_n1) | (~node9(s24))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 0.96/1.02 tff(2426,plain,
% 0.96/1.02 (~node9(s24)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2425, 686, 2410])).
% 0.96/1.02 tff(2427,plain,
% 0.96/1.02 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2428,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2429,plain,
% 0.96/1.02 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 0.96/1.02 tff(2430,plain,
% 0.96/1.02 (~m_main_v_state2(s24, c_n2)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2429, 697, 2389])).
% 0.96/1.02 tff(2431,plain,
% 0.96/1.02 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s24, c_n2) | (~node8(s24)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s24, c_n2) | (~node8(s24)))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2432,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s24, c_n2) | (~node8(s24)))),
% 0.96/1.02 inference(quant_inst,[status(thm)],[])).
% 0.96/1.02 tff(2433,plain,
% 0.96/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s24, c_n2) | (~node8(s24))),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 0.96/1.02 tff(2434,plain,
% 0.96/1.02 (~node8(s24)),
% 0.96/1.02 inference(unit_resolution,[status(thm)],[2433, 271, 2430])).
% 0.96/1.02 tff(2435,plain,
% 0.96/1.02 (succ(s24, s25) <=> succ(s24, s25)),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.02 tff(2436,axiom,(succ(s24, s25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound25')).
% 0.96/1.02 tff(2437,plain,
% 0.96/1.02 (succ(s24, s25)),
% 0.96/1.02 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 0.96/1.02 tff(2438,plain,
% 0.96/1.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25))),
% 0.96/1.02 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2439,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2440,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 0.96/1.03 tff(2441,plain,
% 0.96/1.03 (trans(s24, s25)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2440, 2437, 32])).
% 0.96/1.03 tff(2442,plain,
% 0.96/1.03 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s24, s25)) | node14(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s24, s25)) | node14(s24, s25))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2443,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s24, s25)) | node14(s24, s25))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2444,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s24, s25)) | node14(s24, s25)),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 0.96/1.03 tff(2445,plain,
% 0.96/1.03 (node14(s24, s25)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2444, 46, 2441])).
% 0.96/1.03 tff(2446,plain,
% 0.96/1.03 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2447,plain,
% 0.96/1.03 (((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2)) <=> (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2448,plain,
% 0.96/1.03 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2))))),
% 0.96/1.03 inference(monotonicity,[status(thm)],[2447])).
% 0.96/1.03 tff(2449,plain,
% 0.96/1.03 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))),
% 0.96/1.03 inference(transitivity,[status(thm)],[2448, 2446])).
% 0.96/1.03 tff(2450,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2451,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 0.96/1.03 tff(2452,plain,
% 0.96/1.03 (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~m_main_v_state2(s24, c_c2))),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2451, 726, 2445])).
% 0.96/1.03 tff(2453,plain,
% 0.96/1.03 (m_main_v_state2(s25, c_n2)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2452, 2434, 2389, 2426, 2422, 2414, 2397])).
% 0.96/1.03 tff(2454,plain,
% 0.96/1.03 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2455,plain,
% 0.96/1.03 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2)))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2456,plain,
% 0.96/1.03 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 0.96/1.03 tff(2457,plain,
% 0.96/1.03 (~m_main_v_state2(s25, c_c2)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2456, 697, 2453])).
% 0.96/1.03 tff(2458,plain,
% 0.96/1.03 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s25, c_c2) | (~node3(s25)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s25, c_c2) | (~node3(s25)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2459,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s25, c_c2) | (~node3(s25)))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2460,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s25, c_c2) | (~node3(s25))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 0.96/1.03 tff(2461,plain,
% 0.96/1.03 (~node3(s25)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2460, 399, 2457])).
% 0.96/1.03 tff(2462,plain,
% 0.96/1.03 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s24, c_n1) | (~node1(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s24, c_n1) | (~node1(s24)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2463,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s24, c_n1) | (~node1(s24)))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2464,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s24, c_n1) | (~node1(s24))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 0.96/1.03 tff(2465,plain,
% 0.96/1.03 (~node1(s24)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2464, 421, 2410])).
% 0.96/1.03 tff(2466,plain,
% 0.96/1.03 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s23, s24)) | node18(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s23, s24)) | node18(s23, s24))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2467,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s23, s24)) | node18(s23, s24))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2468,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s23, s24)) | node18(s23, s24)),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2467, 2466])).
% 0.96/1.03 tff(2469,plain,
% 0.96/1.03 (node18(s23, s24)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2468, 125, 2380])).
% 0.96/1.03 tff(2470,plain,
% 0.96/1.03 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2471,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2472,plain,
% 0.96/1.03 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2)),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2471, 2470])).
% 0.96/1.03 tff(2473,plain,
% 0.96/1.03 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | m_main_v_turn(s24, c_2)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2472, 760, 2469])).
% 0.96/1.03 tff(2474,plain,
% 0.96/1.03 (m_main_v_turn(s24, c_2)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2473, 2333, 2369])).
% 0.96/1.03 tff(2475,plain,
% 0.96/1.03 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2476,plain,
% 0.96/1.03 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2)))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2477,plain,
% 0.96/1.03 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 0.96/1.03 tff(2478,plain,
% 0.96/1.03 (~m_main_v_turn(s24, c_1)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2477, 156, 2474])).
% 0.96/1.03 tff(2479,plain,
% 0.96/1.03 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s24, c_1) | (~node5(s24)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s24, c_1) | (~node5(s24)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2480,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s24, c_1) | (~node5(s24)))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2481,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s24, c_1) | (~node5(s24))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 0.96/1.03 tff(2482,plain,
% 0.96/1.03 (~node5(s24)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2481, 776, 2478])).
% 0.96/1.03 tff(2483,plain,
% 0.96/1.03 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s24, c_n1) | (~node2(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s24, c_n1) | (~node2(s24)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2484,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s24, c_n1) | (~node2(s24)))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2485,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s24, c_n1) | (~node2(s24))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2484, 2483])).
% 0.96/1.03 tff(2486,plain,
% 0.96/1.03 (~node2(s24)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2485, 787, 2410])).
% 0.96/1.03 tff(2487,plain,
% 0.96/1.03 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s24, c_n1) | (~node3(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s24, c_n1) | (~node3(s24)))),
% 0.96/1.03 inference(rewrite,[status(thm)],[])).
% 0.96/1.03 tff(2488,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s24, c_n1) | (~node3(s24)))),
% 0.96/1.03 inference(quant_inst,[status(thm)],[])).
% 0.96/1.03 tff(2489,plain,
% 0.96/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s24, c_n1) | (~node3(s24))),
% 0.96/1.03 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 0.96/1.03 tff(2490,plain,
% 0.96/1.03 (~node3(s24)),
% 0.96/1.03 inference(unit_resolution,[status(thm)],[2489, 798, 2410])).
% 0.96/1.03 tff(2491,plain,
% 0.96/1.03 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s24, c_n2) | (~node4(s24)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s24, c_n2) | (~node4(s24)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2492,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s24, c_n2) | (~node4(s24)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2493,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s24, c_n2) | (~node4(s24))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 0.96/1.04 tff(2494,plain,
% 0.96/1.04 (~node4(s24)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2493, 388, 2430])).
% 0.96/1.04 tff(2495,plain,
% 0.96/1.04 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s24, s25)) | node7(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s24, s25)) | node7(s24, s25))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2496,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s24, s25)) | node7(s24, s25))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2497,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s24, s25)) | node7(s24, s25)),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 0.96/1.04 tff(2498,plain,
% 0.96/1.04 (node7(s24, s25)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2497, 206, 2441])).
% 0.96/1.04 tff(2499,plain,
% 0.96/1.04 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2500,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2501,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 0.96/1.04 tff(2502,plain,
% 0.96/1.04 (m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2501, 820, 2498])).
% 0.96/1.04 tff(2503,plain,
% 0.96/1.04 (node6(s24, s25)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2502, 2494, 2418, 2490, 2486, 2482, 2465])).
% 0.96/1.04 tff(2504,plain,
% 0.96/1.04 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2505,plain,
% 0.96/1.04 (((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1))) <=> (m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2506,plain,
% 0.96/1.04 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25))))),
% 0.96/1.04 inference(monotonicity,[status(thm)],[2505])).
% 0.96/1.04 tff(2507,plain,
% 0.96/1.04 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))),
% 0.96/1.04 inference(transitivity,[status(thm)],[2506, 2504])).
% 0.96/1.04 tff(2508,plain,
% 0.96/1.04 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2509,plain,
% 0.96/1.04 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 0.96/1.04 tff(2510,plain,
% 0.96/1.04 (~m_main_v_state1(s25, c_n1)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2509, 835, 2410, 2503])).
% 0.96/1.04 tff(2511,plain,
% 0.96/1.04 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s25, c_n1) | (~node2(s25)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s25, c_n1) | (~node2(s25)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2512,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s25, c_n1) | (~node2(s25)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2513,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s25, c_n1) | (~node2(s25))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 0.96/1.04 tff(2514,plain,
% 0.96/1.04 (~node2(s25)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2513, 787, 2510])).
% 0.96/1.04 tff(2515,plain,
% 0.96/1.04 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2516,plain,
% 0.96/1.04 (((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1)) <=> ((~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2517,plain,
% 0.96/1.04 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25))))),
% 0.96/1.04 inference(monotonicity,[status(thm)],[2516])).
% 0.96/1.04 tff(2518,plain,
% 0.96/1.04 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))),
% 0.96/1.04 inference(transitivity,[status(thm)],[2517, 2515])).
% 0.96/1.04 tff(2519,plain,
% 0.96/1.04 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2520,plain,
% 0.96/1.04 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 0.96/1.04 tff(2521,plain,
% 0.96/1.04 (m_main_v_state1(s25, c_t1)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2520, 856, 2406, 2503])).
% 0.96/1.04 tff(2522,plain,
% 0.96/1.04 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2523,plain,
% 0.96/1.04 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2524,plain,
% 0.96/1.04 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2523, 2522])).
% 0.96/1.04 tff(2525,plain,
% 0.96/1.04 (~m_main_v_state2(s25, c_t2)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2524, 77, 2453])).
% 0.96/1.04 tff(2526,plain,
% 0.96/1.04 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s25, c_t2) | (~node1(s25)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s25, c_t2) | (~node1(s25)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2527,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s25, c_t2) | (~node1(s25)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2528,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s25, c_t2) | (~node1(s25))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 0.96/1.04 tff(2529,plain,
% 0.96/1.04 (~node1(s25)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2528, 195, 2525])).
% 0.96/1.04 tff(2530,plain,
% 0.96/1.04 (succ(s25, s26) <=> succ(s25, s26)),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2531,axiom,(succ(s25, s26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound26')).
% 0.96/1.04 tff(2532,plain,
% 0.96/1.04 (succ(s25, s26)),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2531, 2530])).
% 0.96/1.04 tff(2533,plain,
% 0.96/1.04 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2534,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2535,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 0.96/1.04 tff(2536,plain,
% 0.96/1.04 (trans(s25, s26)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2535, 2532, 32])).
% 0.96/1.04 tff(2537,plain,
% 0.96/1.04 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s25, s26)) | node7(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s25, s26)) | node7(s25, s26))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2538,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s25, s26)) | node7(s25, s26))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2539,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s25, s26)) | node7(s25, s26)),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2538, 2537])).
% 0.96/1.04 tff(2540,plain,
% 0.96/1.04 (node7(s25, s26)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2539, 206, 2536])).
% 0.96/1.04 tff(2541,plain,
% 0.96/1.04 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2542,plain,
% 0.96/1.04 (((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1)) <=> ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2543,plain,
% 0.96/1.04 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26))))),
% 0.96/1.04 inference(monotonicity,[status(thm)],[2542])).
% 0.96/1.04 tff(2544,plain,
% 0.96/1.04 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))),
% 0.96/1.04 inference(transitivity,[status(thm)],[2543, 2541])).
% 0.96/1.04 tff(2545,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2546,plain,
% 0.96/1.04 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 0.96/1.04 tff(2547,plain,
% 0.96/1.04 ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2546, 892, 2540])).
% 0.96/1.04 tff(2548,plain,
% 0.96/1.04 (m_main_v_state1(s26, c_c1)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2547, 2529, 2453, 2521, 2514, 2461])).
% 0.96/1.04 tff(2549,plain,
% 0.96/1.04 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2550,plain,
% 0.96/1.04 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2551,plain,
% 0.96/1.04 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1))),
% 0.96/1.04 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 0.96/1.04 tff(2552,plain,
% 0.96/1.04 (~m_main_v_state1(s26, c_t1)),
% 0.96/1.04 inference(unit_resolution,[status(thm)],[2551, 539, 2548])).
% 0.96/1.04 tff(2553,plain,
% 0.96/1.04 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s26, c_t1) | (~node5(s26)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s26, c_t1) | (~node5(s26)))),
% 0.96/1.04 inference(rewrite,[status(thm)],[])).
% 0.96/1.04 tff(2554,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s26, c_t1) | (~node5(s26)))),
% 0.96/1.04 inference(quant_inst,[status(thm)],[])).
% 0.96/1.04 tff(2555,plain,
% 0.96/1.04 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s26, c_t1) | (~node5(s26))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2554, 2553])).
% 0.96/1.05 tff(2556,plain,
% 0.96/1.05 (~node5(s26)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2555, 550, 2552])).
% 0.96/1.05 tff(2557,plain,
% 0.96/1.05 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s25, s26)) | node14(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s25, s26)) | node14(s25, s26))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2558,plain,
% 0.96/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s25, s26)) | node14(s25, s26))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2559,plain,
% 0.96/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s25, s26)) | node14(s25, s26)),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 0.96/1.05 tff(2560,plain,
% 0.96/1.05 (node14(s25, s26)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2559, 46, 2536])).
% 0.96/1.05 tff(2561,plain,
% 0.96/1.05 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2562,plain,
% 0.96/1.05 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2563,plain,
% 0.96/1.05 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2)),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2562, 2561])).
% 0.96/1.05 tff(2564,plain,
% 0.96/1.05 ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state2(s26, c_t2)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2563, 922, 2560])).
% 0.96/1.05 tff(2565,plain,
% 0.96/1.05 (m_main_v_state2(s26, c_t2)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2564, 2521, 2453])).
% 0.96/1.05 tff(2566,plain,
% 0.96/1.05 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2)))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2567,plain,
% 0.96/1.05 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2)))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2568,plain,
% 0.96/1.05 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 0.96/1.05 tff(2569,plain,
% 0.96/1.05 (~m_main_v_state2(s26, c_n2)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2568, 77, 2565])).
% 0.96/1.05 tff(2570,plain,
% 0.96/1.05 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s26, c_n2) | (~node4(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s26, c_n2) | (~node4(s26)))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2571,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s26, c_n2) | (~node4(s26)))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2572,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s26, c_n2) | (~node4(s26))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2571, 2570])).
% 0.96/1.05 tff(2573,plain,
% 0.96/1.05 (~node4(s26)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2572, 388, 2569])).
% 0.96/1.05 tff(2574,plain,
% 0.96/1.05 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2)))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2575,plain,
% 0.96/1.05 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2)))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2576,plain,
% 0.96/1.05 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 0.96/1.05 tff(2577,plain,
% 0.96/1.05 (~m_main_v_state2(s26, c_c2)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2576, 260, 2565])).
% 0.96/1.05 tff(2578,plain,
% 0.96/1.05 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s26, c_c2) | (~node3(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s26, c_c2) | (~node3(s26)))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2579,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s26, c_c2) | (~node3(s26)))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2580,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s26, c_c2) | (~node3(s26))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 0.96/1.05 tff(2581,plain,
% 0.96/1.05 (~node3(s26)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2580, 399, 2577])).
% 0.96/1.05 tff(2582,plain,
% 0.96/1.05 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s26, c_n2) | (~node2(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s26, c_n2) | (~node2(s26)))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2583,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s26, c_n2) | (~node2(s26)))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2584,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s26, c_n2) | (~node2(s26))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2583, 2582])).
% 0.96/1.05 tff(2585,plain,
% 0.96/1.05 (~node2(s26)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2584, 410, 2569])).
% 0.96/1.05 tff(2586,plain,
% 0.96/1.05 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2587,plain,
% 0.96/1.05 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2588,plain,
% 0.96/1.05 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 0.96/1.05 tff(2589,plain,
% 0.96/1.05 (~m_main_v_state1(s26, c_n1)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2588, 454, 2548])).
% 0.96/1.05 tff(2590,plain,
% 0.96/1.05 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s26, c_n1) | (~node1(s26)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s26, c_n1) | (~node1(s26)))),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2591,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s26, c_n1) | (~node1(s26)))),
% 0.96/1.05 inference(quant_inst,[status(thm)],[])).
% 0.96/1.05 tff(2592,plain,
% 0.96/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s26, c_n1) | (~node1(s26))),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 0.96/1.05 tff(2593,plain,
% 0.96/1.05 (~node1(s26)),
% 0.96/1.05 inference(unit_resolution,[status(thm)],[2592, 421, 2589])).
% 0.96/1.05 tff(2594,plain,
% 0.96/1.05 (succ(s26, s27) <=> succ(s26, s27)),
% 0.96/1.05 inference(rewrite,[status(thm)],[])).
% 0.96/1.05 tff(2595,axiom,(succ(s26, s27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound27')).
% 0.96/1.05 tff(2596,plain,
% 0.96/1.05 (succ(s26, s27)),
% 0.96/1.05 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 1.03/1.05 tff(2597,plain,
% 1.03/1.05 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27))),
% 1.03/1.05 inference(rewrite,[status(thm)],[])).
% 1.03/1.05 tff(2598,plain,
% 1.03/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))),
% 1.03/1.05 inference(quant_inst,[status(thm)],[])).
% 1.03/1.05 tff(2599,plain,
% 1.03/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27)),
% 1.03/1.05 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 1.03/1.05 tff(2600,plain,
% 1.03/1.05 (trans(s26, s27)),
% 1.03/1.05 inference(unit_resolution,[status(thm)],[2599, 2596, 32])).
% 1.03/1.05 tff(2601,plain,
% 1.03/1.05 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s26, s27)) | node7(s26, s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s26, s27)) | node7(s26, s27))),
% 1.03/1.05 inference(rewrite,[status(thm)],[])).
% 1.03/1.05 tff(2602,plain,
% 1.03/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s26, s27)) | node7(s26, s27))),
% 1.03/1.05 inference(quant_inst,[status(thm)],[])).
% 1.03/1.05 tff(2603,plain,
% 1.03/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s26, s27)) | node7(s26, s27)),
% 1.03/1.05 inference(modus_ponens,[status(thm)],[2602, 2601])).
% 1.03/1.05 tff(2604,plain,
% 1.03/1.05 (node7(s26, s27)),
% 1.03/1.05 inference(unit_resolution,[status(thm)],[2603, 206, 2600])).
% 1.03/1.05 tff(2605,plain,
% 1.03/1.05 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)))),
% 1.03/1.05 inference(rewrite,[status(thm)],[])).
% 1.03/1.05 tff(2606,plain,
% 1.03/1.05 (((~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)) | m_main_v_state1(s27, c_n1)) <=> (m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)))),
% 1.03/1.05 inference(rewrite,[status(thm)],[])).
% 1.03/1.05 tff(2607,plain,
% 1.03/1.05 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)) | m_main_v_state1(s27, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27))))),
% 1.03/1.05 inference(monotonicity,[status(thm)],[2606])).
% 1.03/1.05 tff(2608,plain,
% 1.03/1.05 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)) | m_main_v_state1(s27, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)))),
% 1.03/1.05 inference(transitivity,[status(thm)],[2607, 2605])).
% 1.03/1.05 tff(2609,plain,
% 1.03/1.05 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27)) | m_main_v_state1(s27, c_n1))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2610,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26) | (~node7(s26, s27))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 1.03/1.06 tff(2611,plain,
% 1.03/1.06 (m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2610, 584, 2604])).
% 1.03/1.06 tff(2612,plain,
% 1.03/1.06 (m_main_v_state1(s27, c_n1)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2611, 2593, 2548, 2585, 2581, 2573, 2556])).
% 1.03/1.06 tff(2613,plain,
% 1.03/1.06 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s25, c_t2) | (~node15(s25)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s25, c_t2) | (~node15(s25)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2614,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s25, c_t2) | (~node15(s25)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2615,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s25, c_t2) | (~node15(s25))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 1.03/1.06 tff(2616,plain,
% 1.03/1.06 (~node15(s25)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2615, 103, 2525])).
% 1.03/1.06 tff(2617,plain,
% 1.03/1.06 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s25, s26)) | node18(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s25, s26)) | node18(s25, s26))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2618,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s25, s26)) | node18(s25, s26))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2619,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s25, s26)) | node18(s25, s26)),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 1.03/1.06 tff(2620,plain,
% 1.03/1.06 (node18(s25, s26)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2619, 125, 2536])).
% 1.03/1.06 tff(2621,plain,
% 1.03/1.06 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s25) | (~node18(s25, s26)) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s25) | (~node18(s25, s26)) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2622,plain,
% 1.03/1.06 (((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node15(s25) | (~node18(s25, s26)) | m_main_v_turn(s26, c_1)) <=> (node15(s25) | (~node18(s25, s26)) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2623,plain,
% 1.03/1.06 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node15(s25) | (~node18(s25, s26)) | m_main_v_turn(s26, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s25) | (~node18(s25, s26)) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1)))),
% 1.03/1.06 inference(monotonicity,[status(thm)],[2622])).
% 1.03/1.06 tff(2624,plain,
% 1.03/1.06 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node15(s25) | (~node18(s25, s26)) | m_main_v_turn(s26, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s25) | (~node18(s25, s26)) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1))),
% 1.03/1.06 inference(transitivity,[status(thm)],[2623, 2621])).
% 1.03/1.06 tff(2625,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node15(s25) | (~node18(s25, s26)) | m_main_v_turn(s26, c_1))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2626,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s25) | (~node18(s25, s26)) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1)),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 1.03/1.06 tff(2627,plain,
% 1.03/1.06 (node15(s25) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2626, 992, 2620])).
% 1.03/1.06 tff(2628,plain,
% 1.03/1.06 (m_main_v_turn(s26, c_1)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2627, 2616, 2453, 2521])).
% 1.03/1.06 tff(2629,plain,
% 1.03/1.06 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s26, c_1)) | (~m_main_v_turn(s26, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s26, c_1)) | (~m_main_v_turn(s26, c_2)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2630,plain,
% 1.03/1.06 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s26, c_1)) | (~m_main_v_turn(s26, c_2)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2631,plain,
% 1.03/1.06 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s26, c_1)) | (~m_main_v_turn(s26, c_2))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 1.03/1.06 tff(2632,plain,
% 1.03/1.06 (~m_main_v_turn(s26, c_2)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2631, 156, 2628])).
% 1.03/1.06 tff(2633,plain,
% 1.03/1.06 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s26, c_2) | (~node12(s26)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s26, c_2) | (~node12(s26)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2634,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s26, c_2) | (~node12(s26)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2635,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s26, c_2) | (~node12(s26))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 1.03/1.06 tff(2636,plain,
% 1.03/1.06 (~node12(s26)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2635, 184, 2632])).
% 1.03/1.06 tff(2637,plain,
% 1.03/1.06 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s26, c_n2) | (~node8(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s26, c_n2) | (~node8(s26)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2638,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s26, c_n2) | (~node8(s26)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2639,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s26, c_n2) | (~node8(s26))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 1.03/1.06 tff(2640,plain,
% 1.03/1.06 (~node8(s26)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2639, 271, 2569])).
% 1.03/1.06 tff(2641,plain,
% 1.03/1.06 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s26, c_n2) | (~node9(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s26, c_n2) | (~node9(s26)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2642,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s26, c_n2) | (~node9(s26)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2643,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s26, c_n2) | (~node9(s26))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 1.03/1.06 tff(2644,plain,
% 1.03/1.06 (~node9(s26)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2643, 88, 2569])).
% 1.03/1.06 tff(2645,plain,
% 1.03/1.06 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s26, c_n2) | (~node10(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s26, c_n2) | (~node10(s26)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2646,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s26, c_n2) | (~node10(s26)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2647,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s26, c_n2) | (~node10(s26))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.03/1.06 tff(2648,plain,
% 1.03/1.06 (~node10(s26)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2647, 249, 2569])).
% 1.03/1.06 tff(2649,plain,
% 1.03/1.06 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s26, c_n1) | (~node11(s26)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s26, c_n1) | (~node11(s26)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2650,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s26, c_n1) | (~node11(s26)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2651,plain,
% 1.03/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s26, c_n1) | (~node11(s26))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2650, 2649])).
% 1.03/1.06 tff(2652,plain,
% 1.03/1.06 (~node11(s26)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2651, 238, 2589])).
% 1.03/1.06 tff(2653,plain,
% 1.03/1.06 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s26, s27)) | node14(s26, s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s26, s27)) | node14(s26, s27))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2654,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s26, s27)) | node14(s26, s27))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2655,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s26, s27)) | node14(s26, s27)),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 1.03/1.06 tff(2656,plain,
% 1.03/1.06 (node14(s26, s27)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2655, 46, 2600])).
% 1.03/1.06 tff(2657,plain,
% 1.03/1.06 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s26, c_c2) | node9(s26) | node8(s26) | node10(s26) | node11(s26) | node12(s26) | node13(s26, s27) | (~node14(s26, s27)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s26, c_c2) | node9(s26) | node8(s26) | node10(s26) | node11(s26) | node12(s26) | node13(s26, s27) | (~node14(s26, s27)))),
% 1.03/1.06 inference(rewrite,[status(thm)],[])).
% 1.03/1.06 tff(2658,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s26, c_c2) | node9(s26) | node8(s26) | node10(s26) | node11(s26) | node12(s26) | node13(s26, s27) | (~node14(s26, s27)))),
% 1.03/1.06 inference(quant_inst,[status(thm)],[])).
% 1.03/1.06 tff(2659,plain,
% 1.03/1.06 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s26, c_c2) | node9(s26) | node8(s26) | node10(s26) | node11(s26) | node12(s26) | node13(s26, s27) | (~node14(s26, s27))),
% 1.03/1.06 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 1.03/1.06 tff(2660,plain,
% 1.03/1.06 (m_main_v_state2(s26, c_c2) | node9(s26) | node8(s26) | node10(s26) | node11(s26) | node12(s26) | node13(s26, s27)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2659, 296, 2656])).
% 1.03/1.06 tff(2661,plain,
% 1.03/1.06 (node13(s26, s27)),
% 1.03/1.06 inference(unit_resolution,[status(thm)],[2660, 2652, 2577, 2648, 2644, 2640, 2636])).
% 1.03/1.06 tff(2662,plain,
% 1.03/1.06 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2) | (~node13(s26, s27)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2) | (~node13(s26, s27)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2663,plain,
% 1.03/1.07 (((~node13(s26, s27)) | (~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2)) <=> ((~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2) | (~node13(s26, s27)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2664,plain,
% 1.03/1.07 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s26, s27)) | (~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2) | (~node13(s26, s27))))),
% 1.03/1.07 inference(monotonicity,[status(thm)],[2663])).
% 1.03/1.07 tff(2665,plain,
% 1.03/1.07 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s26, s27)) | (~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2) | (~node13(s26, s27)))),
% 1.03/1.07 inference(transitivity,[status(thm)],[2664, 2662])).
% 1.03/1.07 tff(2666,plain,
% 1.03/1.07 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s26, s27)) | (~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2667,plain,
% 1.03/1.07 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s26, c_t2)) | m_main_v_state2(s27, c_t2) | (~node13(s26, s27))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2666, 2665])).
% 1.03/1.07 tff(2668,plain,
% 1.03/1.07 (m_main_v_state2(s27, c_t2)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2667, 518, 2565, 2661])).
% 1.03/1.07 tff(2669,plain,
% 1.03/1.07 (succ(s27, s28) <=> succ(s27, s28)),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2670,axiom,(succ(s27, s28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound28')).
% 1.03/1.07 tff(2671,plain,
% 1.03/1.07 (succ(s27, s28)),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 1.03/1.07 tff(2672,plain,
% 1.03/1.07 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2673,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2674,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28)),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.03/1.07 tff(2675,plain,
% 1.03/1.07 (trans(s27, s28)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2674, 2671, 32])).
% 1.03/1.07 tff(2676,plain,
% 1.03/1.07 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s27, s28)) | node7(s27, s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s27, s28)) | node7(s27, s28))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2677,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s27, s28)) | node7(s27, s28))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2678,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s27, s28)) | node7(s27, s28)),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 1.03/1.07 tff(2679,plain,
% 1.03/1.07 (node7(s27, s28)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2678, 206, 2675])).
% 1.03/1.07 tff(2680,plain,
% 1.03/1.07 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node7(s27, s28)) | m_main_v_state1(s28, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node7(s27, s28)) | m_main_v_state1(s28, c_t1))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2681,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node7(s27, s28)) | m_main_v_state1(s28, c_t1))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2682,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node7(s27, s28)) | m_main_v_state1(s28, c_t1)),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 1.03/1.07 tff(2683,plain,
% 1.03/1.07 ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | m_main_v_state1(s28, c_t1)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2682, 651, 2679])).
% 1.03/1.07 tff(2684,plain,
% 1.03/1.07 (m_main_v_state1(s28, c_t1)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2683, 2668, 2612])).
% 1.03/1.07 tff(2685,plain,
% 1.03/1.07 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s28, c_n1)) | (~m_main_v_state1(s28, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s28, c_n1)) | (~m_main_v_state1(s28, c_t1)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2686,plain,
% 1.03/1.07 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s28, c_n1)) | (~m_main_v_state1(s28, c_t1)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2687,plain,
% 1.03/1.07 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s28, c_n1)) | (~m_main_v_state1(s28, c_t1))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2686, 2685])).
% 1.03/1.07 tff(2688,plain,
% 1.03/1.07 (~m_main_v_state1(s28, c_n1)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2687, 10, 2684])).
% 1.03/1.07 tff(2689,plain,
% 1.03/1.07 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s28, c_n1) | (~node1(s28)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s28, c_n1) | (~node1(s28)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2690,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s28, c_n1) | (~node1(s28)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2691,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s28, c_n1) | (~node1(s28))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2690, 2689])).
% 1.03/1.07 tff(2692,plain,
% 1.03/1.07 (~node1(s28)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2691, 421, 2688])).
% 1.03/1.07 tff(2693,plain,
% 1.03/1.07 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s27, s28)) | node18(s27, s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s27, s28)) | node18(s27, s28))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2694,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s27, s28)) | node18(s27, s28))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2695,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s27, s28)) | node18(s27, s28)),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.03/1.07 tff(2696,plain,
% 1.03/1.07 (node18(s27, s28)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2695, 125, 2675])).
% 1.03/1.07 tff(2697,plain,
% 1.03/1.07 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node18(s27, s28)) | m_main_v_turn(s28, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node18(s27, s28)) | m_main_v_turn(s28, c_2))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2698,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node18(s27, s28)) | m_main_v_turn(s28, c_2))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2699,plain,
% 1.03/1.07 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node18(s27, s28)) | m_main_v_turn(s28, c_2)),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2698, 2697])).
% 1.03/1.07 tff(2700,plain,
% 1.03/1.07 ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | m_main_v_turn(s28, c_2)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2699, 760, 2696])).
% 1.03/1.07 tff(2701,plain,
% 1.03/1.07 (m_main_v_turn(s28, c_2)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2700, 2668, 2612])).
% 1.03/1.07 tff(2702,plain,
% 1.03/1.07 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s28, c_1)) | (~m_main_v_turn(s28, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s28, c_1)) | (~m_main_v_turn(s28, c_2)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2703,plain,
% 1.03/1.07 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s28, c_1)) | (~m_main_v_turn(s28, c_2)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2704,plain,
% 1.03/1.07 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s28, c_1)) | (~m_main_v_turn(s28, c_2))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 1.03/1.07 tff(2705,plain,
% 1.03/1.07 (~m_main_v_turn(s28, c_1)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2704, 156, 2701])).
% 1.03/1.07 tff(2706,plain,
% 1.03/1.07 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s28, c_1) | (~node5(s28)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s28, c_1) | (~node5(s28)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2707,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s28, c_1) | (~node5(s28)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2708,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s28, c_1) | (~node5(s28))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 1.03/1.07 tff(2709,plain,
% 1.03/1.07 (~node5(s28)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2708, 776, 2705])).
% 1.03/1.07 tff(2710,plain,
% 1.03/1.07 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s28, c_n1) | (~node2(s28)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s28, c_n1) | (~node2(s28)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2711,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s28, c_n1) | (~node2(s28)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2712,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s28, c_n1) | (~node2(s28))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 1.03/1.07 tff(2713,plain,
% 1.03/1.07 (~node2(s28)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2712, 787, 2688])).
% 1.03/1.07 tff(2714,plain,
% 1.03/1.07 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s28, c_n1) | (~node3(s28)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s28, c_n1) | (~node3(s28)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2715,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s28, c_n1) | (~node3(s28)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2716,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s28, c_n1) | (~node3(s28))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 1.03/1.07 tff(2717,plain,
% 1.03/1.07 (~node3(s28)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2716, 798, 2688])).
% 1.03/1.07 tff(2718,plain,
% 1.03/1.07 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s28, c_t1)) | (~m_main_v_state1(s28, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s28, c_t1)) | (~m_main_v_state1(s28, c_c1)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2719,plain,
% 1.03/1.07 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s28, c_t1)) | (~m_main_v_state1(s28, c_c1)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2720,plain,
% 1.03/1.07 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s28, c_t1)) | (~m_main_v_state1(s28, c_c1))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 1.03/1.07 tff(2721,plain,
% 1.03/1.07 (~m_main_v_state1(s28, c_c1)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2720, 539, 2684])).
% 1.03/1.07 tff(2722,plain,
% 1.03/1.07 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)) | (~node13(s26, s27)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)) | (~node13(s26, s27)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2723,plain,
% 1.03/1.07 (((~node13(s26, s27)) | m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2))) <=> (m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)) | (~node13(s26, s27)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2724,plain,
% 1.03/1.07 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s26, s27)) | m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)) | (~node13(s26, s27))))),
% 1.03/1.07 inference(monotonicity,[status(thm)],[2723])).
% 1.03/1.07 tff(2725,plain,
% 1.03/1.07 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s26, s27)) | m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)) | (~node13(s26, s27)))),
% 1.03/1.07 inference(transitivity,[status(thm)],[2724, 2722])).
% 1.03/1.07 tff(2726,plain,
% 1.03/1.07 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s26, s27)) | m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2727,plain,
% 1.03/1.07 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s26, c_n2) | (~m_main_v_state2(s27, c_n2)) | (~node13(s26, s27))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.03/1.07 tff(2728,plain,
% 1.03/1.07 (~m_main_v_state2(s27, c_n2)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2727, 311, 2569, 2661])).
% 1.03/1.07 tff(2729,plain,
% 1.03/1.07 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s27, c_n2) | (~node9(s27)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s27, c_n2) | (~node9(s27)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2730,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s27, c_n2) | (~node9(s27)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2731,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s27, c_n2) | (~node9(s27))),
% 1.03/1.07 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 1.03/1.07 tff(2732,plain,
% 1.03/1.07 (~node9(s27)),
% 1.03/1.07 inference(unit_resolution,[status(thm)],[2731, 88, 2728])).
% 1.03/1.07 tff(2733,plain,
% 1.03/1.07 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s27, c_n2) | (~node10(s27)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s27, c_n2) | (~node10(s27)))),
% 1.03/1.07 inference(rewrite,[status(thm)],[])).
% 1.03/1.07 tff(2734,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s27, c_n2) | (~node10(s27)))),
% 1.03/1.07 inference(quant_inst,[status(thm)],[])).
% 1.03/1.07 tff(2735,plain,
% 1.03/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s27, c_n2) | (~node10(s27))),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 1.03/1.08 tff(2736,plain,
% 1.03/1.08 (~node10(s27)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2735, 249, 2728])).
% 1.03/1.08 tff(2737,plain,
% 1.03/1.08 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s27, c_n2) | (~node8(s27)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s27, c_n2) | (~node8(s27)))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2738,plain,
% 1.03/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s27, c_n2) | (~node8(s27)))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2739,plain,
% 1.03/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s27, c_n2) | (~node8(s27))),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 1.03/1.08 tff(2740,plain,
% 1.03/1.08 (~node8(s27)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2739, 271, 2728])).
% 1.03/1.08 tff(2741,plain,
% 1.03/1.08 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s27, s28)) | node14(s27, s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s27, s28)) | node14(s27, s28))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2742,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s27, s28)) | node14(s27, s28))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2743,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s27, s28)) | node14(s27, s28)),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 1.03/1.08 tff(2744,plain,
% 1.03/1.08 (node14(s27, s28)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2743, 46, 2675])).
% 1.03/1.08 tff(2745,plain,
% 1.03/1.08 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | node9(s27) | node8(s27) | node10(s27) | (~node14(s27, s28)) | m_main_v_state2(s28, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | node9(s27) | node8(s27) | node10(s27) | (~node14(s27, s28)) | m_main_v_state2(s28, c_c2))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2746,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | node9(s27) | node8(s27) | node10(s27) | (~node14(s27, s28)) | m_main_v_state2(s28, c_c2))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2747,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | node9(s27) | node8(s27) | node10(s27) | (~node14(s27, s28)) | m_main_v_state2(s28, c_c2)),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 1.03/1.08 tff(2748,plain,
% 1.03/1.08 ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | node9(s27) | node8(s27) | node10(s27) | m_main_v_state2(s28, c_c2)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2747, 617, 2744])).
% 1.03/1.08 tff(2749,plain,
% 1.03/1.08 (m_main_v_state2(s28, c_c2)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2748, 2740, 2612, 2668, 2736, 2732])).
% 1.03/1.08 tff(2750,plain,
% 1.03/1.08 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s28, c_n2)) | (~m_main_v_state2(s28, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s28, c_n2)) | (~m_main_v_state2(s28, c_c2)))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2751,plain,
% 1.03/1.08 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s28, c_n2)) | (~m_main_v_state2(s28, c_c2)))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2752,plain,
% 1.03/1.08 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s28, c_n2)) | (~m_main_v_state2(s28, c_c2))),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 1.03/1.08 tff(2753,plain,
% 1.03/1.08 (~m_main_v_state2(s28, c_n2)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2752, 697, 2749])).
% 1.03/1.08 tff(2754,plain,
% 1.03/1.08 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s28, c_n2) | (~node4(s28)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s28, c_n2) | (~node4(s28)))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2755,plain,
% 1.03/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s28, c_n2) | (~node4(s28)))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2756,plain,
% 1.03/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s28, c_n2) | (~node4(s28))),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 1.03/1.08 tff(2757,plain,
% 1.03/1.08 (~node4(s28)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2756, 388, 2753])).
% 1.03/1.08 tff(2758,plain,
% 1.03/1.08 (succ(s28, s29) <=> succ(s28, s29)),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2759,axiom,(succ(s28, s29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound29')).
% 1.03/1.08 tff(2760,plain,
% 1.03/1.08 (succ(s28, s29)),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 1.03/1.08 tff(2761,plain,
% 1.03/1.08 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2762,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2763,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29)),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 1.03/1.08 tff(2764,plain,
% 1.03/1.08 (trans(s28, s29)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2763, 2760, 32])).
% 1.03/1.08 tff(2765,plain,
% 1.03/1.08 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s28, s29)) | node7(s28, s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s28, s29)) | node7(s28, s29))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2766,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s28, s29)) | node7(s28, s29))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2767,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s28, s29)) | node7(s28, s29)),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2766, 2765])).
% 1.03/1.08 tff(2768,plain,
% 1.03/1.08 (node7(s28, s29)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2767, 206, 2764])).
% 1.03/1.08 tff(2769,plain,
% 1.03/1.08 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s28, c_c1) | node1(s28) | node2(s28) | node3(s28) | node4(s28) | node5(s28) | node6(s28, s29) | (~node7(s28, s29)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s28, c_c1) | node1(s28) | node2(s28) | node3(s28) | node4(s28) | node5(s28) | node6(s28, s29) | (~node7(s28, s29)))),
% 1.03/1.08 inference(rewrite,[status(thm)],[])).
% 1.03/1.08 tff(2770,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s28, c_c1) | node1(s28) | node2(s28) | node3(s28) | node4(s28) | node5(s28) | node6(s28, s29) | (~node7(s28, s29)))),
% 1.03/1.08 inference(quant_inst,[status(thm)],[])).
% 1.03/1.08 tff(2771,plain,
% 1.03/1.08 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s28, c_c1) | node1(s28) | node2(s28) | node3(s28) | node4(s28) | node5(s28) | node6(s28, s29) | (~node7(s28, s29))),
% 1.03/1.08 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.03/1.08 tff(2772,plain,
% 1.03/1.08 (m_main_v_state1(s28, c_c1) | node1(s28) | node2(s28) | node3(s28) | node4(s28) | node5(s28) | node6(s28, s29)),
% 1.03/1.08 inference(unit_resolution,[status(thm)],[2771, 820, 2768])).
% 1.06/1.08 tff(2773,plain,
% 1.06/1.08 (node6(s28, s29)),
% 1.06/1.08 inference(unit_resolution,[status(thm)],[2772, 2757, 2721, 2717, 2713, 2709, 2692])).
% 1.06/1.08 tff(2774,plain,
% 1.06/1.08 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1) | (~node6(s28, s29)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1) | (~node6(s28, s29)))),
% 1.06/1.08 inference(rewrite,[status(thm)],[])).
% 1.06/1.08 tff(2775,plain,
% 1.06/1.08 (((~node6(s28, s29)) | (~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1)) <=> ((~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1) | (~node6(s28, s29)))),
% 1.06/1.08 inference(rewrite,[status(thm)],[])).
% 1.06/1.08 tff(2776,plain,
% 1.06/1.08 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s28, s29)) | (~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1) | (~node6(s28, s29))))),
% 1.06/1.08 inference(monotonicity,[status(thm)],[2775])).
% 1.06/1.08 tff(2777,plain,
% 1.06/1.08 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s28, s29)) | (~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1) | (~node6(s28, s29)))),
% 1.06/1.08 inference(transitivity,[status(thm)],[2776, 2774])).
% 1.06/1.08 tff(2778,plain,
% 1.06/1.08 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s28, s29)) | (~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1))),
% 1.06/1.08 inference(quant_inst,[status(thm)],[])).
% 1.06/1.08 tff(2779,plain,
% 1.06/1.08 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s28, c_t1)) | m_main_v_state1(s29, c_t1) | (~node6(s28, s29))),
% 1.06/1.08 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 1.06/1.08 tff(2780,plain,
% 1.06/1.08 (m_main_v_state1(s29, c_t1)),
% 1.06/1.08 inference(unit_resolution,[status(thm)],[2779, 856, 2684, 2773])).
% 1.06/1.08 tff(2781,plain,
% 1.06/1.08 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s28, c_t2)) | (~m_main_v_state2(s28, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s28, c_t2)) | (~m_main_v_state2(s28, c_c2)))),
% 1.06/1.08 inference(rewrite,[status(thm)],[])).
% 1.06/1.08 tff(2782,plain,
% 1.06/1.08 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s28, c_t2)) | (~m_main_v_state2(s28, c_c2)))),
% 1.06/1.08 inference(quant_inst,[status(thm)],[])).
% 1.06/1.08 tff(2783,plain,
% 1.06/1.08 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s28, c_t2)) | (~m_main_v_state2(s28, c_c2))),
% 1.06/1.08 inference(modus_ponens,[status(thm)],[2782, 2781])).
% 1.06/1.08 tff(2784,plain,
% 1.06/1.08 (~m_main_v_state2(s28, c_t2)),
% 1.06/1.08 inference(unit_resolution,[status(thm)],[2783, 260, 2749])).
% 1.06/1.08 tff(2785,plain,
% 1.06/1.08 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s28, c_t2) | (~node12(s28)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s28, c_t2) | (~node12(s28)))),
% 1.06/1.08 inference(rewrite,[status(thm)],[])).
% 1.06/1.08 tff(2786,plain,
% 1.06/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s28, c_t2) | (~node12(s28)))),
% 1.06/1.08 inference(quant_inst,[status(thm)],[])).
% 1.06/1.08 tff(2787,plain,
% 1.06/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s28, c_t2) | (~node12(s28))),
% 1.06/1.08 inference(modus_ponens,[status(thm)],[2786, 2785])).
% 1.06/1.08 tff(2788,plain,
% 1.06/1.08 (~node12(s28)),
% 1.06/1.08 inference(unit_resolution,[status(thm)],[2787, 633, 2784])).
% 1.06/1.08 tff(2789,plain,
% 1.06/1.08 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s28, c_n1) | (~node11(s28)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s28, c_n1) | (~node11(s28)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2790,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s28, c_n1) | (~node11(s28)))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2791,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s28, c_n1) | (~node11(s28))),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 1.06/1.09 tff(2792,plain,
% 1.06/1.09 (~node11(s28)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2791, 238, 2688])).
% 1.06/1.09 tff(2793,plain,
% 1.06/1.09 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s28, c_c1) | (~node10(s28)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s28, c_c1) | (~node10(s28)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2794,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s28, c_c1) | (~node10(s28)))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2795,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s28, c_c1) | (~node10(s28))),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 1.06/1.09 tff(2796,plain,
% 1.06/1.09 (~node10(s28)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2795, 675, 2721])).
% 1.06/1.09 tff(2797,plain,
% 1.06/1.09 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s28, c_n1) | (~node9(s28)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s28, c_n1) | (~node9(s28)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2798,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s28, c_n1) | (~node9(s28)))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2799,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s28, c_n1) | (~node9(s28))),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 1.06/1.09 tff(2800,plain,
% 1.06/1.09 (~node9(s28)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2799, 686, 2688])).
% 1.06/1.09 tff(2801,plain,
% 1.06/1.09 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s28, c_n2) | (~node8(s28)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s28, c_n2) | (~node8(s28)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2802,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s28, c_n2) | (~node8(s28)))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2803,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s28, c_n2) | (~node8(s28))),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2802, 2801])).
% 1.06/1.09 tff(2804,plain,
% 1.06/1.09 (~node8(s28)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2803, 271, 2753])).
% 1.06/1.09 tff(2805,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s28, s29)) | node14(s28, s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s28, s29)) | node14(s28, s29))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2806,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s28, s29)) | node14(s28, s29))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2807,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s28, s29)) | node14(s28, s29)),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 1.06/1.09 tff(2808,plain,
% 1.06/1.09 (node14(s28, s29)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2807, 46, 2764])).
% 1.06/1.09 tff(2809,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | (~m_main_v_state2(s28, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | (~m_main_v_state2(s28, c_c2)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2810,plain,
% 1.06/1.09 (((~m_main_v_state2(s28, c_c2)) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | m_main_v_state2(s29, c_n2)) <=> (m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | (~m_main_v_state2(s28, c_c2)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2811,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s28, c_c2)) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | m_main_v_state2(s29, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | (~m_main_v_state2(s28, c_c2))))),
% 1.06/1.09 inference(monotonicity,[status(thm)],[2810])).
% 1.06/1.09 tff(2812,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s28, c_c2)) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | m_main_v_state2(s29, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | (~m_main_v_state2(s28, c_c2)))),
% 1.06/1.09 inference(transitivity,[status(thm)],[2811, 2809])).
% 1.06/1.09 tff(2813,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s28, c_c2)) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | m_main_v_state2(s29, c_n2))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2814,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | (~m_main_v_state2(s28, c_c2))),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2813, 2812])).
% 1.06/1.09 tff(2815,plain,
% 1.06/1.09 (m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~m_main_v_state2(s28, c_c2))),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2814, 726, 2808])).
% 1.06/1.09 tff(2816,plain,
% 1.06/1.09 (m_main_v_state2(s29, c_n2)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2815, 2804, 2749, 2800, 2796, 2792, 2788])).
% 1.06/1.09 tff(2817,plain,
% 1.06/1.09 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_t2)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2818,plain,
% 1.06/1.09 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_t2)))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2819,plain,
% 1.06/1.09 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_t2))),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 1.06/1.09 tff(2820,plain,
% 1.06/1.09 (~m_main_v_state2(s29, c_t2)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2819, 77, 2816])).
% 1.06/1.09 tff(2821,plain,
% 1.06/1.09 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s29, c_t2) | (~node15(s29)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s29, c_t2) | (~node15(s29)))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2822,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s29, c_t2) | (~node15(s29)))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2823,plain,
% 1.06/1.09 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s29, c_t2) | (~node15(s29))),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 1.06/1.09 tff(2824,plain,
% 1.06/1.09 (~node15(s29)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2823, 103, 2820])).
% 1.06/1.09 tff(2825,plain,
% 1.06/1.09 (succ(s29, s30) <=> succ(s29, s30)),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2826,axiom,(succ(s29, s30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound30')).
% 1.06/1.09 tff(2827,plain,
% 1.06/1.09 (succ(s29, s30)),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 1.06/1.09 tff(2828,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2829,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2830,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30)),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 1.06/1.09 tff(2831,plain,
% 1.06/1.09 (trans(s29, s30)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2830, 2827, 32])).
% 1.06/1.09 tff(2832,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s29, s30)) | node18(s29, s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s29, s30)) | node18(s29, s30))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2833,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s29, s30)) | node18(s29, s30))),
% 1.06/1.09 inference(quant_inst,[status(thm)],[])).
% 1.06/1.09 tff(2834,plain,
% 1.06/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s29, s30)) | node18(s29, s30)),
% 1.06/1.09 inference(modus_ponens,[status(thm)],[2833, 2832])).
% 1.06/1.09 tff(2835,plain,
% 1.06/1.09 (node18(s29, s30)),
% 1.06/1.09 inference(unit_resolution,[status(thm)],[2834, 125, 2831])).
% 1.06/1.09 tff(2836,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s29) | (~node18(s29, s30)) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s29) | (~node18(s29, s30)) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2837,plain,
% 1.06/1.09 (((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node15(s29) | (~node18(s29, s30)) | m_main_v_turn(s30, c_1)) <=> (node15(s29) | (~node18(s29, s30)) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1))),
% 1.06/1.09 inference(rewrite,[status(thm)],[])).
% 1.06/1.09 tff(2838,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node15(s29) | (~node18(s29, s30)) | m_main_v_turn(s30, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s29) | (~node18(s29, s30)) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1)))),
% 1.06/1.09 inference(monotonicity,[status(thm)],[2837])).
% 1.06/1.09 tff(2839,plain,
% 1.06/1.09 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node15(s29) | (~node18(s29, s30)) | m_main_v_turn(s30, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s29) | (~node18(s29, s30)) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1))),
% 1.06/1.10 inference(transitivity,[status(thm)],[2838, 2836])).
% 1.06/1.10 tff(2840,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node15(s29) | (~node18(s29, s30)) | m_main_v_turn(s30, c_1))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2841,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s29) | (~node18(s29, s30)) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1)),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2840, 2839])).
% 1.06/1.10 tff(2842,plain,
% 1.06/1.10 (node15(s29) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2841, 992, 2835])).
% 1.06/1.10 tff(2843,plain,
% 1.06/1.10 (m_main_v_turn(s30, c_1)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2842, 2824, 2816, 2780])).
% 1.06/1.10 tff(2844,plain,
% 1.06/1.10 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s30, c_1)) | (~m_main_v_turn(s30, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s30, c_1)) | (~m_main_v_turn(s30, c_2)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2845,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s30, c_1)) | (~m_main_v_turn(s30, c_2)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2846,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s30, c_1)) | (~m_main_v_turn(s30, c_2))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 1.06/1.10 tff(2847,plain,
% 1.06/1.10 (~m_main_v_turn(s30, c_2)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2846, 156, 2843])).
% 1.06/1.10 tff(2848,plain,
% 1.06/1.10 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s30, c_2) | (~node12(s30)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s30, c_2) | (~node12(s30)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2849,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s30, c_2) | (~node12(s30)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2850,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s30, c_2) | (~node12(s30))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2849, 2848])).
% 1.06/1.10 tff(2851,plain,
% 1.06/1.10 (~node12(s30)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2850, 184, 2847])).
% 1.06/1.10 tff(2852,plain,
% 1.06/1.10 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s29, s30)) | node14(s29, s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s29, s30)) | node14(s29, s30))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2853,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s29, s30)) | node14(s29, s30))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2854,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s29, s30)) | node14(s29, s30)),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 1.06/1.10 tff(2855,plain,
% 1.06/1.10 (node14(s29, s30)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2854, 46, 2831])).
% 1.06/1.10 tff(2856,plain,
% 1.06/1.10 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | (~node14(s29, s30)) | m_main_v_state2(s30, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | (~node14(s29, s30)) | m_main_v_state2(s30, c_t2))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2857,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | (~node14(s29, s30)) | m_main_v_state2(s30, c_t2))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2858,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | (~node14(s29, s30)) | m_main_v_state2(s30, c_t2)),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2857, 2856])).
% 1.06/1.10 tff(2859,plain,
% 1.06/1.10 ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state2(s30, c_t2)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2858, 922, 2855])).
% 1.06/1.10 tff(2860,plain,
% 1.06/1.10 (m_main_v_state2(s30, c_t2)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2859, 2780, 2816])).
% 1.06/1.10 tff(2861,plain,
% 1.06/1.10 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s30, c_n2)) | (~m_main_v_state2(s30, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s30, c_n2)) | (~m_main_v_state2(s30, c_t2)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2862,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s30, c_n2)) | (~m_main_v_state2(s30, c_t2)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2863,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s30, c_n2)) | (~m_main_v_state2(s30, c_t2))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 1.06/1.10 tff(2864,plain,
% 1.06/1.10 (~m_main_v_state2(s30, c_n2)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2863, 77, 2860])).
% 1.06/1.10 tff(2865,plain,
% 1.06/1.10 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s30, c_n2) | (~node8(s30)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s30, c_n2) | (~node8(s30)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2866,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s30, c_n2) | (~node8(s30)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2867,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s30, c_n2) | (~node8(s30))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2866, 2865])).
% 1.06/1.10 tff(2868,plain,
% 1.06/1.10 (~node8(s30)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2867, 271, 2864])).
% 1.06/1.10 tff(2869,plain,
% 1.06/1.10 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s30, c_n2) | (~node9(s30)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s30, c_n2) | (~node9(s30)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2870,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s30, c_n2) | (~node9(s30)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2871,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s30, c_n2) | (~node9(s30))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 1.06/1.10 tff(2872,plain,
% 1.06/1.10 (~node9(s30)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2871, 88, 2864])).
% 1.06/1.10 tff(2873,plain,
% 1.06/1.10 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s30, c_n2) | (~node10(s30)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s30, c_n2) | (~node10(s30)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2874,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s30, c_n2) | (~node10(s30)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2875,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s30, c_n2) | (~node10(s30))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2874, 2873])).
% 1.06/1.10 tff(2876,plain,
% 1.06/1.10 (~node10(s30)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2875, 249, 2864])).
% 1.06/1.10 tff(2877,plain,
% 1.06/1.10 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s30, c_t2)) | (~m_main_v_state2(s30, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s30, c_t2)) | (~m_main_v_state2(s30, c_c2)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2878,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s30, c_t2)) | (~m_main_v_state2(s30, c_c2)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2879,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s30, c_t2)) | (~m_main_v_state2(s30, c_c2))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2878, 2877])).
% 1.06/1.10 tff(2880,plain,
% 1.06/1.10 (~m_main_v_state2(s30, c_c2)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2879, 260, 2860])).
% 1.06/1.10 tff(2881,plain,
% 1.06/1.10 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_c2)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2882,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_c2)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2883,plain,
% 1.06/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s29, c_n2)) | (~m_main_v_state2(s29, c_c2))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2882, 2881])).
% 1.06/1.10 tff(2884,plain,
% 1.06/1.10 (~m_main_v_state2(s29, c_c2)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2883, 697, 2816])).
% 1.06/1.10 tff(2885,plain,
% 1.06/1.10 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s29, c_c2) | (~node3(s29)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s29, c_c2) | (~node3(s29)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2886,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s29, c_c2) | (~node3(s29)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2887,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s29, c_c2) | (~node3(s29))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2886, 2885])).
% 1.06/1.10 tff(2888,plain,
% 1.06/1.10 (~node3(s29)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2887, 399, 2884])).
% 1.06/1.10 tff(2889,plain,
% 1.06/1.10 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)) | (~node6(s28, s29)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)) | (~node6(s28, s29)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2890,plain,
% 1.06/1.10 (((~node6(s28, s29)) | m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1))) <=> (m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)) | (~node6(s28, s29)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2891,plain,
% 1.06/1.10 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s28, s29)) | m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)) | (~node6(s28, s29))))),
% 1.06/1.10 inference(monotonicity,[status(thm)],[2890])).
% 1.06/1.10 tff(2892,plain,
% 1.06/1.10 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s28, s29)) | m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)) | (~node6(s28, s29)))),
% 1.06/1.10 inference(transitivity,[status(thm)],[2891, 2889])).
% 1.06/1.10 tff(2893,plain,
% 1.06/1.10 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s28, s29)) | m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2894,plain,
% 1.06/1.10 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s28, c_n1) | (~m_main_v_state1(s29, c_n1)) | (~node6(s28, s29))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 1.06/1.10 tff(2895,plain,
% 1.06/1.10 (~m_main_v_state1(s29, c_n1)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2894, 835, 2688, 2773])).
% 1.06/1.10 tff(2896,plain,
% 1.06/1.10 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s29, c_n1) | (~node2(s29)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s29, c_n1) | (~node2(s29)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2897,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s29, c_n1) | (~node2(s29)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2898,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s29, c_n1) | (~node2(s29))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 1.06/1.10 tff(2899,plain,
% 1.06/1.10 (~node2(s29)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2898, 787, 2895])).
% 1.06/1.10 tff(2900,plain,
% 1.06/1.10 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s29, c_t2) | (~node1(s29)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s29, c_t2) | (~node1(s29)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2901,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s29, c_t2) | (~node1(s29)))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2902,plain,
% 1.06/1.10 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s29, c_t2) | (~node1(s29))),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.06/1.10 tff(2903,plain,
% 1.06/1.10 (~node1(s29)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2902, 195, 2820])).
% 1.06/1.10 tff(2904,plain,
% 1.06/1.10 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s29, s30)) | node7(s29, s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s29, s30)) | node7(s29, s30))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2905,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s29, s30)) | node7(s29, s30))),
% 1.06/1.10 inference(quant_inst,[status(thm)],[])).
% 1.06/1.10 tff(2906,plain,
% 1.06/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s29, s30)) | node7(s29, s30)),
% 1.06/1.10 inference(modus_ponens,[status(thm)],[2905, 2904])).
% 1.06/1.10 tff(2907,plain,
% 1.06/1.10 (node7(s29, s30)),
% 1.06/1.10 inference(unit_resolution,[status(thm)],[2906, 206, 2831])).
% 1.06/1.10 tff(2908,plain,
% 1.06/1.10 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state1(s30, c_c1) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state1(s30, c_c1) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2909,plain,
% 1.06/1.10 (((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)) | m_main_v_state1(s30, c_c1)) <=> ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state1(s30, c_c1) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)))),
% 1.06/1.10 inference(rewrite,[status(thm)],[])).
% 1.06/1.10 tff(2910,plain,
% 1.06/1.10 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)) | m_main_v_state1(s30, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state1(s30, c_c1) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30))))),
% 1.06/1.11 inference(monotonicity,[status(thm)],[2909])).
% 1.06/1.11 tff(2911,plain,
% 1.06/1.11 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)) | m_main_v_state1(s30, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state1(s30, c_c1) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)))),
% 1.06/1.11 inference(transitivity,[status(thm)],[2910, 2908])).
% 1.06/1.11 tff(2912,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30)) | m_main_v_state1(s30, c_c1))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2913,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state1(s30, c_c1) | node1(s29) | node2(s29) | node3(s29) | (~node7(s29, s30))),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2912, 2911])).
% 1.06/1.11 tff(2914,plain,
% 1.06/1.11 ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state1(s30, c_c1) | node1(s29) | node2(s29) | node3(s29)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2913, 892, 2907])).
% 1.06/1.11 tff(2915,plain,
% 1.06/1.11 (m_main_v_state1(s30, c_c1)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2914, 2903, 2816, 2780, 2899, 2888])).
% 1.06/1.11 tff(2916,plain,
% 1.06/1.11 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s30, c_n1)) | (~m_main_v_state1(s30, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s30, c_n1)) | (~m_main_v_state1(s30, c_c1)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2917,plain,
% 1.06/1.11 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s30, c_n1)) | (~m_main_v_state1(s30, c_c1)))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2918,plain,
% 1.06/1.11 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s30, c_n1)) | (~m_main_v_state1(s30, c_c1))),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 1.06/1.11 tff(2919,plain,
% 1.06/1.11 (~m_main_v_state1(s30, c_n1)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2918, 454, 2915])).
% 1.06/1.11 tff(2920,plain,
% 1.06/1.11 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s30, c_n1) | (~node11(s30)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s30, c_n1) | (~node11(s30)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2921,plain,
% 1.06/1.11 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s30, c_n1) | (~node11(s30)))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2922,plain,
% 1.06/1.11 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s30, c_n1) | (~node11(s30))),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2921, 2920])).
% 1.06/1.11 tff(2923,plain,
% 1.06/1.11 (~node11(s30)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2922, 238, 2919])).
% 1.06/1.11 tff(2924,plain,
% 1.06/1.11 (succ(s30, s31) <=> succ(s30, s31)),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2925,axiom,(succ(s30, s31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound31')).
% 1.06/1.11 tff(2926,plain,
% 1.06/1.11 (succ(s30, s31)),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 1.06/1.11 tff(2927,plain,
% 1.06/1.11 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2928,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2929,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31)),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2928, 2927])).
% 1.06/1.11 tff(2930,plain,
% 1.06/1.11 (trans(s30, s31)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2929, 2926, 32])).
% 1.06/1.11 tff(2931,plain,
% 1.06/1.11 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s30, s31)) | node14(s30, s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s30, s31)) | node14(s30, s31))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2932,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s30, s31)) | node14(s30, s31))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2933,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s30, s31)) | node14(s30, s31)),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 1.06/1.11 tff(2934,plain,
% 1.06/1.11 (node14(s30, s31)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2933, 46, 2930])).
% 1.06/1.11 tff(2935,plain,
% 1.06/1.11 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31) | (~node14(s30, s31)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31) | (~node14(s30, s31)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2936,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31) | (~node14(s30, s31)))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2937,plain,
% 1.06/1.11 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31) | (~node14(s30, s31))),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 1.06/1.11 tff(2938,plain,
% 1.06/1.11 (m_main_v_state2(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2937, 296, 2934])).
% 1.06/1.11 tff(2939,plain,
% 1.06/1.11 (node13(s30, s31)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2938, 2923, 2880, 2876, 2872, 2868, 2851])).
% 1.06/1.11 tff(2940,plain,
% 1.06/1.11 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2941,plain,
% 1.06/1.11 (((~node13(s30, s31)) | m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2))) <=> (m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2942,plain,
% 1.06/1.11 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s30, s31)) | m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31))))),
% 1.06/1.11 inference(monotonicity,[status(thm)],[2941])).
% 1.06/1.11 tff(2943,plain,
% 1.06/1.11 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s30, s31)) | m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31)))),
% 1.06/1.11 inference(transitivity,[status(thm)],[2942, 2940])).
% 1.06/1.11 tff(2944,plain,
% 1.06/1.11 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s30, s31)) | m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2945,plain,
% 1.06/1.11 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31))),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2944, 2943])).
% 1.06/1.11 tff(2946,plain,
% 1.06/1.11 (~m_main_v_state2(s31, c_n2)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2945, 311, 2864, 2939])).
% 1.06/1.11 tff(2947,plain,
% 1.06/1.11 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s31, c_n2) | (~node9(s31)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s31, c_n2) | (~node9(s31)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2948,plain,
% 1.06/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s31, c_n2) | (~node9(s31)))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2949,plain,
% 1.06/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s31, c_n2) | (~node9(s31))),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2948, 2947])).
% 1.06/1.11 tff(2950,plain,
% 1.06/1.11 (~node9(s31)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2949, 88, 2946])).
% 1.06/1.11 tff(2951,plain,
% 1.06/1.11 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s31, c_n2) | (~node10(s31)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s31, c_n2) | (~node10(s31)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2952,plain,
% 1.06/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s31, c_n2) | (~node10(s31)))),
% 1.06/1.11 inference(quant_inst,[status(thm)],[])).
% 1.06/1.11 tff(2953,plain,
% 1.06/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s31, c_n2) | (~node10(s31))),
% 1.06/1.11 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 1.06/1.11 tff(2954,plain,
% 1.06/1.11 (~node10(s31)),
% 1.06/1.11 inference(unit_resolution,[status(thm)],[2953, 249, 2946])).
% 1.06/1.11 tff(2955,plain,
% 1.06/1.11 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2956,plain,
% 1.06/1.11 (((~node13(s30, s31)) | (~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2)) <=> ((~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31)))),
% 1.06/1.11 inference(rewrite,[status(thm)],[])).
% 1.06/1.11 tff(2957,plain,
% 1.06/1.11 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s30, s31)) | (~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31))))),
% 1.06/1.11 inference(monotonicity,[status(thm)],[2956])).
% 1.06/1.11 tff(2958,plain,
% 1.06/1.11 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s30, s31)) | (~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31)))),
% 1.06/1.11 inference(transitivity,[status(thm)],[2957, 2955])).
% 1.06/1.12 tff(2959,plain,
% 1.06/1.12 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s30, s31)) | (~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2960,plain,
% 1.06/1.12 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 1.06/1.12 tff(2961,plain,
% 1.06/1.12 (m_main_v_state2(s31, c_t2)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2960, 518, 2860, 2939])).
% 1.06/1.12 tff(2962,plain,
% 1.06/1.12 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s30, c_t1)) | (~m_main_v_state1(s30, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s30, c_t1)) | (~m_main_v_state1(s30, c_c1)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2963,plain,
% 1.06/1.12 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s30, c_t1)) | (~m_main_v_state1(s30, c_c1)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2964,plain,
% 1.06/1.12 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s30, c_t1)) | (~m_main_v_state1(s30, c_c1))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 1.06/1.12 tff(2965,plain,
% 1.06/1.12 (~m_main_v_state1(s30, c_t1)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2964, 539, 2915])).
% 1.06/1.12 tff(2966,plain,
% 1.06/1.12 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s30, c_t1) | (~node5(s30)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s30, c_t1) | (~node5(s30)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2967,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s30, c_t1) | (~node5(s30)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2968,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s30, c_t1) | (~node5(s30))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 1.06/1.12 tff(2969,plain,
% 1.06/1.12 (~node5(s30)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2968, 550, 2965])).
% 1.06/1.12 tff(2970,plain,
% 1.06/1.12 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s30, c_n2) | (~node4(s30)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s30, c_n2) | (~node4(s30)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2971,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s30, c_n2) | (~node4(s30)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2972,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s30, c_n2) | (~node4(s30))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2971, 2970])).
% 1.06/1.12 tff(2973,plain,
% 1.06/1.12 (~node4(s30)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2972, 388, 2864])).
% 1.06/1.12 tff(2974,plain,
% 1.06/1.12 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s30, c_c2) | (~node3(s30)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s30, c_c2) | (~node3(s30)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2975,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s30, c_c2) | (~node3(s30)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2976,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s30, c_c2) | (~node3(s30))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 1.06/1.12 tff(2977,plain,
% 1.06/1.12 (~node3(s30)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2976, 399, 2880])).
% 1.06/1.12 tff(2978,plain,
% 1.06/1.12 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s30, c_n2) | (~node2(s30)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s30, c_n2) | (~node2(s30)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2979,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s30, c_n2) | (~node2(s30)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2980,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s30, c_n2) | (~node2(s30))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 1.06/1.12 tff(2981,plain,
% 1.06/1.12 (~node2(s30)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2980, 410, 2864])).
% 1.06/1.12 tff(2982,plain,
% 1.06/1.12 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s30, c_n1) | (~node1(s30)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s30, c_n1) | (~node1(s30)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2983,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s30, c_n1) | (~node1(s30)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2984,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s30, c_n1) | (~node1(s30))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2983, 2982])).
% 1.06/1.12 tff(2985,plain,
% 1.06/1.12 (~node1(s30)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2984, 421, 2919])).
% 1.06/1.12 tff(2986,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s30, s31)) | node7(s30, s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s30, s31)) | node7(s30, s31))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2987,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s30, s31)) | node7(s30, s31))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2988,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s30, s31)) | node7(s30, s31)),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2987, 2986])).
% 1.06/1.12 tff(2989,plain,
% 1.06/1.12 (node7(s30, s31)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2988, 206, 2930])).
% 1.06/1.12 tff(2990,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2991,plain,
% 1.06/1.12 (((~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)) | m_main_v_state1(s31, c_n1)) <=> (m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2992,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)) | m_main_v_state1(s31, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31))))),
% 1.06/1.12 inference(monotonicity,[status(thm)],[2991])).
% 1.06/1.12 tff(2993,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)) | m_main_v_state1(s31, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)))),
% 1.06/1.12 inference(transitivity,[status(thm)],[2992, 2990])).
% 1.06/1.12 tff(2994,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)) | m_main_v_state1(s31, c_n1))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(2995,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 1.06/1.12 tff(2996,plain,
% 1.06/1.12 (m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2995, 584, 2989])).
% 1.06/1.12 tff(2997,plain,
% 1.06/1.12 (m_main_v_state1(s31, c_n1)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[2996, 2985, 2915, 2981, 2977, 2973, 2969])).
% 1.06/1.12 tff(2998,plain,
% 1.06/1.12 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s31, c_n2) | (~node8(s31)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s31, c_n2) | (~node8(s31)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(2999,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s31, c_n2) | (~node8(s31)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(3000,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s31, c_n2) | (~node8(s31))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 1.06/1.12 tff(3001,plain,
% 1.06/1.12 (~node8(s31)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3000, 271, 2946])).
% 1.06/1.12 tff(3002,plain,
% 1.06/1.12 (succ(s31, s32) <=> succ(s31, s32)),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(3003,axiom,(succ(s31, s32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound32')).
% 1.06/1.12 tff(3004,plain,
% 1.06/1.12 (succ(s31, s32)),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[3003, 3002])).
% 1.06/1.12 tff(3005,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(3006,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(3007,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32)),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 1.06/1.12 tff(3008,plain,
% 1.06/1.12 (trans(s31, s32)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3007, 3004, 32])).
% 1.06/1.12 tff(3009,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s31, s32)) | node14(s31, s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s31, s32)) | node14(s31, s32))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(3010,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s31, s32)) | node14(s31, s32))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(3011,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s31, s32)) | node14(s31, s32)),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[3010, 3009])).
% 1.06/1.12 tff(3012,plain,
% 1.06/1.12 (node14(s31, s32)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3011, 46, 3008])).
% 1.06/1.12 tff(3013,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | node9(s31) | node8(s31) | node10(s31) | (~node14(s31, s32)) | m_main_v_state2(s32, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | node9(s31) | node8(s31) | node10(s31) | (~node14(s31, s32)) | m_main_v_state2(s32, c_c2))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(3014,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | node9(s31) | node8(s31) | node10(s31) | (~node14(s31, s32)) | m_main_v_state2(s32, c_c2))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(3015,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | node9(s31) | node8(s31) | node10(s31) | (~node14(s31, s32)) | m_main_v_state2(s32, c_c2)),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 1.06/1.12 tff(3016,plain,
% 1.06/1.12 ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | node9(s31) | node8(s31) | node10(s31) | m_main_v_state2(s32, c_c2)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3015, 617, 3012])).
% 1.06/1.12 tff(3017,plain,
% 1.06/1.12 (m_main_v_state2(s32, c_c2)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3016, 3001, 2997, 2961, 2954, 2950])).
% 1.06/1.12 tff(3018,plain,
% 1.06/1.12 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s32, c_t2)) | (~m_main_v_state2(s32, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s32, c_t2)) | (~m_main_v_state2(s32, c_c2)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(3019,plain,
% 1.06/1.12 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s32, c_t2)) | (~m_main_v_state2(s32, c_c2)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(3020,plain,
% 1.06/1.12 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s32, c_t2)) | (~m_main_v_state2(s32, c_c2))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 1.06/1.12 tff(3021,plain,
% 1.06/1.12 (~m_main_v_state2(s32, c_t2)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3020, 260, 3017])).
% 1.06/1.12 tff(3022,plain,
% 1.06/1.12 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s32, c_t2) | (~node12(s32)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s32, c_t2) | (~node12(s32)))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(3023,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s32, c_t2) | (~node12(s32)))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(3024,plain,
% 1.06/1.12 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s32, c_t2) | (~node12(s32))),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 1.06/1.12 tff(3025,plain,
% 1.06/1.12 (~node12(s32)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3024, 633, 3021])).
% 1.06/1.12 tff(3026,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s31, s32)) | node7(s31, s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s31, s32)) | node7(s31, s32))),
% 1.06/1.12 inference(rewrite,[status(thm)],[])).
% 1.06/1.12 tff(3027,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s31, s32)) | node7(s31, s32))),
% 1.06/1.12 inference(quant_inst,[status(thm)],[])).
% 1.06/1.12 tff(3028,plain,
% 1.06/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s31, s32)) | node7(s31, s32)),
% 1.06/1.12 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 1.06/1.12 tff(3029,plain,
% 1.06/1.12 (node7(s31, s32)),
% 1.06/1.12 inference(unit_resolution,[status(thm)],[3028, 206, 3008])).
% 1.06/1.12 tff(3030,plain,
% 1.06/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3031,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3032,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1)),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3031, 3030])).
% 1.11/1.13 tff(3033,plain,
% 1.11/1.13 ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | m_main_v_state1(s32, c_t1)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3032, 651, 3029])).
% 1.11/1.13 tff(3034,plain,
% 1.11/1.13 (m_main_v_state1(s32, c_t1)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3033, 2961, 2997])).
% 1.11/1.13 tff(3035,plain,
% 1.11/1.13 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s32, c_n1)) | (~m_main_v_state1(s32, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s32, c_n1)) | (~m_main_v_state1(s32, c_t1)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3036,plain,
% 1.11/1.13 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s32, c_n1)) | (~m_main_v_state1(s32, c_t1)))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3037,plain,
% 1.11/1.13 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s32, c_n1)) | (~m_main_v_state1(s32, c_t1))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 1.11/1.13 tff(3038,plain,
% 1.11/1.13 (~m_main_v_state1(s32, c_n1)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3037, 10, 3034])).
% 1.11/1.13 tff(3039,plain,
% 1.11/1.13 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s32, c_n1) | (~node11(s32)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s32, c_n1) | (~node11(s32)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3040,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s32, c_n1) | (~node11(s32)))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3041,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s32, c_n1) | (~node11(s32))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3040, 3039])).
% 1.11/1.13 tff(3042,plain,
% 1.11/1.13 (~node11(s32)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3041, 238, 3038])).
% 1.11/1.13 tff(3043,plain,
% 1.11/1.13 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s32, c_t1)) | (~m_main_v_state1(s32, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s32, c_t1)) | (~m_main_v_state1(s32, c_c1)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3044,plain,
% 1.11/1.13 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s32, c_t1)) | (~m_main_v_state1(s32, c_c1)))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3045,plain,
% 1.11/1.13 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s32, c_t1)) | (~m_main_v_state1(s32, c_c1))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3044, 3043])).
% 1.11/1.13 tff(3046,plain,
% 1.11/1.13 (~m_main_v_state1(s32, c_c1)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3045, 539, 3034])).
% 1.11/1.13 tff(3047,plain,
% 1.11/1.13 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s32, c_c1) | (~node10(s32)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s32, c_c1) | (~node10(s32)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3048,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s32, c_c1) | (~node10(s32)))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3049,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s32, c_c1) | (~node10(s32))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 1.11/1.13 tff(3050,plain,
% 1.11/1.13 (~node10(s32)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3049, 675, 3046])).
% 1.11/1.13 tff(3051,plain,
% 1.11/1.13 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s32, c_n1) | (~node9(s32)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s32, c_n1) | (~node9(s32)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3052,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s32, c_n1) | (~node9(s32)))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3053,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s32, c_n1) | (~node9(s32))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 1.11/1.13 tff(3054,plain,
% 1.11/1.13 (~node9(s32)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3053, 686, 3038])).
% 1.11/1.13 tff(3055,plain,
% 1.11/1.13 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s32, c_n2)) | (~m_main_v_state2(s32, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s32, c_n2)) | (~m_main_v_state2(s32, c_c2)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3056,plain,
% 1.11/1.13 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s32, c_n2)) | (~m_main_v_state2(s32, c_c2)))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3057,plain,
% 1.11/1.13 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s32, c_n2)) | (~m_main_v_state2(s32, c_c2))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3056, 3055])).
% 1.11/1.13 tff(3058,plain,
% 1.11/1.13 (~m_main_v_state2(s32, c_n2)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3057, 697, 3017])).
% 1.11/1.13 tff(3059,plain,
% 1.11/1.13 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s32, c_n2) | (~node8(s32)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s32, c_n2) | (~node8(s32)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3060,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s32, c_n2) | (~node8(s32)))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3061,plain,
% 1.11/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s32, c_n2) | (~node8(s32))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3060, 3059])).
% 1.11/1.13 tff(3062,plain,
% 1.11/1.13 (~node8(s32)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3061, 271, 3058])).
% 1.11/1.13 tff(3063,plain,
% 1.11/1.13 (succ(s32, s33) <=> succ(s32, s33)),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3064,axiom,(succ(s32, s33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound33')).
% 1.11/1.13 tff(3065,plain,
% 1.11/1.13 (succ(s32, s33)),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3064, 3063])).
% 1.11/1.13 tff(3066,plain,
% 1.11/1.13 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3067,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3068,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33)),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 1.11/1.13 tff(3069,plain,
% 1.11/1.13 (trans(s32, s33)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3068, 3065, 32])).
% 1.11/1.13 tff(3070,plain,
% 1.11/1.13 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s32, s33)) | node14(s32, s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s32, s33)) | node14(s32, s33))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3071,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s32, s33)) | node14(s32, s33))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3072,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s32, s33)) | node14(s32, s33)),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 1.11/1.13 tff(3073,plain,
% 1.11/1.13 (node14(s32, s33)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3072, 46, 3069])).
% 1.11/1.13 tff(3074,plain,
% 1.11/1.13 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | (~m_main_v_state2(s32, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | (~m_main_v_state2(s32, c_c2)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3075,plain,
% 1.11/1.13 (((~m_main_v_state2(s32, c_c2)) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | m_main_v_state2(s33, c_n2)) <=> (m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | (~m_main_v_state2(s32, c_c2)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3076,plain,
% 1.11/1.13 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s32, c_c2)) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | m_main_v_state2(s33, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | (~m_main_v_state2(s32, c_c2))))),
% 1.11/1.13 inference(monotonicity,[status(thm)],[3075])).
% 1.11/1.13 tff(3077,plain,
% 1.11/1.13 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s32, c_c2)) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | m_main_v_state2(s33, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | (~m_main_v_state2(s32, c_c2)))),
% 1.11/1.13 inference(transitivity,[status(thm)],[3076, 3074])).
% 1.11/1.13 tff(3078,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s32, c_c2)) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | m_main_v_state2(s33, c_n2))),
% 1.11/1.13 inference(quant_inst,[status(thm)],[])).
% 1.11/1.13 tff(3079,plain,
% 1.11/1.13 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | (~m_main_v_state2(s32, c_c2))),
% 1.11/1.13 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 1.11/1.13 tff(3080,plain,
% 1.11/1.13 (m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~m_main_v_state2(s32, c_c2))),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3079, 726, 3073])).
% 1.11/1.13 tff(3081,plain,
% 1.11/1.13 (m_main_v_state2(s33, c_n2)),
% 1.11/1.13 inference(unit_resolution,[status(thm)],[3080, 3062, 3017, 3054, 3050, 3042, 3025])).
% 1.11/1.13 tff(3082,plain,
% 1.11/1.13 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_c2)))),
% 1.11/1.13 inference(rewrite,[status(thm)],[])).
% 1.11/1.13 tff(3083,plain,
% 1.11/1.13 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_c2)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3084,plain,
% 1.11/1.14 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_c2))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 1.11/1.14 tff(3085,plain,
% 1.11/1.14 (~m_main_v_state2(s33, c_c2)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3084, 697, 3081])).
% 1.11/1.14 tff(3086,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s33, c_c2) | (~node3(s33)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s33, c_c2) | (~node3(s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3087,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s33, c_c2) | (~node3(s33)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3088,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s33, c_c2) | (~node3(s33))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 1.11/1.14 tff(3089,plain,
% 1.11/1.14 (~node3(s33)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3088, 399, 3085])).
% 1.11/1.14 tff(3090,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s32, c_n1) | (~node1(s32)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s32, c_n1) | (~node1(s32)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3091,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s32, c_n1) | (~node1(s32)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3092,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s32, c_n1) | (~node1(s32))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3091, 3090])).
% 1.11/1.14 tff(3093,plain,
% 1.11/1.14 (~node1(s32)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3092, 421, 3038])).
% 1.11/1.14 tff(3094,plain,
% 1.11/1.14 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s31, s32)) | node18(s31, s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s31, s32)) | node18(s31, s32))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3095,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s31, s32)) | node18(s31, s32))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3096,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s31, s32)) | node18(s31, s32)),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3095, 3094])).
% 1.11/1.14 tff(3097,plain,
% 1.11/1.14 (node18(s31, s32)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3096, 125, 3008])).
% 1.11/1.14 tff(3098,plain,
% 1.11/1.14 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3099,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3100,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2)),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3099, 3098])).
% 1.11/1.14 tff(3101,plain,
% 1.11/1.14 ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | m_main_v_turn(s32, c_2)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3100, 760, 3097])).
% 1.11/1.14 tff(3102,plain,
% 1.11/1.14 (m_main_v_turn(s32, c_2)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3101, 2961, 2997])).
% 1.11/1.14 tff(3103,plain,
% 1.11/1.14 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s32, c_1)) | (~m_main_v_turn(s32, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s32, c_1)) | (~m_main_v_turn(s32, c_2)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3104,plain,
% 1.11/1.14 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s32, c_1)) | (~m_main_v_turn(s32, c_2)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3105,plain,
% 1.11/1.14 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s32, c_1)) | (~m_main_v_turn(s32, c_2))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3104, 3103])).
% 1.11/1.14 tff(3106,plain,
% 1.11/1.14 (~m_main_v_turn(s32, c_1)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3105, 156, 3102])).
% 1.11/1.14 tff(3107,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s32, c_1) | (~node5(s32)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s32, c_1) | (~node5(s32)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3108,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s32, c_1) | (~node5(s32)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3109,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s32, c_1) | (~node5(s32))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3108, 3107])).
% 1.11/1.14 tff(3110,plain,
% 1.11/1.14 (~node5(s32)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3109, 776, 3106])).
% 1.11/1.14 tff(3111,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s32, c_n1) | (~node2(s32)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s32, c_n1) | (~node2(s32)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3112,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s32, c_n1) | (~node2(s32)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3113,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s32, c_n1) | (~node2(s32))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3112, 3111])).
% 1.11/1.14 tff(3114,plain,
% 1.11/1.14 (~node2(s32)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3113, 787, 3038])).
% 1.11/1.14 tff(3115,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s32, c_n1) | (~node3(s32)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s32, c_n1) | (~node3(s32)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3116,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s32, c_n1) | (~node3(s32)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3117,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s32, c_n1) | (~node3(s32))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 1.11/1.14 tff(3118,plain,
% 1.11/1.14 (~node3(s32)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3117, 798, 3038])).
% 1.11/1.14 tff(3119,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s32, c_n2) | (~node4(s32)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s32, c_n2) | (~node4(s32)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3120,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s32, c_n2) | (~node4(s32)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3121,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s32, c_n2) | (~node4(s32))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3120, 3119])).
% 1.11/1.14 tff(3122,plain,
% 1.11/1.14 (~node4(s32)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3121, 388, 3058])).
% 1.11/1.14 tff(3123,plain,
% 1.11/1.14 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s32, s33)) | node7(s32, s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s32, s33)) | node7(s32, s33))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3124,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s32, s33)) | node7(s32, s33))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3125,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s32, s33)) | node7(s32, s33)),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3124, 3123])).
% 1.11/1.14 tff(3126,plain,
% 1.11/1.14 (node7(s32, s33)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3125, 206, 3069])).
% 1.11/1.14 tff(3127,plain,
% 1.11/1.14 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s32, c_c1) | node1(s32) | node2(s32) | node3(s32) | node4(s32) | node5(s32) | node6(s32, s33) | (~node7(s32, s33)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s32, c_c1) | node1(s32) | node2(s32) | node3(s32) | node4(s32) | node5(s32) | node6(s32, s33) | (~node7(s32, s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3128,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s32, c_c1) | node1(s32) | node2(s32) | node3(s32) | node4(s32) | node5(s32) | node6(s32, s33) | (~node7(s32, s33)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3129,plain,
% 1.11/1.14 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s32, c_c1) | node1(s32) | node2(s32) | node3(s32) | node4(s32) | node5(s32) | node6(s32, s33) | (~node7(s32, s33))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3128, 3127])).
% 1.11/1.14 tff(3130,plain,
% 1.11/1.14 (m_main_v_state1(s32, c_c1) | node1(s32) | node2(s32) | node3(s32) | node4(s32) | node5(s32) | node6(s32, s33)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3129, 820, 3126])).
% 1.11/1.14 tff(3131,plain,
% 1.11/1.14 (node6(s32, s33)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3130, 3122, 3046, 3118, 3114, 3110, 3093])).
% 1.11/1.14 tff(3132,plain,
% 1.11/1.14 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3133,plain,
% 1.11/1.14 (((~node6(s32, s33)) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1))) <=> (m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3134,plain,
% 1.11/1.14 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s32, s33)) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33))))),
% 1.11/1.14 inference(monotonicity,[status(thm)],[3133])).
% 1.11/1.14 tff(3135,plain,
% 1.11/1.14 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s32, s33)) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33)))),
% 1.11/1.14 inference(transitivity,[status(thm)],[3134, 3132])).
% 1.11/1.14 tff(3136,plain,
% 1.11/1.14 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s32, s33)) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3137,plain,
% 1.11/1.14 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3136, 3135])).
% 1.11/1.14 tff(3138,plain,
% 1.11/1.14 (~m_main_v_state1(s33, c_n1)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3137, 835, 3038, 3131])).
% 1.11/1.14 tff(3139,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s33, c_n1) | (~node2(s33)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s33, c_n1) | (~node2(s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3140,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s33, c_n1) | (~node2(s33)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3141,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s33, c_n1) | (~node2(s33))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 1.11/1.14 tff(3142,plain,
% 1.11/1.14 (~node2(s33)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3141, 787, 3138])).
% 1.11/1.14 tff(3143,plain,
% 1.11/1.14 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1) | (~node6(s32, s33)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1) | (~node6(s32, s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3144,plain,
% 1.11/1.14 (((~node6(s32, s33)) | (~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1)) <=> ((~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1) | (~node6(s32, s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3145,plain,
% 1.11/1.14 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s32, s33)) | (~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1) | (~node6(s32, s33))))),
% 1.11/1.14 inference(monotonicity,[status(thm)],[3144])).
% 1.11/1.14 tff(3146,plain,
% 1.11/1.14 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s32, s33)) | (~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1) | (~node6(s32, s33)))),
% 1.11/1.14 inference(transitivity,[status(thm)],[3145, 3143])).
% 1.11/1.14 tff(3147,plain,
% 1.11/1.14 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s32, s33)) | (~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3148,plain,
% 1.11/1.14 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s32, c_t1)) | m_main_v_state1(s33, c_t1) | (~node6(s32, s33))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3147, 3146])).
% 1.11/1.14 tff(3149,plain,
% 1.11/1.14 (m_main_v_state1(s33, c_t1)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3148, 856, 3034, 3131])).
% 1.11/1.14 tff(3150,plain,
% 1.11/1.14 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_t2)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3151,plain,
% 1.11/1.14 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_t2)))),
% 1.11/1.14 inference(quant_inst,[status(thm)],[])).
% 1.11/1.14 tff(3152,plain,
% 1.11/1.14 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s33, c_n2)) | (~m_main_v_state2(s33, c_t2))),
% 1.11/1.14 inference(modus_ponens,[status(thm)],[3151, 3150])).
% 1.11/1.14 tff(3153,plain,
% 1.11/1.14 (~m_main_v_state2(s33, c_t2)),
% 1.11/1.14 inference(unit_resolution,[status(thm)],[3152, 77, 3081])).
% 1.11/1.14 tff(3154,plain,
% 1.11/1.14 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s33, c_t2) | (~node1(s33)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s33, c_t2) | (~node1(s33)))),
% 1.11/1.14 inference(rewrite,[status(thm)],[])).
% 1.11/1.14 tff(3155,plain,
% 1.11/1.14 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s33, c_t2) | (~node1(s33)))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3156,plain,
% 1.11/1.15 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s33, c_t2) | (~node1(s33))),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3155, 3154])).
% 1.11/1.15 tff(3157,plain,
% 1.11/1.15 (~node1(s33)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3156, 195, 3153])).
% 1.11/1.15 tff(3158,plain,
% 1.11/1.15 (succ(s33, s34) <=> succ(s33, s34)),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3159,axiom,(succ(s33, s34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound34')).
% 1.11/1.15 tff(3160,plain,
% 1.11/1.15 (succ(s33, s34)),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3159, 3158])).
% 1.11/1.15 tff(3161,plain,
% 1.11/1.15 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3162,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3163,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34)),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3162, 3161])).
% 1.11/1.15 tff(3164,plain,
% 1.11/1.15 (trans(s33, s34)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3163, 3160, 32])).
% 1.11/1.15 tff(3165,plain,
% 1.11/1.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s33, s34)) | node7(s33, s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s33, s34)) | node7(s33, s34))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3166,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s33, s34)) | node7(s33, s34))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3167,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s33, s34)) | node7(s33, s34)),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3166, 3165])).
% 1.11/1.15 tff(3168,plain,
% 1.11/1.15 (node7(s33, s34)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3167, 206, 3164])).
% 1.11/1.15 tff(3169,plain,
% 1.11/1.15 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state1(s34, c_c1) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state1(s34, c_c1) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3170,plain,
% 1.11/1.15 (((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)) | m_main_v_state1(s34, c_c1)) <=> ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state1(s34, c_c1) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3171,plain,
% 1.11/1.15 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)) | m_main_v_state1(s34, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state1(s34, c_c1) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34))))),
% 1.11/1.15 inference(monotonicity,[status(thm)],[3170])).
% 1.11/1.15 tff(3172,plain,
% 1.11/1.15 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)) | m_main_v_state1(s34, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state1(s34, c_c1) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)))),
% 1.11/1.15 inference(transitivity,[status(thm)],[3171, 3169])).
% 1.11/1.15 tff(3173,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34)) | m_main_v_state1(s34, c_c1))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3174,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state1(s34, c_c1) | node1(s33) | node2(s33) | node3(s33) | (~node7(s33, s34))),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 1.11/1.15 tff(3175,plain,
% 1.11/1.15 ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state1(s34, c_c1) | node1(s33) | node2(s33) | node3(s33)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3174, 892, 3168])).
% 1.11/1.15 tff(3176,plain,
% 1.11/1.15 (m_main_v_state1(s34, c_c1)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3175, 3157, 3081, 3149, 3142, 3089])).
% 1.11/1.15 tff(3177,plain,
% 1.11/1.15 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s34, c_t1)) | (~m_main_v_state1(s34, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s34, c_t1)) | (~m_main_v_state1(s34, c_c1)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3178,plain,
% 1.11/1.15 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s34, c_t1)) | (~m_main_v_state1(s34, c_c1)))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3179,plain,
% 1.11/1.15 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s34, c_t1)) | (~m_main_v_state1(s34, c_c1))),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 1.11/1.15 tff(3180,plain,
% 1.11/1.15 (~m_main_v_state1(s34, c_t1)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3179, 539, 3176])).
% 1.11/1.15 tff(3181,plain,
% 1.11/1.15 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s34, c_t1) | (~node5(s34)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s34, c_t1) | (~node5(s34)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3182,plain,
% 1.11/1.15 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s34, c_t1) | (~node5(s34)))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3183,plain,
% 1.11/1.15 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s34, c_t1) | (~node5(s34))),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3182, 3181])).
% 1.11/1.15 tff(3184,plain,
% 1.11/1.15 (~node5(s34)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3183, 550, 3180])).
% 1.11/1.15 tff(3185,plain,
% 1.11/1.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s33, s34)) | node14(s33, s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s33, s34)) | node14(s33, s34))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3186,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s33, s34)) | node14(s33, s34))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3187,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s33, s34)) | node14(s33, s34)),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.11/1.15 tff(3188,plain,
% 1.11/1.15 (node14(s33, s34)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3187, 46, 3164])).
% 1.11/1.15 tff(3189,plain,
% 1.11/1.15 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | (~node14(s33, s34)) | m_main_v_state2(s34, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | (~node14(s33, s34)) | m_main_v_state2(s34, c_t2))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3190,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | (~node14(s33, s34)) | m_main_v_state2(s34, c_t2))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3191,plain,
% 1.11/1.15 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | (~node14(s33, s34)) | m_main_v_state2(s34, c_t2)),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3190, 3189])).
% 1.11/1.15 tff(3192,plain,
% 1.11/1.15 ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state2(s34, c_t2)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3191, 922, 3188])).
% 1.11/1.15 tff(3193,plain,
% 1.11/1.15 (m_main_v_state2(s34, c_t2)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3192, 3149, 3081])).
% 1.11/1.15 tff(3194,plain,
% 1.11/1.15 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s34, c_n2)) | (~m_main_v_state2(s34, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s34, c_n2)) | (~m_main_v_state2(s34, c_t2)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3195,plain,
% 1.11/1.15 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s34, c_n2)) | (~m_main_v_state2(s34, c_t2)))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3196,plain,
% 1.11/1.15 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s34, c_n2)) | (~m_main_v_state2(s34, c_t2))),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 1.11/1.15 tff(3197,plain,
% 1.11/1.15 (~m_main_v_state2(s34, c_n2)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3196, 77, 3193])).
% 1.11/1.15 tff(3198,plain,
% 1.11/1.15 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s34, c_n2) | (~node4(s34)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s34, c_n2) | (~node4(s34)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3199,plain,
% 1.11/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s34, c_n2) | (~node4(s34)))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3200,plain,
% 1.11/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s34, c_n2) | (~node4(s34))),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 1.11/1.15 tff(3201,plain,
% 1.11/1.15 (~node4(s34)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3200, 388, 3197])).
% 1.11/1.15 tff(3202,plain,
% 1.11/1.15 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s34, c_t2)) | (~m_main_v_state2(s34, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s34, c_t2)) | (~m_main_v_state2(s34, c_c2)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3203,plain,
% 1.11/1.15 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s34, c_t2)) | (~m_main_v_state2(s34, c_c2)))),
% 1.11/1.15 inference(quant_inst,[status(thm)],[])).
% 1.11/1.15 tff(3204,plain,
% 1.11/1.15 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s34, c_t2)) | (~m_main_v_state2(s34, c_c2))),
% 1.11/1.15 inference(modus_ponens,[status(thm)],[3203, 3202])).
% 1.11/1.15 tff(3205,plain,
% 1.11/1.15 (~m_main_v_state2(s34, c_c2)),
% 1.11/1.15 inference(unit_resolution,[status(thm)],[3204, 260, 3193])).
% 1.11/1.15 tff(3206,plain,
% 1.11/1.15 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s34, c_c2) | (~node3(s34)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s34, c_c2) | (~node3(s34)))),
% 1.11/1.15 inference(rewrite,[status(thm)],[])).
% 1.11/1.15 tff(3207,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s34, c_c2) | (~node3(s34)))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3208,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s34, c_c2) | (~node3(s34))),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 1.14/1.16 tff(3209,plain,
% 1.14/1.16 (~node3(s34)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3208, 399, 3205])).
% 1.14/1.16 tff(3210,plain,
% 1.14/1.16 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s34, c_n2) | (~node2(s34)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s34, c_n2) | (~node2(s34)))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3211,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s34, c_n2) | (~node2(s34)))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3212,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s34, c_n2) | (~node2(s34))),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3211, 3210])).
% 1.14/1.16 tff(3213,plain,
% 1.14/1.16 (~node2(s34)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3212, 410, 3197])).
% 1.14/1.16 tff(3214,plain,
% 1.14/1.16 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s34, c_n1)) | (~m_main_v_state1(s34, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s34, c_n1)) | (~m_main_v_state1(s34, c_c1)))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3215,plain,
% 1.14/1.16 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s34, c_n1)) | (~m_main_v_state1(s34, c_c1)))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3216,plain,
% 1.14/1.16 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s34, c_n1)) | (~m_main_v_state1(s34, c_c1))),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 1.14/1.16 tff(3217,plain,
% 1.14/1.16 (~m_main_v_state1(s34, c_n1)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3216, 454, 3176])).
% 1.14/1.16 tff(3218,plain,
% 1.14/1.16 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s34, c_n1) | (~node1(s34)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s34, c_n1) | (~node1(s34)))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3219,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s34, c_n1) | (~node1(s34)))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3220,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s34, c_n1) | (~node1(s34))),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 1.14/1.16 tff(3221,plain,
% 1.14/1.16 (~node1(s34)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3220, 421, 3217])).
% 1.14/1.16 tff(3222,plain,
% 1.14/1.16 (succ(s34, s35) <=> succ(s34, s35)),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3223,axiom,(succ(s34, s35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound35')).
% 1.14/1.16 tff(3224,plain,
% 1.14/1.16 (succ(s34, s35)),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3223, 3222])).
% 1.14/1.16 tff(3225,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3226,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3227,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35)),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3226, 3225])).
% 1.14/1.16 tff(3228,plain,
% 1.14/1.16 (trans(s34, s35)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3227, 3224, 32])).
% 1.14/1.16 tff(3229,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s34, s35)) | node7(s34, s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s34, s35)) | node7(s34, s35))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3230,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s34, s35)) | node7(s34, s35))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3231,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s34, s35)) | node7(s34, s35)),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 1.14/1.16 tff(3232,plain,
% 1.14/1.16 (node7(s34, s35)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3231, 206, 3228])).
% 1.14/1.16 tff(3233,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3234,plain,
% 1.14/1.16 (((~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)) | m_main_v_state1(s35, c_n1)) <=> (m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3235,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)) | m_main_v_state1(s35, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35))))),
% 1.14/1.16 inference(monotonicity,[status(thm)],[3234])).
% 1.14/1.16 tff(3236,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)) | m_main_v_state1(s35, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)))),
% 1.14/1.16 inference(transitivity,[status(thm)],[3235, 3233])).
% 1.14/1.16 tff(3237,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)) | m_main_v_state1(s35, c_n1))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3238,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35))),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 1.14/1.16 tff(3239,plain,
% 1.14/1.16 (m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3238, 584, 3232])).
% 1.14/1.16 tff(3240,plain,
% 1.14/1.16 (m_main_v_state1(s35, c_n1)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3239, 3221, 3176, 3213, 3209, 3201, 3184])).
% 1.14/1.16 tff(3241,plain,
% 1.14/1.16 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s33, c_t2) | (~node15(s33)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s33, c_t2) | (~node15(s33)))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3242,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s33, c_t2) | (~node15(s33)))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3243,plain,
% 1.14/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s33, c_t2) | (~node15(s33))),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3242, 3241])).
% 1.14/1.16 tff(3244,plain,
% 1.14/1.16 (~node15(s33)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3243, 103, 3153])).
% 1.14/1.16 tff(3245,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s33, s34)) | node18(s33, s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s33, s34)) | node18(s33, s34))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3246,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s33, s34)) | node18(s33, s34))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3247,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s33, s34)) | node18(s33, s34)),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3246, 3245])).
% 1.14/1.16 tff(3248,plain,
% 1.14/1.16 (node18(s33, s34)),
% 1.14/1.16 inference(unit_resolution,[status(thm)],[3247, 125, 3164])).
% 1.14/1.16 tff(3249,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s33) | (~node18(s33, s34)) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s33) | (~node18(s33, s34)) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3250,plain,
% 1.14/1.16 (((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node15(s33) | (~node18(s33, s34)) | m_main_v_turn(s34, c_1)) <=> (node15(s33) | (~node18(s33, s34)) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1))),
% 1.14/1.16 inference(rewrite,[status(thm)],[])).
% 1.14/1.16 tff(3251,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node15(s33) | (~node18(s33, s34)) | m_main_v_turn(s34, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s33) | (~node18(s33, s34)) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1)))),
% 1.14/1.16 inference(monotonicity,[status(thm)],[3250])).
% 1.14/1.16 tff(3252,plain,
% 1.14/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node15(s33) | (~node18(s33, s34)) | m_main_v_turn(s34, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s33) | (~node18(s33, s34)) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1))),
% 1.14/1.16 inference(transitivity,[status(thm)],[3251, 3249])).
% 1.14/1.16 tff(3253,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node15(s33) | (~node18(s33, s34)) | m_main_v_turn(s34, c_1))),
% 1.14/1.16 inference(quant_inst,[status(thm)],[])).
% 1.14/1.16 tff(3254,plain,
% 1.14/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s33) | (~node18(s33, s34)) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1)),
% 1.14/1.16 inference(modus_ponens,[status(thm)],[3253, 3252])).
% 1.14/1.16 tff(3255,plain,
% 1.14/1.16 (node15(s33) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3254, 992, 3248])).
% 1.14/1.17 tff(3256,plain,
% 1.14/1.17 (m_main_v_turn(s34, c_1)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3255, 3244, 3081, 3149])).
% 1.14/1.17 tff(3257,plain,
% 1.14/1.17 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s34, c_1)) | (~m_main_v_turn(s34, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s34, c_1)) | (~m_main_v_turn(s34, c_2)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3258,plain,
% 1.14/1.17 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s34, c_1)) | (~m_main_v_turn(s34, c_2)))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3259,plain,
% 1.14/1.17 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s34, c_1)) | (~m_main_v_turn(s34, c_2))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 1.14/1.17 tff(3260,plain,
% 1.14/1.17 (~m_main_v_turn(s34, c_2)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3259, 156, 3256])).
% 1.14/1.17 tff(3261,plain,
% 1.14/1.17 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s34, c_2) | (~node12(s34)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s34, c_2) | (~node12(s34)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3262,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s34, c_2) | (~node12(s34)))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3263,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s34, c_2) | (~node12(s34))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 1.14/1.17 tff(3264,plain,
% 1.14/1.17 (~node12(s34)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3263, 184, 3260])).
% 1.14/1.17 tff(3265,plain,
% 1.14/1.17 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s34, c_n2) | (~node8(s34)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s34, c_n2) | (~node8(s34)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3266,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s34, c_n2) | (~node8(s34)))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3267,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s34, c_n2) | (~node8(s34))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3266, 3265])).
% 1.14/1.17 tff(3268,plain,
% 1.14/1.17 (~node8(s34)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3267, 271, 3197])).
% 1.14/1.17 tff(3269,plain,
% 1.14/1.17 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s34, c_n2) | (~node9(s34)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s34, c_n2) | (~node9(s34)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3270,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s34, c_n2) | (~node9(s34)))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3271,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s34, c_n2) | (~node9(s34))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 1.14/1.17 tff(3272,plain,
% 1.14/1.17 (~node9(s34)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3271, 88, 3197])).
% 1.14/1.17 tff(3273,plain,
% 1.14/1.17 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s34, c_n2) | (~node10(s34)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s34, c_n2) | (~node10(s34)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3274,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s34, c_n2) | (~node10(s34)))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3275,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s34, c_n2) | (~node10(s34))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 1.14/1.17 tff(3276,plain,
% 1.14/1.17 (~node10(s34)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3275, 249, 3197])).
% 1.14/1.17 tff(3277,plain,
% 1.14/1.17 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s34, c_n1) | (~node11(s34)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s34, c_n1) | (~node11(s34)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3278,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s34, c_n1) | (~node11(s34)))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3279,plain,
% 1.14/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s34, c_n1) | (~node11(s34))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3278, 3277])).
% 1.14/1.17 tff(3280,plain,
% 1.14/1.17 (~node11(s34)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3279, 238, 3217])).
% 1.14/1.17 tff(3281,plain,
% 1.14/1.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s34, s35)) | node14(s34, s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s34, s35)) | node14(s34, s35))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3282,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s34, s35)) | node14(s34, s35))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3283,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s34, s35)) | node14(s34, s35)),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 1.14/1.17 tff(3284,plain,
% 1.14/1.17 (node14(s34, s35)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3283, 46, 3228])).
% 1.14/1.17 tff(3285,plain,
% 1.14/1.17 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35) | (~node14(s34, s35)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35) | (~node14(s34, s35)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3286,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35) | (~node14(s34, s35)))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3287,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35) | (~node14(s34, s35))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 1.14/1.17 tff(3288,plain,
% 1.14/1.17 (m_main_v_state2(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3287, 296, 3284])).
% 1.14/1.17 tff(3289,plain,
% 1.14/1.17 (node13(s34, s35)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3288, 3280, 3205, 3276, 3272, 3268, 3264])).
% 1.14/1.17 tff(3290,plain,
% 1.14/1.17 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2) | (~node13(s34, s35)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2) | (~node13(s34, s35)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3291,plain,
% 1.14/1.17 (((~node13(s34, s35)) | (~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2)) <=> ((~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2) | (~node13(s34, s35)))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3292,plain,
% 1.14/1.17 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s34, s35)) | (~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2) | (~node13(s34, s35))))),
% 1.14/1.17 inference(monotonicity,[status(thm)],[3291])).
% 1.14/1.17 tff(3293,plain,
% 1.14/1.17 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s34, s35)) | (~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2) | (~node13(s34, s35)))),
% 1.14/1.17 inference(transitivity,[status(thm)],[3292, 3290])).
% 1.14/1.17 tff(3294,plain,
% 1.14/1.17 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s34, s35)) | (~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3295,plain,
% 1.14/1.17 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s34, c_t2)) | m_main_v_state2(s35, c_t2) | (~node13(s34, s35))),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3294, 3293])).
% 1.14/1.17 tff(3296,plain,
% 1.14/1.17 (m_main_v_state2(s35, c_t2)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3295, 518, 3193, 3289])).
% 1.14/1.17 tff(3297,plain,
% 1.14/1.17 (succ(s35, s36) <=> succ(s35, s36)),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3298,axiom,(succ(s35, s36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound36')).
% 1.14/1.17 tff(3299,plain,
% 1.14/1.17 (succ(s35, s36)),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3298, 3297])).
% 1.14/1.17 tff(3300,plain,
% 1.14/1.17 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3301,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3302,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36)),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3301, 3300])).
% 1.14/1.17 tff(3303,plain,
% 1.14/1.17 (trans(s35, s36)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3302, 3299, 32])).
% 1.14/1.17 tff(3304,plain,
% 1.14/1.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s35, s36)) | node7(s35, s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s35, s36)) | node7(s35, s36))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3305,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s35, s36)) | node7(s35, s36))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3306,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s35, s36)) | node7(s35, s36)),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3305, 3304])).
% 1.14/1.17 tff(3307,plain,
% 1.14/1.17 (node7(s35, s36)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3306, 206, 3303])).
% 1.14/1.17 tff(3308,plain,
% 1.14/1.17 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node7(s35, s36)) | m_main_v_state1(s36, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node7(s35, s36)) | m_main_v_state1(s36, c_t1))),
% 1.14/1.17 inference(rewrite,[status(thm)],[])).
% 1.14/1.17 tff(3309,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node7(s35, s36)) | m_main_v_state1(s36, c_t1))),
% 1.14/1.17 inference(quant_inst,[status(thm)],[])).
% 1.14/1.17 tff(3310,plain,
% 1.14/1.17 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node7(s35, s36)) | m_main_v_state1(s36, c_t1)),
% 1.14/1.17 inference(modus_ponens,[status(thm)],[3309, 3308])).
% 1.14/1.17 tff(3311,plain,
% 1.14/1.17 ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | m_main_v_state1(s36, c_t1)),
% 1.14/1.17 inference(unit_resolution,[status(thm)],[3310, 651, 3307])).
% 1.14/1.18 tff(3312,plain,
% 1.14/1.18 (m_main_v_state1(s36, c_t1)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3311, 3296, 3240])).
% 1.14/1.18 tff(3313,plain,
% 1.14/1.18 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s36, c_n1)) | (~m_main_v_state1(s36, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s36, c_n1)) | (~m_main_v_state1(s36, c_t1)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3314,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s36, c_n1)) | (~m_main_v_state1(s36, c_t1)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3315,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s36, c_n1)) | (~m_main_v_state1(s36, c_t1))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3314, 3313])).
% 1.14/1.18 tff(3316,plain,
% 1.14/1.18 (~m_main_v_state1(s36, c_n1)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3315, 10, 3312])).
% 1.14/1.18 tff(3317,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s36, c_n1) | (~node1(s36)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s36, c_n1) | (~node1(s36)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3318,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s36, c_n1) | (~node1(s36)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3319,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s36, c_n1) | (~node1(s36))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3318, 3317])).
% 1.14/1.18 tff(3320,plain,
% 1.14/1.18 (~node1(s36)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3319, 421, 3316])).
% 1.14/1.18 tff(3321,plain,
% 1.14/1.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s35, s36)) | node18(s35, s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s35, s36)) | node18(s35, s36))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3322,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s35, s36)) | node18(s35, s36))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3323,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s35, s36)) | node18(s35, s36)),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3322, 3321])).
% 1.14/1.18 tff(3324,plain,
% 1.14/1.18 (node18(s35, s36)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3323, 125, 3303])).
% 1.14/1.18 tff(3325,plain,
% 1.14/1.18 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node18(s35, s36)) | m_main_v_turn(s36, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node18(s35, s36)) | m_main_v_turn(s36, c_2))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3326,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node18(s35, s36)) | m_main_v_turn(s36, c_2))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3327,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node18(s35, s36)) | m_main_v_turn(s36, c_2)),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 1.14/1.18 tff(3328,plain,
% 1.14/1.18 ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | m_main_v_turn(s36, c_2)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3327, 760, 3324])).
% 1.14/1.18 tff(3329,plain,
% 1.14/1.18 (m_main_v_turn(s36, c_2)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3328, 3296, 3240])).
% 1.14/1.18 tff(3330,plain,
% 1.14/1.18 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s36, c_1)) | (~m_main_v_turn(s36, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s36, c_1)) | (~m_main_v_turn(s36, c_2)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3331,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s36, c_1)) | (~m_main_v_turn(s36, c_2)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3332,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s36, c_1)) | (~m_main_v_turn(s36, c_2))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3331, 3330])).
% 1.14/1.18 tff(3333,plain,
% 1.14/1.18 (~m_main_v_turn(s36, c_1)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3332, 156, 3329])).
% 1.14/1.18 tff(3334,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s36, c_1) | (~node5(s36)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s36, c_1) | (~node5(s36)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3335,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s36, c_1) | (~node5(s36)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3336,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s36, c_1) | (~node5(s36))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3335, 3334])).
% 1.14/1.18 tff(3337,plain,
% 1.14/1.18 (~node5(s36)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3336, 776, 3333])).
% 1.14/1.18 tff(3338,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s36, c_n1) | (~node2(s36)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s36, c_n1) | (~node2(s36)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3339,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s36, c_n1) | (~node2(s36)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3340,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s36, c_n1) | (~node2(s36))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 1.14/1.18 tff(3341,plain,
% 1.14/1.18 (~node2(s36)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3340, 787, 3316])).
% 1.14/1.18 tff(3342,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s36, c_n1) | (~node3(s36)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s36, c_n1) | (~node3(s36)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3343,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s36, c_n1) | (~node3(s36)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3344,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s36, c_n1) | (~node3(s36))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3343, 3342])).
% 1.14/1.18 tff(3345,plain,
% 1.14/1.18 (~node3(s36)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3344, 798, 3316])).
% 1.14/1.18 tff(3346,plain,
% 1.14/1.18 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s36, c_t1)) | (~m_main_v_state1(s36, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s36, c_t1)) | (~m_main_v_state1(s36, c_c1)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3347,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s36, c_t1)) | (~m_main_v_state1(s36, c_c1)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3348,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s36, c_t1)) | (~m_main_v_state1(s36, c_c1))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 1.14/1.18 tff(3349,plain,
% 1.14/1.18 (~m_main_v_state1(s36, c_c1)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3348, 539, 3312])).
% 1.14/1.18 tff(3350,plain,
% 1.14/1.18 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)) | (~node13(s34, s35)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)) | (~node13(s34, s35)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3351,plain,
% 1.14/1.18 (((~node13(s34, s35)) | m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2))) <=> (m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)) | (~node13(s34, s35)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3352,plain,
% 1.14/1.18 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s34, s35)) | m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)) | (~node13(s34, s35))))),
% 1.14/1.18 inference(monotonicity,[status(thm)],[3351])).
% 1.14/1.18 tff(3353,plain,
% 1.14/1.18 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s34, s35)) | m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)) | (~node13(s34, s35)))),
% 1.14/1.18 inference(transitivity,[status(thm)],[3352, 3350])).
% 1.14/1.18 tff(3354,plain,
% 1.14/1.18 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s34, s35)) | m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3355,plain,
% 1.14/1.18 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s34, c_n2) | (~m_main_v_state2(s35, c_n2)) | (~node13(s34, s35))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3354, 3353])).
% 1.14/1.18 tff(3356,plain,
% 1.14/1.18 (~m_main_v_state2(s35, c_n2)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3355, 311, 3197, 3289])).
% 1.14/1.18 tff(3357,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s35, c_n2) | (~node9(s35)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s35, c_n2) | (~node9(s35)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3358,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s35, c_n2) | (~node9(s35)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3359,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s35, c_n2) | (~node9(s35))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3358, 3357])).
% 1.14/1.18 tff(3360,plain,
% 1.14/1.18 (~node9(s35)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3359, 88, 3356])).
% 1.14/1.18 tff(3361,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s35, c_n2) | (~node10(s35)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s35, c_n2) | (~node10(s35)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3362,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s35, c_n2) | (~node10(s35)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3363,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s35, c_n2) | (~node10(s35))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 1.14/1.18 tff(3364,plain,
% 1.14/1.18 (~node10(s35)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3363, 249, 3356])).
% 1.14/1.18 tff(3365,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s35, c_n2) | (~node8(s35)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s35, c_n2) | (~node8(s35)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3366,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s35, c_n2) | (~node8(s35)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3367,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s35, c_n2) | (~node8(s35))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3366, 3365])).
% 1.14/1.18 tff(3368,plain,
% 1.14/1.18 (~node8(s35)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3367, 271, 3356])).
% 1.14/1.18 tff(3369,plain,
% 1.14/1.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s35, s36)) | node14(s35, s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s35, s36)) | node14(s35, s36))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3370,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s35, s36)) | node14(s35, s36))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3371,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s35, s36)) | node14(s35, s36)),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3370, 3369])).
% 1.14/1.18 tff(3372,plain,
% 1.14/1.18 (node14(s35, s36)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3371, 46, 3303])).
% 1.14/1.18 tff(3373,plain,
% 1.14/1.18 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | node9(s35) | node8(s35) | node10(s35) | (~node14(s35, s36)) | m_main_v_state2(s36, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | node9(s35) | node8(s35) | node10(s35) | (~node14(s35, s36)) | m_main_v_state2(s36, c_c2))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3374,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | node9(s35) | node8(s35) | node10(s35) | (~node14(s35, s36)) | m_main_v_state2(s36, c_c2))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3375,plain,
% 1.14/1.18 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | node9(s35) | node8(s35) | node10(s35) | (~node14(s35, s36)) | m_main_v_state2(s36, c_c2)),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3374, 3373])).
% 1.14/1.18 tff(3376,plain,
% 1.14/1.18 ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | node9(s35) | node8(s35) | node10(s35) | m_main_v_state2(s36, c_c2)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3375, 617, 3372])).
% 1.14/1.18 tff(3377,plain,
% 1.14/1.18 (m_main_v_state2(s36, c_c2)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3376, 3368, 3240, 3296, 3364, 3360])).
% 1.14/1.18 tff(3378,plain,
% 1.14/1.18 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s36, c_n2)) | (~m_main_v_state2(s36, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s36, c_n2)) | (~m_main_v_state2(s36, c_c2)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3379,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s36, c_n2)) | (~m_main_v_state2(s36, c_c2)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3380,plain,
% 1.14/1.18 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s36, c_n2)) | (~m_main_v_state2(s36, c_c2))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3379, 3378])).
% 1.14/1.18 tff(3381,plain,
% 1.14/1.18 (~m_main_v_state2(s36, c_n2)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3380, 697, 3377])).
% 1.14/1.18 tff(3382,plain,
% 1.14/1.18 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s36, c_n2) | (~node4(s36)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s36, c_n2) | (~node4(s36)))),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.18 tff(3383,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s36, c_n2) | (~node4(s36)))),
% 1.14/1.18 inference(quant_inst,[status(thm)],[])).
% 1.14/1.18 tff(3384,plain,
% 1.14/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s36, c_n2) | (~node4(s36))),
% 1.14/1.18 inference(modus_ponens,[status(thm)],[3383, 3382])).
% 1.14/1.18 tff(3385,plain,
% 1.14/1.18 (~node4(s36)),
% 1.14/1.18 inference(unit_resolution,[status(thm)],[3384, 388, 3381])).
% 1.14/1.18 tff(3386,plain,
% 1.14/1.18 (succ(s36, s37) <=> succ(s36, s37)),
% 1.14/1.18 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3387,axiom,(succ(s36, s37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound37')).
% 1.14/1.19 tff(3388,plain,
% 1.14/1.19 (succ(s36, s37)),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3387, 3386])).
% 1.14/1.19 tff(3389,plain,
% 1.14/1.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3390,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3391,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37)),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 1.14/1.19 tff(3392,plain,
% 1.14/1.19 (trans(s36, s37)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3391, 3388, 32])).
% 1.14/1.19 tff(3393,plain,
% 1.14/1.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s36, s37)) | node7(s36, s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s36, s37)) | node7(s36, s37))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3394,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s36, s37)) | node7(s36, s37))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3395,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s36, s37)) | node7(s36, s37)),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3394, 3393])).
% 1.14/1.19 tff(3396,plain,
% 1.14/1.19 (node7(s36, s37)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3395, 206, 3392])).
% 1.14/1.19 tff(3397,plain,
% 1.14/1.19 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s36, c_c1) | node1(s36) | node2(s36) | node3(s36) | node4(s36) | node5(s36) | node6(s36, s37) | (~node7(s36, s37)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s36, c_c1) | node1(s36) | node2(s36) | node3(s36) | node4(s36) | node5(s36) | node6(s36, s37) | (~node7(s36, s37)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3398,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s36, c_c1) | node1(s36) | node2(s36) | node3(s36) | node4(s36) | node5(s36) | node6(s36, s37) | (~node7(s36, s37)))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3399,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s36, c_c1) | node1(s36) | node2(s36) | node3(s36) | node4(s36) | node5(s36) | node6(s36, s37) | (~node7(s36, s37))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 1.14/1.19 tff(3400,plain,
% 1.14/1.19 (m_main_v_state1(s36, c_c1) | node1(s36) | node2(s36) | node3(s36) | node4(s36) | node5(s36) | node6(s36, s37)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3399, 820, 3396])).
% 1.14/1.19 tff(3401,plain,
% 1.14/1.19 (node6(s36, s37)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3400, 3385, 3349, 3345, 3341, 3337, 3320])).
% 1.14/1.19 tff(3402,plain,
% 1.14/1.19 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1) | (~node6(s36, s37)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1) | (~node6(s36, s37)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3403,plain,
% 1.14/1.19 (((~node6(s36, s37)) | (~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1)) <=> ((~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1) | (~node6(s36, s37)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3404,plain,
% 1.14/1.19 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s36, s37)) | (~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1) | (~node6(s36, s37))))),
% 1.14/1.19 inference(monotonicity,[status(thm)],[3403])).
% 1.14/1.19 tff(3405,plain,
% 1.14/1.19 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s36, s37)) | (~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1) | (~node6(s36, s37)))),
% 1.14/1.19 inference(transitivity,[status(thm)],[3404, 3402])).
% 1.14/1.19 tff(3406,plain,
% 1.14/1.19 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s36, s37)) | (~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3407,plain,
% 1.14/1.19 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s36, c_t1)) | m_main_v_state1(s37, c_t1) | (~node6(s36, s37))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3406, 3405])).
% 1.14/1.19 tff(3408,plain,
% 1.14/1.19 (m_main_v_state1(s37, c_t1)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3407, 856, 3312, 3401])).
% 1.14/1.19 tff(3409,plain,
% 1.14/1.19 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s36, c_t2)) | (~m_main_v_state2(s36, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s36, c_t2)) | (~m_main_v_state2(s36, c_c2)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3410,plain,
% 1.14/1.19 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s36, c_t2)) | (~m_main_v_state2(s36, c_c2)))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3411,plain,
% 1.14/1.19 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s36, c_t2)) | (~m_main_v_state2(s36, c_c2))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3410, 3409])).
% 1.14/1.19 tff(3412,plain,
% 1.14/1.19 (~m_main_v_state2(s36, c_t2)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3411, 260, 3377])).
% 1.14/1.19 tff(3413,plain,
% 1.14/1.19 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s36, c_t2) | (~node12(s36)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s36, c_t2) | (~node12(s36)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3414,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s36, c_t2) | (~node12(s36)))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3415,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s36, c_t2) | (~node12(s36))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3414, 3413])).
% 1.14/1.19 tff(3416,plain,
% 1.14/1.19 (~node12(s36)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3415, 633, 3412])).
% 1.14/1.19 tff(3417,plain,
% 1.14/1.19 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s36, c_n1) | (~node11(s36)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s36, c_n1) | (~node11(s36)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3418,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s36, c_n1) | (~node11(s36)))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3419,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s36, c_n1) | (~node11(s36))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 1.14/1.19 tff(3420,plain,
% 1.14/1.19 (~node11(s36)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3419, 238, 3316])).
% 1.14/1.19 tff(3421,plain,
% 1.14/1.19 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s36, c_c1) | (~node10(s36)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s36, c_c1) | (~node10(s36)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3422,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s36, c_c1) | (~node10(s36)))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3423,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s36, c_c1) | (~node10(s36))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3422, 3421])).
% 1.14/1.19 tff(3424,plain,
% 1.14/1.19 (~node10(s36)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3423, 675, 3349])).
% 1.14/1.19 tff(3425,plain,
% 1.14/1.19 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s36, c_n1) | (~node9(s36)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s36, c_n1) | (~node9(s36)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3426,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s36, c_n1) | (~node9(s36)))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3427,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s36, c_n1) | (~node9(s36))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3426, 3425])).
% 1.14/1.19 tff(3428,plain,
% 1.14/1.19 (~node9(s36)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3427, 686, 3316])).
% 1.14/1.19 tff(3429,plain,
% 1.14/1.19 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s36, c_n2) | (~node8(s36)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s36, c_n2) | (~node8(s36)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3430,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s36, c_n2) | (~node8(s36)))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3431,plain,
% 1.14/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s36, c_n2) | (~node8(s36))),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3430, 3429])).
% 1.14/1.19 tff(3432,plain,
% 1.14/1.19 (~node8(s36)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3431, 271, 3381])).
% 1.14/1.19 tff(3433,plain,
% 1.14/1.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s36, s37)) | node14(s36, s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s36, s37)) | node14(s36, s37))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3434,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s36, s37)) | node14(s36, s37))),
% 1.14/1.19 inference(quant_inst,[status(thm)],[])).
% 1.14/1.19 tff(3435,plain,
% 1.14/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s36, s37)) | node14(s36, s37)),
% 1.14/1.19 inference(modus_ponens,[status(thm)],[3434, 3433])).
% 1.14/1.19 tff(3436,plain,
% 1.14/1.19 (node14(s36, s37)),
% 1.14/1.19 inference(unit_resolution,[status(thm)],[3435, 46, 3392])).
% 1.14/1.19 tff(3437,plain,
% 1.14/1.19 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | (~m_main_v_state2(s36, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | (~m_main_v_state2(s36, c_c2)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3438,plain,
% 1.14/1.19 (((~m_main_v_state2(s36, c_c2)) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | m_main_v_state2(s37, c_n2)) <=> (m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | (~m_main_v_state2(s36, c_c2)))),
% 1.14/1.19 inference(rewrite,[status(thm)],[])).
% 1.14/1.19 tff(3439,plain,
% 1.14/1.19 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s36, c_c2)) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | m_main_v_state2(s37, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | (~m_main_v_state2(s36, c_c2))))),
% 1.14/1.20 inference(monotonicity,[status(thm)],[3438])).
% 1.14/1.20 tff(3440,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s36, c_c2)) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | m_main_v_state2(s37, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | (~m_main_v_state2(s36, c_c2)))),
% 1.14/1.20 inference(transitivity,[status(thm)],[3439, 3437])).
% 1.14/1.20 tff(3441,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s36, c_c2)) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | m_main_v_state2(s37, c_n2))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3442,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | (~m_main_v_state2(s36, c_c2))),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3441, 3440])).
% 1.14/1.20 tff(3443,plain,
% 1.14/1.20 (m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~m_main_v_state2(s36, c_c2))),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3442, 726, 3436])).
% 1.14/1.20 tff(3444,plain,
% 1.14/1.20 (m_main_v_state2(s37, c_n2)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3443, 3432, 3377, 3428, 3424, 3420, 3416])).
% 1.14/1.20 tff(3445,plain,
% 1.14/1.20 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_t2)))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3446,plain,
% 1.14/1.20 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_t2)))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3447,plain,
% 1.14/1.20 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_t2))),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3446, 3445])).
% 1.14/1.20 tff(3448,plain,
% 1.14/1.20 (~m_main_v_state2(s37, c_t2)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3447, 77, 3444])).
% 1.14/1.20 tff(3449,plain,
% 1.14/1.20 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s37, c_t2) | (~node15(s37)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s37, c_t2) | (~node15(s37)))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3450,plain,
% 1.14/1.20 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s37, c_t2) | (~node15(s37)))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3451,plain,
% 1.14/1.20 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s37, c_t2) | (~node15(s37))),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3450, 3449])).
% 1.14/1.20 tff(3452,plain,
% 1.14/1.20 (~node15(s37)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3451, 103, 3448])).
% 1.14/1.20 tff(3453,plain,
% 1.14/1.20 (succ(s37, s38) <=> succ(s37, s38)),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3454,axiom,(succ(s37, s38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound38')).
% 1.14/1.20 tff(3455,plain,
% 1.14/1.20 (succ(s37, s38)),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.14/1.20 tff(3456,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3457,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3458,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38)),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3457, 3456])).
% 1.14/1.20 tff(3459,plain,
% 1.14/1.20 (trans(s37, s38)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3458, 3455, 32])).
% 1.14/1.20 tff(3460,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s37, s38)) | node18(s37, s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s37, s38)) | node18(s37, s38))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3461,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s37, s38)) | node18(s37, s38))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3462,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s37, s38)) | node18(s37, s38)),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.14/1.20 tff(3463,plain,
% 1.14/1.20 (node18(s37, s38)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3462, 125, 3459])).
% 1.14/1.20 tff(3464,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s37) | (~node18(s37, s38)) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s37) | (~node18(s37, s38)) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3465,plain,
% 1.14/1.20 (((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node15(s37) | (~node18(s37, s38)) | m_main_v_turn(s38, c_1)) <=> (node15(s37) | (~node18(s37, s38)) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3466,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node15(s37) | (~node18(s37, s38)) | m_main_v_turn(s38, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s37) | (~node18(s37, s38)) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1)))),
% 1.14/1.20 inference(monotonicity,[status(thm)],[3465])).
% 1.14/1.20 tff(3467,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node15(s37) | (~node18(s37, s38)) | m_main_v_turn(s38, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s37) | (~node18(s37, s38)) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1))),
% 1.14/1.20 inference(transitivity,[status(thm)],[3466, 3464])).
% 1.14/1.20 tff(3468,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node15(s37) | (~node18(s37, s38)) | m_main_v_turn(s38, c_1))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3469,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s37) | (~node18(s37, s38)) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1)),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3468, 3467])).
% 1.14/1.20 tff(3470,plain,
% 1.14/1.20 (node15(s37) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3469, 992, 3463])).
% 1.14/1.20 tff(3471,plain,
% 1.14/1.20 (m_main_v_turn(s38, c_1)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3470, 3452, 3444, 3408])).
% 1.14/1.20 tff(3472,plain,
% 1.14/1.20 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s38, c_1)) | (~m_main_v_turn(s38, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s38, c_1)) | (~m_main_v_turn(s38, c_2)))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3473,plain,
% 1.14/1.20 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s38, c_1)) | (~m_main_v_turn(s38, c_2)))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3474,plain,
% 1.14/1.20 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s38, c_1)) | (~m_main_v_turn(s38, c_2))),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3473, 3472])).
% 1.14/1.20 tff(3475,plain,
% 1.14/1.20 (~m_main_v_turn(s38, c_2)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3474, 156, 3471])).
% 1.14/1.20 tff(3476,plain,
% 1.14/1.20 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s38, c_2) | (~node12(s38)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s38, c_2) | (~node12(s38)))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3477,plain,
% 1.14/1.20 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s38, c_2) | (~node12(s38)))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3478,plain,
% 1.14/1.20 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s38, c_2) | (~node12(s38))),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3477, 3476])).
% 1.14/1.20 tff(3479,plain,
% 1.14/1.20 (~node12(s38)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3478, 184, 3475])).
% 1.14/1.20 tff(3480,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s37, s38)) | node14(s37, s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s37, s38)) | node14(s37, s38))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3481,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s37, s38)) | node14(s37, s38))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3482,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s37, s38)) | node14(s37, s38)),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 1.14/1.20 tff(3483,plain,
% 1.14/1.20 (node14(s37, s38)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3482, 46, 3459])).
% 1.14/1.20 tff(3484,plain,
% 1.14/1.20 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | (~node14(s37, s38)) | m_main_v_state2(s38, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | (~node14(s37, s38)) | m_main_v_state2(s38, c_t2))),
% 1.14/1.20 inference(rewrite,[status(thm)],[])).
% 1.14/1.20 tff(3485,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | (~node14(s37, s38)) | m_main_v_state2(s38, c_t2))),
% 1.14/1.20 inference(quant_inst,[status(thm)],[])).
% 1.14/1.20 tff(3486,plain,
% 1.14/1.20 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | (~node14(s37, s38)) | m_main_v_state2(s38, c_t2)),
% 1.14/1.20 inference(modus_ponens,[status(thm)],[3485, 3484])).
% 1.14/1.20 tff(3487,plain,
% 1.14/1.20 ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state2(s38, c_t2)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3486, 922, 3483])).
% 1.14/1.20 tff(3488,plain,
% 1.14/1.20 (m_main_v_state2(s38, c_t2)),
% 1.14/1.20 inference(unit_resolution,[status(thm)],[3487, 3408, 3444])).
% 1.14/1.20 tff(3489,plain,
% 1.14/1.20 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s38, c_n2)) | (~m_main_v_state2(s38, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s38, c_n2)) | (~m_main_v_state2(s38, c_t2)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3490,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s38, c_n2)) | (~m_main_v_state2(s38, c_t2)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3491,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s38, c_n2)) | (~m_main_v_state2(s38, c_t2))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3490, 3489])).
% 1.14/1.21 tff(3492,plain,
% 1.14/1.21 (~m_main_v_state2(s38, c_n2)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3491, 77, 3488])).
% 1.14/1.21 tff(3493,plain,
% 1.14/1.21 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s38, c_n2) | (~node8(s38)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s38, c_n2) | (~node8(s38)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3494,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s38, c_n2) | (~node8(s38)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3495,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s38, c_n2) | (~node8(s38))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 1.14/1.21 tff(3496,plain,
% 1.14/1.21 (~node8(s38)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3495, 271, 3492])).
% 1.14/1.21 tff(3497,plain,
% 1.14/1.21 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s38, c_n2) | (~node9(s38)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s38, c_n2) | (~node9(s38)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3498,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s38, c_n2) | (~node9(s38)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3499,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s38, c_n2) | (~node9(s38))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3498, 3497])).
% 1.14/1.21 tff(3500,plain,
% 1.14/1.21 (~node9(s38)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3499, 88, 3492])).
% 1.14/1.21 tff(3501,plain,
% 1.14/1.21 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s38, c_n2) | (~node10(s38)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s38, c_n2) | (~node10(s38)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3502,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s38, c_n2) | (~node10(s38)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3503,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s38, c_n2) | (~node10(s38))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3502, 3501])).
% 1.14/1.21 tff(3504,plain,
% 1.14/1.21 (~node10(s38)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3503, 249, 3492])).
% 1.14/1.21 tff(3505,plain,
% 1.14/1.21 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s38, c_t2)) | (~m_main_v_state2(s38, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s38, c_t2)) | (~m_main_v_state2(s38, c_c2)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3506,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s38, c_t2)) | (~m_main_v_state2(s38, c_c2)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3507,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s38, c_t2)) | (~m_main_v_state2(s38, c_c2))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3506, 3505])).
% 1.14/1.21 tff(3508,plain,
% 1.14/1.21 (~m_main_v_state2(s38, c_c2)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3507, 260, 3488])).
% 1.14/1.21 tff(3509,plain,
% 1.14/1.21 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_c2)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3510,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_c2)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3511,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s37, c_n2)) | (~m_main_v_state2(s37, c_c2))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 1.14/1.21 tff(3512,plain,
% 1.14/1.21 (~m_main_v_state2(s37, c_c2)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3511, 697, 3444])).
% 1.14/1.21 tff(3513,plain,
% 1.14/1.21 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s37, c_c2) | (~node3(s37)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s37, c_c2) | (~node3(s37)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3514,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s37, c_c2) | (~node3(s37)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3515,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s37, c_c2) | (~node3(s37))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 1.14/1.21 tff(3516,plain,
% 1.14/1.21 (~node3(s37)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3515, 399, 3512])).
% 1.14/1.21 tff(3517,plain,
% 1.14/1.21 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)) | (~node6(s36, s37)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)) | (~node6(s36, s37)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3518,plain,
% 1.14/1.21 (((~node6(s36, s37)) | m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1))) <=> (m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)) | (~node6(s36, s37)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3519,plain,
% 1.14/1.21 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s36, s37)) | m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)) | (~node6(s36, s37))))),
% 1.14/1.21 inference(monotonicity,[status(thm)],[3518])).
% 1.14/1.21 tff(3520,plain,
% 1.14/1.21 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s36, s37)) | m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)) | (~node6(s36, s37)))),
% 1.14/1.21 inference(transitivity,[status(thm)],[3519, 3517])).
% 1.14/1.21 tff(3521,plain,
% 1.14/1.21 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s36, s37)) | m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3522,plain,
% 1.14/1.21 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s36, c_n1) | (~m_main_v_state1(s37, c_n1)) | (~node6(s36, s37))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 1.14/1.21 tff(3523,plain,
% 1.14/1.21 (~m_main_v_state1(s37, c_n1)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3522, 835, 3316, 3401])).
% 1.14/1.21 tff(3524,plain,
% 1.14/1.21 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s37, c_n1) | (~node2(s37)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s37, c_n1) | (~node2(s37)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3525,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s37, c_n1) | (~node2(s37)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3526,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s37, c_n1) | (~node2(s37))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3525, 3524])).
% 1.14/1.21 tff(3527,plain,
% 1.14/1.21 (~node2(s37)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3526, 787, 3523])).
% 1.14/1.21 tff(3528,plain,
% 1.14/1.21 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s37, c_t2) | (~node1(s37)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s37, c_t2) | (~node1(s37)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3529,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s37, c_t2) | (~node1(s37)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3530,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s37, c_t2) | (~node1(s37))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3529, 3528])).
% 1.14/1.21 tff(3531,plain,
% 1.14/1.21 (~node1(s37)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3530, 195, 3448])).
% 1.14/1.21 tff(3532,plain,
% 1.14/1.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s37, s38)) | node7(s37, s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s37, s38)) | node7(s37, s38))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3533,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s37, s38)) | node7(s37, s38))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3534,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s37, s38)) | node7(s37, s38)),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 1.14/1.21 tff(3535,plain,
% 1.14/1.21 (node7(s37, s38)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3534, 206, 3459])).
% 1.14/1.21 tff(3536,plain,
% 1.14/1.21 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state1(s38, c_c1) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state1(s38, c_c1) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3537,plain,
% 1.14/1.21 (((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)) | m_main_v_state1(s38, c_c1)) <=> ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state1(s38, c_c1) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3538,plain,
% 1.14/1.21 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)) | m_main_v_state1(s38, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state1(s38, c_c1) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38))))),
% 1.14/1.21 inference(monotonicity,[status(thm)],[3537])).
% 1.14/1.21 tff(3539,plain,
% 1.14/1.21 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)) | m_main_v_state1(s38, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state1(s38, c_c1) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)))),
% 1.14/1.21 inference(transitivity,[status(thm)],[3538, 3536])).
% 1.14/1.21 tff(3540,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38)) | m_main_v_state1(s38, c_c1))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3541,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state1(s38, c_c1) | node1(s37) | node2(s37) | node3(s37) | (~node7(s37, s38))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3540, 3539])).
% 1.14/1.21 tff(3542,plain,
% 1.14/1.21 ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state1(s38, c_c1) | node1(s37) | node2(s37) | node3(s37)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3541, 892, 3535])).
% 1.14/1.21 tff(3543,plain,
% 1.14/1.21 (m_main_v_state1(s38, c_c1)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3542, 3531, 3444, 3408, 3527, 3516])).
% 1.14/1.21 tff(3544,plain,
% 1.14/1.21 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s38, c_n1)) | (~m_main_v_state1(s38, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s38, c_n1)) | (~m_main_v_state1(s38, c_c1)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3545,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s38, c_n1)) | (~m_main_v_state1(s38, c_c1)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3546,plain,
% 1.14/1.21 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s38, c_n1)) | (~m_main_v_state1(s38, c_c1))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 1.14/1.21 tff(3547,plain,
% 1.14/1.21 (~m_main_v_state1(s38, c_n1)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3546, 454, 3543])).
% 1.14/1.21 tff(3548,plain,
% 1.14/1.21 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s38, c_n1) | (~node11(s38)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s38, c_n1) | (~node11(s38)))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3549,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s38, c_n1) | (~node11(s38)))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3550,plain,
% 1.14/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s38, c_n1) | (~node11(s38))),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3549, 3548])).
% 1.14/1.21 tff(3551,plain,
% 1.14/1.21 (~node11(s38)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3550, 238, 3547])).
% 1.14/1.21 tff(3552,plain,
% 1.14/1.21 (succ(s38, s39) <=> succ(s38, s39)),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3553,axiom,(succ(s38, s39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound39')).
% 1.14/1.21 tff(3554,plain,
% 1.14/1.21 (succ(s38, s39)),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 1.14/1.21 tff(3555,plain,
% 1.14/1.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3556,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3557,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39)),
% 1.14/1.21 inference(modus_ponens,[status(thm)],[3556, 3555])).
% 1.14/1.21 tff(3558,plain,
% 1.14/1.21 (trans(s38, s39)),
% 1.14/1.21 inference(unit_resolution,[status(thm)],[3557, 3554, 32])).
% 1.14/1.21 tff(3559,plain,
% 1.14/1.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s38, s39)) | node14(s38, s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s38, s39)) | node14(s38, s39))),
% 1.14/1.21 inference(rewrite,[status(thm)],[])).
% 1.14/1.21 tff(3560,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s38, s39)) | node14(s38, s39))),
% 1.14/1.21 inference(quant_inst,[status(thm)],[])).
% 1.14/1.21 tff(3561,plain,
% 1.14/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s38, s39)) | node14(s38, s39)),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3560, 3559])).
% 1.14/1.22 tff(3562,plain,
% 1.14/1.22 (node14(s38, s39)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3561, 46, 3558])).
% 1.14/1.22 tff(3563,plain,
% 1.14/1.22 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s38, c_c2) | node9(s38) | node8(s38) | node10(s38) | node11(s38) | node12(s38) | node13(s38, s39) | (~node14(s38, s39)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s38, c_c2) | node9(s38) | node8(s38) | node10(s38) | node11(s38) | node12(s38) | node13(s38, s39) | (~node14(s38, s39)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3564,plain,
% 1.14/1.22 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s38, c_c2) | node9(s38) | node8(s38) | node10(s38) | node11(s38) | node12(s38) | node13(s38, s39) | (~node14(s38, s39)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3565,plain,
% 1.14/1.22 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s38, c_c2) | node9(s38) | node8(s38) | node10(s38) | node11(s38) | node12(s38) | node13(s38, s39) | (~node14(s38, s39))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3564, 3563])).
% 1.14/1.22 tff(3566,plain,
% 1.14/1.22 (m_main_v_state2(s38, c_c2) | node9(s38) | node8(s38) | node10(s38) | node11(s38) | node12(s38) | node13(s38, s39)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3565, 296, 3562])).
% 1.14/1.22 tff(3567,plain,
% 1.14/1.22 (node13(s38, s39)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3566, 3551, 3508, 3504, 3500, 3496, 3479])).
% 1.14/1.22 tff(3568,plain,
% 1.14/1.22 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3569,plain,
% 1.14/1.22 (((~node13(s38, s39)) | m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2))) <=> (m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3570,plain,
% 1.14/1.22 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s38, s39)) | m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39))))),
% 1.14/1.22 inference(monotonicity,[status(thm)],[3569])).
% 1.14/1.22 tff(3571,plain,
% 1.14/1.22 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s38, s39)) | m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39)))),
% 1.14/1.22 inference(transitivity,[status(thm)],[3570, 3568])).
% 1.14/1.22 tff(3572,plain,
% 1.14/1.22 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s38, s39)) | m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3573,plain,
% 1.14/1.22 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3572, 3571])).
% 1.14/1.22 tff(3574,plain,
% 1.14/1.22 (~m_main_v_state2(s39, c_n2)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3573, 311, 3492, 3567])).
% 1.14/1.22 tff(3575,plain,
% 1.14/1.22 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s39, c_n2) | (~node9(s39)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s39, c_n2) | (~node9(s39)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3576,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s39, c_n2) | (~node9(s39)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3577,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s39, c_n2) | (~node9(s39))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3576, 3575])).
% 1.14/1.22 tff(3578,plain,
% 1.14/1.22 (~node9(s39)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3577, 88, 3574])).
% 1.14/1.22 tff(3579,plain,
% 1.14/1.22 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s39, c_n2) | (~node10(s39)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s39, c_n2) | (~node10(s39)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3580,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s39, c_n2) | (~node10(s39)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3581,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s39, c_n2) | (~node10(s39))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 1.14/1.22 tff(3582,plain,
% 1.14/1.22 (~node10(s39)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3581, 249, 3574])).
% 1.14/1.22 tff(3583,plain,
% 1.14/1.22 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3584,plain,
% 1.14/1.22 (((~node13(s38, s39)) | (~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2)) <=> ((~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3585,plain,
% 1.14/1.22 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s38, s39)) | (~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39))))),
% 1.14/1.22 inference(monotonicity,[status(thm)],[3584])).
% 1.14/1.22 tff(3586,plain,
% 1.14/1.22 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s38, s39)) | (~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39)))),
% 1.14/1.22 inference(transitivity,[status(thm)],[3585, 3583])).
% 1.14/1.22 tff(3587,plain,
% 1.14/1.22 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s38, s39)) | (~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3588,plain,
% 1.14/1.22 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 1.14/1.22 tff(3589,plain,
% 1.14/1.22 (m_main_v_state2(s39, c_t2)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3588, 518, 3488, 3567])).
% 1.14/1.22 tff(3590,plain,
% 1.14/1.22 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s38, c_t1)) | (~m_main_v_state1(s38, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s38, c_t1)) | (~m_main_v_state1(s38, c_c1)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3591,plain,
% 1.14/1.22 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s38, c_t1)) | (~m_main_v_state1(s38, c_c1)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3592,plain,
% 1.14/1.22 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s38, c_t1)) | (~m_main_v_state1(s38, c_c1))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 1.14/1.22 tff(3593,plain,
% 1.14/1.22 (~m_main_v_state1(s38, c_t1)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3592, 539, 3543])).
% 1.14/1.22 tff(3594,plain,
% 1.14/1.22 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s38, c_t1) | (~node5(s38)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s38, c_t1) | (~node5(s38)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3595,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s38, c_t1) | (~node5(s38)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3596,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s38, c_t1) | (~node5(s38))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3595, 3594])).
% 1.14/1.22 tff(3597,plain,
% 1.14/1.22 (~node5(s38)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3596, 550, 3593])).
% 1.14/1.22 tff(3598,plain,
% 1.14/1.22 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s38, c_n2) | (~node4(s38)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s38, c_n2) | (~node4(s38)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3599,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s38, c_n2) | (~node4(s38)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3600,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s38, c_n2) | (~node4(s38))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3599, 3598])).
% 1.14/1.22 tff(3601,plain,
% 1.14/1.22 (~node4(s38)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3600, 388, 3492])).
% 1.14/1.22 tff(3602,plain,
% 1.14/1.22 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s38, c_c2) | (~node3(s38)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s38, c_c2) | (~node3(s38)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3603,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s38, c_c2) | (~node3(s38)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3604,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s38, c_c2) | (~node3(s38))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3603, 3602])).
% 1.14/1.22 tff(3605,plain,
% 1.14/1.22 (~node3(s38)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3604, 399, 3508])).
% 1.14/1.22 tff(3606,plain,
% 1.14/1.22 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s38, c_n2) | (~node2(s38)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s38, c_n2) | (~node2(s38)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3607,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s38, c_n2) | (~node2(s38)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3608,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s38, c_n2) | (~node2(s38))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 1.14/1.22 tff(3609,plain,
% 1.14/1.22 (~node2(s38)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3608, 410, 3492])).
% 1.14/1.22 tff(3610,plain,
% 1.14/1.22 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s38, c_n1) | (~node1(s38)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s38, c_n1) | (~node1(s38)))),
% 1.14/1.22 inference(rewrite,[status(thm)],[])).
% 1.14/1.22 tff(3611,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s38, c_n1) | (~node1(s38)))),
% 1.14/1.22 inference(quant_inst,[status(thm)],[])).
% 1.14/1.22 tff(3612,plain,
% 1.14/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s38, c_n1) | (~node1(s38))),
% 1.14/1.22 inference(modus_ponens,[status(thm)],[3611, 3610])).
% 1.14/1.22 tff(3613,plain,
% 1.14/1.22 (~node1(s38)),
% 1.14/1.22 inference(unit_resolution,[status(thm)],[3612, 421, 3547])).
% 1.21/1.23 tff(3614,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s38, s39)) | node7(s38, s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s38, s39)) | node7(s38, s39))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3615,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s38, s39)) | node7(s38, s39))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3616,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s38, s39)) | node7(s38, s39)),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3615, 3614])).
% 1.21/1.23 tff(3617,plain,
% 1.21/1.23 (node7(s38, s39)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3616, 206, 3558])).
% 1.21/1.23 tff(3618,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3619,plain,
% 1.21/1.23 (((~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)) | m_main_v_state1(s39, c_n1)) <=> (m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3620,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)) | m_main_v_state1(s39, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39))))),
% 1.21/1.23 inference(monotonicity,[status(thm)],[3619])).
% 1.21/1.23 tff(3621,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)) | m_main_v_state1(s39, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)))),
% 1.21/1.23 inference(transitivity,[status(thm)],[3620, 3618])).
% 1.21/1.23 tff(3622,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)) | m_main_v_state1(s39, c_n1))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3623,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39))),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3622, 3621])).
% 1.21/1.23 tff(3624,plain,
% 1.21/1.23 (m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3623, 584, 3617])).
% 1.21/1.23 tff(3625,plain,
% 1.21/1.23 (m_main_v_state1(s39, c_n1)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3624, 3613, 3543, 3609, 3605, 3601, 3597])).
% 1.21/1.23 tff(3626,plain,
% 1.21/1.23 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s39, c_n2) | (~node8(s39)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s39, c_n2) | (~node8(s39)))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3627,plain,
% 1.21/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s39, c_n2) | (~node8(s39)))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3628,plain,
% 1.21/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s39, c_n2) | (~node8(s39))),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 1.21/1.23 tff(3629,plain,
% 1.21/1.23 (~node8(s39)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3628, 271, 3574])).
% 1.21/1.23 tff(3630,plain,
% 1.21/1.23 (succ(s39, s40) <=> succ(s39, s40)),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3631,axiom,(succ(s39, s40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound40')).
% 1.21/1.23 tff(3632,plain,
% 1.21/1.23 (succ(s39, s40)),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3631, 3630])).
% 1.21/1.23 tff(3633,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3634,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3635,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40)),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3634, 3633])).
% 1.21/1.23 tff(3636,plain,
% 1.21/1.23 (trans(s39, s40)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3635, 3632, 32])).
% 1.21/1.23 tff(3637,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s39, s40)) | node14(s39, s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s39, s40)) | node14(s39, s40))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3638,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s39, s40)) | node14(s39, s40))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3639,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s39, s40)) | node14(s39, s40)),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3638, 3637])).
% 1.21/1.23 tff(3640,plain,
% 1.21/1.23 (node14(s39, s40)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3639, 46, 3636])).
% 1.21/1.23 tff(3641,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | node9(s39) | node8(s39) | node10(s39) | (~node14(s39, s40)) | m_main_v_state2(s40, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | node9(s39) | node8(s39) | node10(s39) | (~node14(s39, s40)) | m_main_v_state2(s40, c_c2))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3642,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | node9(s39) | node8(s39) | node10(s39) | (~node14(s39, s40)) | m_main_v_state2(s40, c_c2))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3643,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | node9(s39) | node8(s39) | node10(s39) | (~node14(s39, s40)) | m_main_v_state2(s40, c_c2)),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3642, 3641])).
% 1.21/1.23 tff(3644,plain,
% 1.21/1.23 ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | node9(s39) | node8(s39) | node10(s39) | m_main_v_state2(s40, c_c2)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3643, 617, 3640])).
% 1.21/1.23 tff(3645,plain,
% 1.21/1.23 (m_main_v_state2(s40, c_c2)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3644, 3629, 3625, 3589, 3582, 3578])).
% 1.21/1.23 tff(3646,plain,
% 1.21/1.23 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s40, c_t2)) | (~m_main_v_state2(s40, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s40, c_t2)) | (~m_main_v_state2(s40, c_c2)))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3647,plain,
% 1.21/1.23 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s40, c_t2)) | (~m_main_v_state2(s40, c_c2)))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3648,plain,
% 1.21/1.23 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s40, c_t2)) | (~m_main_v_state2(s40, c_c2))),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3647, 3646])).
% 1.21/1.23 tff(3649,plain,
% 1.21/1.23 (~m_main_v_state2(s40, c_t2)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3648, 260, 3645])).
% 1.21/1.23 tff(3650,plain,
% 1.21/1.23 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s40, c_t2) | (~node12(s40)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s40, c_t2) | (~node12(s40)))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3651,plain,
% 1.21/1.23 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s40, c_t2) | (~node12(s40)))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3652,plain,
% 1.21/1.23 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s40, c_t2) | (~node12(s40))),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.21/1.23 tff(3653,plain,
% 1.21/1.23 (~node12(s40)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3652, 633, 3649])).
% 1.21/1.23 tff(3654,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s39, s40)) | node7(s39, s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s39, s40)) | node7(s39, s40))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3655,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s39, s40)) | node7(s39, s40))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3656,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s39, s40)) | node7(s39, s40)),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3655, 3654])).
% 1.21/1.23 tff(3657,plain,
% 1.21/1.23 (node7(s39, s40)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3656, 206, 3636])).
% 1.21/1.23 tff(3658,plain,
% 1.21/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(3659,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(3660,plain,
% 1.21/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1)),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[3659, 3658])).
% 1.21/1.23 tff(3661,plain,
% 1.21/1.23 ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | m_main_v_state1(s40, c_t1)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3660, 651, 3657])).
% 1.21/1.23 tff(3662,plain,
% 1.21/1.23 (m_main_v_state1(s40, c_t1)),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[3661, 3589, 3625])).
% 1.21/1.23 tff(3663,plain,
% 1.21/1.23 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s40, c_n1)) | (~m_main_v_state1(s40, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s40, c_n1)) | (~m_main_v_state1(s40, c_t1)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3664,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s40, c_n1)) | (~m_main_v_state1(s40, c_t1)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3665,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s40, c_n1)) | (~m_main_v_state1(s40, c_t1))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3664, 3663])).
% 1.21/1.24 tff(3666,plain,
% 1.21/1.24 (~m_main_v_state1(s40, c_n1)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3665, 10, 3662])).
% 1.21/1.24 tff(3667,plain,
% 1.21/1.24 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s40, c_n1) | (~node11(s40)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s40, c_n1) | (~node11(s40)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3668,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s40, c_n1) | (~node11(s40)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3669,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s40, c_n1) | (~node11(s40))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3668, 3667])).
% 1.21/1.24 tff(3670,plain,
% 1.21/1.24 (~node11(s40)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3669, 238, 3666])).
% 1.21/1.24 tff(3671,plain,
% 1.21/1.24 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s40, c_t1)) | (~m_main_v_state1(s40, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s40, c_t1)) | (~m_main_v_state1(s40, c_c1)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3672,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s40, c_t1)) | (~m_main_v_state1(s40, c_c1)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3673,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s40, c_t1)) | (~m_main_v_state1(s40, c_c1))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3672, 3671])).
% 1.21/1.24 tff(3674,plain,
% 1.21/1.24 (~m_main_v_state1(s40, c_c1)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3673, 539, 3662])).
% 1.21/1.24 tff(3675,plain,
% 1.21/1.24 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s40, c_c1) | (~node10(s40)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s40, c_c1) | (~node10(s40)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3676,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s40, c_c1) | (~node10(s40)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3677,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s40, c_c1) | (~node10(s40))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3676, 3675])).
% 1.21/1.24 tff(3678,plain,
% 1.21/1.24 (~node10(s40)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3677, 675, 3674])).
% 1.21/1.24 tff(3679,plain,
% 1.21/1.24 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s40, c_n1) | (~node9(s40)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s40, c_n1) | (~node9(s40)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3680,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s40, c_n1) | (~node9(s40)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3681,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s40, c_n1) | (~node9(s40))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3680, 3679])).
% 1.21/1.24 tff(3682,plain,
% 1.21/1.24 (~node9(s40)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3681, 686, 3666])).
% 1.21/1.24 tff(3683,plain,
% 1.21/1.24 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s40, c_n2)) | (~m_main_v_state2(s40, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s40, c_n2)) | (~m_main_v_state2(s40, c_c2)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3684,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s40, c_n2)) | (~m_main_v_state2(s40, c_c2)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3685,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s40, c_n2)) | (~m_main_v_state2(s40, c_c2))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3684, 3683])).
% 1.21/1.24 tff(3686,plain,
% 1.21/1.24 (~m_main_v_state2(s40, c_n2)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3685, 697, 3645])).
% 1.21/1.24 tff(3687,plain,
% 1.21/1.24 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s40, c_n2) | (~node8(s40)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s40, c_n2) | (~node8(s40)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3688,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s40, c_n2) | (~node8(s40)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3689,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s40, c_n2) | (~node8(s40))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3688, 3687])).
% 1.21/1.24 tff(3690,plain,
% 1.21/1.24 (~node8(s40)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3689, 271, 3686])).
% 1.21/1.24 tff(3691,plain,
% 1.21/1.24 (succ(s40, s41) <=> succ(s40, s41)),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3692,axiom,(succ(s40, s41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound41')).
% 1.21/1.24 tff(3693,plain,
% 1.21/1.24 (succ(s40, s41)),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3692, 3691])).
% 1.21/1.24 tff(3694,plain,
% 1.21/1.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3695,plain,
% 1.21/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3696,plain,
% 1.21/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41)),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3695, 3694])).
% 1.21/1.24 tff(3697,plain,
% 1.21/1.24 (trans(s40, s41)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3696, 3693, 32])).
% 1.21/1.24 tff(3698,plain,
% 1.21/1.24 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s40, s41)) | node14(s40, s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s40, s41)) | node14(s40, s41))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3699,plain,
% 1.21/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s40, s41)) | node14(s40, s41))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3700,plain,
% 1.21/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s40, s41)) | node14(s40, s41)),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3699, 3698])).
% 1.21/1.24 tff(3701,plain,
% 1.21/1.24 (node14(s40, s41)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3700, 46, 3697])).
% 1.21/1.24 tff(3702,plain,
% 1.21/1.24 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3703,plain,
% 1.21/1.24 (((~m_main_v_state2(s40, c_c2)) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | m_main_v_state2(s41, c_n2)) <=> (m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3704,plain,
% 1.21/1.24 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s40, c_c2)) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | m_main_v_state2(s41, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2))))),
% 1.21/1.24 inference(monotonicity,[status(thm)],[3703])).
% 1.21/1.24 tff(3705,plain,
% 1.21/1.24 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s40, c_c2)) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | m_main_v_state2(s41, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2)))),
% 1.21/1.24 inference(transitivity,[status(thm)],[3704, 3702])).
% 1.21/1.24 tff(3706,plain,
% 1.21/1.24 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s40, c_c2)) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | m_main_v_state2(s41, c_n2))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3707,plain,
% 1.21/1.24 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3706, 3705])).
% 1.21/1.24 tff(3708,plain,
% 1.21/1.24 (m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~m_main_v_state2(s40, c_c2))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3707, 726, 3701])).
% 1.21/1.24 tff(3709,plain,
% 1.21/1.24 (m_main_v_state2(s41, c_n2)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3708, 3690, 3645, 3682, 3678, 3670, 3653])).
% 1.21/1.24 tff(3710,plain,
% 1.21/1.24 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_c2)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3711,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_c2)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3712,plain,
% 1.21/1.24 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_c2))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3711, 3710])).
% 1.21/1.24 tff(3713,plain,
% 1.21/1.24 (~m_main_v_state2(s41, c_c2)),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[3712, 697, 3709])).
% 1.21/1.24 tff(3714,plain,
% 1.21/1.24 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s41, c_c2) | (~node3(s41)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s41, c_c2) | (~node3(s41)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(3715,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s41, c_c2) | (~node3(s41)))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(3716,plain,
% 1.21/1.24 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s41, c_c2) | (~node3(s41))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 1.21/1.25 tff(3717,plain,
% 1.21/1.25 (~node3(s41)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3716, 399, 3713])).
% 1.21/1.25 tff(3718,plain,
% 1.21/1.25 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s40, c_n1) | (~node1(s40)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s40, c_n1) | (~node1(s40)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3719,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s40, c_n1) | (~node1(s40)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3720,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s40, c_n1) | (~node1(s40))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3719, 3718])).
% 1.21/1.25 tff(3721,plain,
% 1.21/1.25 (~node1(s40)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3720, 421, 3666])).
% 1.21/1.25 tff(3722,plain,
% 1.21/1.25 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s39, s40)) | node18(s39, s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s39, s40)) | node18(s39, s40))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3723,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s39, s40)) | node18(s39, s40))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3724,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s39, s40)) | node18(s39, s40)),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 1.21/1.25 tff(3725,plain,
% 1.21/1.25 (node18(s39, s40)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3724, 125, 3636])).
% 1.21/1.25 tff(3726,plain,
% 1.21/1.25 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node18(s39, s40)) | m_main_v_turn(s40, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node18(s39, s40)) | m_main_v_turn(s40, c_2))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3727,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node18(s39, s40)) | m_main_v_turn(s40, c_2))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3728,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node18(s39, s40)) | m_main_v_turn(s40, c_2)),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3727, 3726])).
% 1.21/1.25 tff(3729,plain,
% 1.21/1.25 ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | m_main_v_turn(s40, c_2)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3728, 760, 3725])).
% 1.21/1.25 tff(3730,plain,
% 1.21/1.25 (m_main_v_turn(s40, c_2)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3729, 3589, 3625])).
% 1.21/1.25 tff(3731,plain,
% 1.21/1.25 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s40, c_1)) | (~m_main_v_turn(s40, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s40, c_1)) | (~m_main_v_turn(s40, c_2)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3732,plain,
% 1.21/1.25 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s40, c_1)) | (~m_main_v_turn(s40, c_2)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3733,plain,
% 1.21/1.25 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s40, c_1)) | (~m_main_v_turn(s40, c_2))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 1.21/1.25 tff(3734,plain,
% 1.21/1.25 (~m_main_v_turn(s40, c_1)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3733, 156, 3730])).
% 1.21/1.25 tff(3735,plain,
% 1.21/1.25 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s40, c_1) | (~node5(s40)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s40, c_1) | (~node5(s40)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3736,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s40, c_1) | (~node5(s40)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3737,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s40, c_1) | (~node5(s40))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3736, 3735])).
% 1.21/1.25 tff(3738,plain,
% 1.21/1.25 (~node5(s40)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3737, 776, 3734])).
% 1.21/1.25 tff(3739,plain,
% 1.21/1.25 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s40, c_n1) | (~node2(s40)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s40, c_n1) | (~node2(s40)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3740,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s40, c_n1) | (~node2(s40)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3741,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s40, c_n1) | (~node2(s40))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 1.21/1.25 tff(3742,plain,
% 1.21/1.25 (~node2(s40)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3741, 787, 3666])).
% 1.21/1.25 tff(3743,plain,
% 1.21/1.25 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s40, c_n1) | (~node3(s40)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s40, c_n1) | (~node3(s40)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3744,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s40, c_n1) | (~node3(s40)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3745,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s40, c_n1) | (~node3(s40))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 1.21/1.25 tff(3746,plain,
% 1.21/1.25 (~node3(s40)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3745, 798, 3666])).
% 1.21/1.25 tff(3747,plain,
% 1.21/1.25 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s40, c_n2) | (~node4(s40)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s40, c_n2) | (~node4(s40)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3748,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s40, c_n2) | (~node4(s40)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3749,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s40, c_n2) | (~node4(s40))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.21/1.25 tff(3750,plain,
% 1.21/1.25 (~node4(s40)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3749, 388, 3686])).
% 1.21/1.25 tff(3751,plain,
% 1.21/1.25 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s40, s41)) | node7(s40, s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s40, s41)) | node7(s40, s41))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3752,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s40, s41)) | node7(s40, s41))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3753,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s40, s41)) | node7(s40, s41)),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3752, 3751])).
% 1.21/1.25 tff(3754,plain,
% 1.21/1.25 (node7(s40, s41)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3753, 206, 3697])).
% 1.21/1.25 tff(3755,plain,
% 1.21/1.25 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41) | (~node7(s40, s41)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41) | (~node7(s40, s41)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3756,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41) | (~node7(s40, s41)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3757,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41) | (~node7(s40, s41))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3756, 3755])).
% 1.21/1.25 tff(3758,plain,
% 1.21/1.25 (m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3757, 820, 3754])).
% 1.21/1.25 tff(3759,plain,
% 1.21/1.25 (node6(s40, s41)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3758, 3750, 3674, 3746, 3742, 3738, 3721])).
% 1.21/1.25 tff(3760,plain,
% 1.21/1.25 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)) | (~node6(s40, s41)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)) | (~node6(s40, s41)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3761,plain,
% 1.21/1.25 (((~node6(s40, s41)) | m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1))) <=> (m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)) | (~node6(s40, s41)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3762,plain,
% 1.21/1.25 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s40, s41)) | m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)) | (~node6(s40, s41))))),
% 1.21/1.25 inference(monotonicity,[status(thm)],[3761])).
% 1.21/1.25 tff(3763,plain,
% 1.21/1.25 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s40, s41)) | m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)) | (~node6(s40, s41)))),
% 1.21/1.25 inference(transitivity,[status(thm)],[3762, 3760])).
% 1.21/1.25 tff(3764,plain,
% 1.21/1.25 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s40, s41)) | m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3765,plain,
% 1.21/1.25 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s40, c_n1) | (~m_main_v_state1(s41, c_n1)) | (~node6(s40, s41))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3764, 3763])).
% 1.21/1.25 tff(3766,plain,
% 1.21/1.25 (~m_main_v_state1(s41, c_n1)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3765, 835, 3666, 3759])).
% 1.21/1.25 tff(3767,plain,
% 1.21/1.25 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s41, c_n1) | (~node2(s41)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s41, c_n1) | (~node2(s41)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3768,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s41, c_n1) | (~node2(s41)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3769,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s41, c_n1) | (~node2(s41))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3768, 3767])).
% 1.21/1.25 tff(3770,plain,
% 1.21/1.25 (~node2(s41)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3769, 787, 3766])).
% 1.21/1.25 tff(3771,plain,
% 1.21/1.25 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1) | (~node6(s40, s41)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1) | (~node6(s40, s41)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3772,plain,
% 1.21/1.25 (((~node6(s40, s41)) | (~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1)) <=> ((~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1) | (~node6(s40, s41)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3773,plain,
% 1.21/1.25 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s40, s41)) | (~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1) | (~node6(s40, s41))))),
% 1.21/1.25 inference(monotonicity,[status(thm)],[3772])).
% 1.21/1.25 tff(3774,plain,
% 1.21/1.25 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s40, s41)) | (~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1) | (~node6(s40, s41)))),
% 1.21/1.25 inference(transitivity,[status(thm)],[3773, 3771])).
% 1.21/1.25 tff(3775,plain,
% 1.21/1.25 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s40, s41)) | (~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3776,plain,
% 1.21/1.25 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s40, c_t1)) | m_main_v_state1(s41, c_t1) | (~node6(s40, s41))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3775, 3774])).
% 1.21/1.25 tff(3777,plain,
% 1.21/1.25 (m_main_v_state1(s41, c_t1)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3776, 856, 3662, 3759])).
% 1.21/1.25 tff(3778,plain,
% 1.21/1.25 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_t2)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3779,plain,
% 1.21/1.25 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_t2)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3780,plain,
% 1.21/1.25 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s41, c_n2)) | (~m_main_v_state2(s41, c_t2))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3779, 3778])).
% 1.21/1.25 tff(3781,plain,
% 1.21/1.25 (~m_main_v_state2(s41, c_t2)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3780, 77, 3709])).
% 1.21/1.25 tff(3782,plain,
% 1.21/1.25 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s41, c_t2) | (~node1(s41)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s41, c_t2) | (~node1(s41)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3783,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s41, c_t2) | (~node1(s41)))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(3784,plain,
% 1.21/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s41, c_t2) | (~node1(s41))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3783, 3782])).
% 1.21/1.25 tff(3785,plain,
% 1.21/1.25 (~node1(s41)),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[3784, 195, 3781])).
% 1.21/1.25 tff(3786,plain,
% 1.21/1.25 (succ(s41, s42) <=> succ(s41, s42)),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3787,axiom,(succ(s41, s42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound42')).
% 1.21/1.25 tff(3788,plain,
% 1.21/1.25 (succ(s41, s42)),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[3787, 3786])).
% 1.21/1.25 tff(3789,plain,
% 1.21/1.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(3790,plain,
% 1.21/1.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3791,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42)),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3790, 3789])).
% 1.21/1.26 tff(3792,plain,
% 1.21/1.26 (trans(s41, s42)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3791, 3788, 32])).
% 1.21/1.26 tff(3793,plain,
% 1.21/1.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s41, s42)) | node7(s41, s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s41, s42)) | node7(s41, s42))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3794,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s41, s42)) | node7(s41, s42))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3795,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s41, s42)) | node7(s41, s42)),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3794, 3793])).
% 1.21/1.26 tff(3796,plain,
% 1.21/1.26 (node7(s41, s42)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3795, 206, 3792])).
% 1.21/1.26 tff(3797,plain,
% 1.21/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state1(s42, c_c1) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state1(s42, c_c1) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3798,plain,
% 1.21/1.26 (((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)) | m_main_v_state1(s42, c_c1)) <=> ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state1(s42, c_c1) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3799,plain,
% 1.21/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)) | m_main_v_state1(s42, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state1(s42, c_c1) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42))))),
% 1.21/1.26 inference(monotonicity,[status(thm)],[3798])).
% 1.21/1.26 tff(3800,plain,
% 1.21/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)) | m_main_v_state1(s42, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state1(s42, c_c1) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)))),
% 1.21/1.26 inference(transitivity,[status(thm)],[3799, 3797])).
% 1.21/1.26 tff(3801,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42)) | m_main_v_state1(s42, c_c1))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3802,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state1(s42, c_c1) | node1(s41) | node2(s41) | node3(s41) | (~node7(s41, s42))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 1.21/1.26 tff(3803,plain,
% 1.21/1.26 ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state1(s42, c_c1) | node1(s41) | node2(s41) | node3(s41)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3802, 892, 3796])).
% 1.21/1.26 tff(3804,plain,
% 1.21/1.26 (m_main_v_state1(s42, c_c1)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3803, 3785, 3709, 3777, 3770, 3717])).
% 1.21/1.26 tff(3805,plain,
% 1.21/1.26 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s42, c_t1)) | (~m_main_v_state1(s42, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s42, c_t1)) | (~m_main_v_state1(s42, c_c1)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3806,plain,
% 1.21/1.26 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s42, c_t1)) | (~m_main_v_state1(s42, c_c1)))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3807,plain,
% 1.21/1.26 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s42, c_t1)) | (~m_main_v_state1(s42, c_c1))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3806, 3805])).
% 1.21/1.26 tff(3808,plain,
% 1.21/1.26 (~m_main_v_state1(s42, c_t1)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3807, 539, 3804])).
% 1.21/1.26 tff(3809,plain,
% 1.21/1.26 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s42, c_t1) | (~node5(s42)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s42, c_t1) | (~node5(s42)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3810,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s42, c_t1) | (~node5(s42)))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3811,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s42, c_t1) | (~node5(s42))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 1.21/1.26 tff(3812,plain,
% 1.21/1.26 (~node5(s42)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3811, 550, 3808])).
% 1.21/1.26 tff(3813,plain,
% 1.21/1.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s41, s42)) | node14(s41, s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s41, s42)) | node14(s41, s42))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3814,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s41, s42)) | node14(s41, s42))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3815,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s41, s42)) | node14(s41, s42)),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3814, 3813])).
% 1.21/1.26 tff(3816,plain,
% 1.21/1.26 (node14(s41, s42)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3815, 46, 3792])).
% 1.21/1.26 tff(3817,plain,
% 1.21/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | (~node14(s41, s42)) | m_main_v_state2(s42, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | (~node14(s41, s42)) | m_main_v_state2(s42, c_t2))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3818,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | (~node14(s41, s42)) | m_main_v_state2(s42, c_t2))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3819,plain,
% 1.21/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | (~node14(s41, s42)) | m_main_v_state2(s42, c_t2)),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3818, 3817])).
% 1.21/1.26 tff(3820,plain,
% 1.21/1.26 ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state2(s42, c_t2)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3819, 922, 3816])).
% 1.21/1.26 tff(3821,plain,
% 1.21/1.26 (m_main_v_state2(s42, c_t2)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3820, 3777, 3709])).
% 1.21/1.26 tff(3822,plain,
% 1.21/1.26 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s42, c_n2)) | (~m_main_v_state2(s42, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s42, c_n2)) | (~m_main_v_state2(s42, c_t2)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3823,plain,
% 1.21/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s42, c_n2)) | (~m_main_v_state2(s42, c_t2)))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3824,plain,
% 1.21/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s42, c_n2)) | (~m_main_v_state2(s42, c_t2))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3823, 3822])).
% 1.21/1.26 tff(3825,plain,
% 1.21/1.26 (~m_main_v_state2(s42, c_n2)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3824, 77, 3821])).
% 1.21/1.26 tff(3826,plain,
% 1.21/1.26 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s42, c_n2) | (~node4(s42)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s42, c_n2) | (~node4(s42)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3827,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s42, c_n2) | (~node4(s42)))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3828,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s42, c_n2) | (~node4(s42))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 1.21/1.26 tff(3829,plain,
% 1.21/1.26 (~node4(s42)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3828, 388, 3825])).
% 1.21/1.26 tff(3830,plain,
% 1.21/1.26 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s42, c_t2)) | (~m_main_v_state2(s42, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s42, c_t2)) | (~m_main_v_state2(s42, c_c2)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3831,plain,
% 1.21/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s42, c_t2)) | (~m_main_v_state2(s42, c_c2)))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3832,plain,
% 1.21/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s42, c_t2)) | (~m_main_v_state2(s42, c_c2))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3831, 3830])).
% 1.21/1.26 tff(3833,plain,
% 1.21/1.26 (~m_main_v_state2(s42, c_c2)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3832, 260, 3821])).
% 1.21/1.26 tff(3834,plain,
% 1.21/1.26 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s42, c_c2) | (~node3(s42)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s42, c_c2) | (~node3(s42)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3835,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s42, c_c2) | (~node3(s42)))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3836,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s42, c_c2) | (~node3(s42))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 1.21/1.26 tff(3837,plain,
% 1.21/1.26 (~node3(s42)),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3836, 399, 3833])).
% 1.21/1.26 tff(3838,plain,
% 1.21/1.26 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s42, c_n2) | (~node2(s42)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s42, c_n2) | (~node2(s42)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(3839,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s42, c_n2) | (~node2(s42)))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(3840,plain,
% 1.21/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s42, c_n2) | (~node2(s42))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 1.25/1.27 tff(3841,plain,
% 1.25/1.27 (~node2(s42)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3840, 410, 3825])).
% 1.25/1.27 tff(3842,plain,
% 1.25/1.27 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s42, c_n1)) | (~m_main_v_state1(s42, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s42, c_n1)) | (~m_main_v_state1(s42, c_c1)))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3843,plain,
% 1.25/1.27 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s42, c_n1)) | (~m_main_v_state1(s42, c_c1)))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3844,plain,
% 1.25/1.27 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s42, c_n1)) | (~m_main_v_state1(s42, c_c1))),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3843, 3842])).
% 1.25/1.27 tff(3845,plain,
% 1.25/1.27 (~m_main_v_state1(s42, c_n1)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3844, 454, 3804])).
% 1.25/1.27 tff(3846,plain,
% 1.25/1.27 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s42, c_n1) | (~node1(s42)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s42, c_n1) | (~node1(s42)))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3847,plain,
% 1.25/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s42, c_n1) | (~node1(s42)))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3848,plain,
% 1.25/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s42, c_n1) | (~node1(s42))),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 1.25/1.27 tff(3849,plain,
% 1.25/1.27 (~node1(s42)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3848, 421, 3845])).
% 1.25/1.27 tff(3850,plain,
% 1.25/1.27 (succ(s42, s43) <=> succ(s42, s43)),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3851,axiom,(succ(s42, s43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound43')).
% 1.25/1.27 tff(3852,plain,
% 1.25/1.27 (succ(s42, s43)),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3851, 3850])).
% 1.25/1.27 tff(3853,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3854,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3855,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43)),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3854, 3853])).
% 1.25/1.27 tff(3856,plain,
% 1.25/1.27 (trans(s42, s43)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3855, 3852, 32])).
% 1.25/1.27 tff(3857,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s42, s43)) | node7(s42, s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s42, s43)) | node7(s42, s43))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3858,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s42, s43)) | node7(s42, s43))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3859,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s42, s43)) | node7(s42, s43)),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3858, 3857])).
% 1.25/1.27 tff(3860,plain,
% 1.25/1.27 (node7(s42, s43)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3859, 206, 3856])).
% 1.25/1.27 tff(3861,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3862,plain,
% 1.25/1.27 (((~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)) | m_main_v_state1(s43, c_n1)) <=> (m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3863,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)) | m_main_v_state1(s43, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43))))),
% 1.25/1.27 inference(monotonicity,[status(thm)],[3862])).
% 1.25/1.27 tff(3864,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)) | m_main_v_state1(s43, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)))),
% 1.25/1.27 inference(transitivity,[status(thm)],[3863, 3861])).
% 1.25/1.27 tff(3865,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)) | m_main_v_state1(s43, c_n1))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3866,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43))),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3865, 3864])).
% 1.25/1.27 tff(3867,plain,
% 1.25/1.27 (m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3866, 584, 3860])).
% 1.25/1.27 tff(3868,plain,
% 1.25/1.27 (m_main_v_state1(s43, c_n1)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3867, 3849, 3804, 3841, 3837, 3829, 3812])).
% 1.25/1.27 tff(3869,plain,
% 1.25/1.27 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s41, c_t2) | (~node15(s41)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s41, c_t2) | (~node15(s41)))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3870,plain,
% 1.25/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s41, c_t2) | (~node15(s41)))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3871,plain,
% 1.25/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s41, c_t2) | (~node15(s41))),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3870, 3869])).
% 1.25/1.27 tff(3872,plain,
% 1.25/1.27 (~node15(s41)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3871, 103, 3781])).
% 1.25/1.27 tff(3873,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s41, s42)) | node18(s41, s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s41, s42)) | node18(s41, s42))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3874,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s41, s42)) | node18(s41, s42))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3875,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s41, s42)) | node18(s41, s42)),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 1.25/1.27 tff(3876,plain,
% 1.25/1.27 (node18(s41, s42)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3875, 125, 3792])).
% 1.25/1.27 tff(3877,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s41) | (~node18(s41, s42)) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s41) | (~node18(s41, s42)) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3878,plain,
% 1.25/1.27 (((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node15(s41) | (~node18(s41, s42)) | m_main_v_turn(s42, c_1)) <=> (node15(s41) | (~node18(s41, s42)) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3879,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node15(s41) | (~node18(s41, s42)) | m_main_v_turn(s42, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s41) | (~node18(s41, s42)) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1)))),
% 1.25/1.27 inference(monotonicity,[status(thm)],[3878])).
% 1.25/1.27 tff(3880,plain,
% 1.25/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node15(s41) | (~node18(s41, s42)) | m_main_v_turn(s42, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s41) | (~node18(s41, s42)) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1))),
% 1.25/1.27 inference(transitivity,[status(thm)],[3879, 3877])).
% 1.25/1.27 tff(3881,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node15(s41) | (~node18(s41, s42)) | m_main_v_turn(s42, c_1))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3882,plain,
% 1.25/1.27 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s41) | (~node18(s41, s42)) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1)),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3881, 3880])).
% 1.25/1.27 tff(3883,plain,
% 1.25/1.27 (node15(s41) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3882, 992, 3876])).
% 1.25/1.27 tff(3884,plain,
% 1.25/1.27 (m_main_v_turn(s42, c_1)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3883, 3872, 3709, 3777])).
% 1.25/1.27 tff(3885,plain,
% 1.25/1.27 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s42, c_1)) | (~m_main_v_turn(s42, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s42, c_1)) | (~m_main_v_turn(s42, c_2)))),
% 1.25/1.27 inference(rewrite,[status(thm)],[])).
% 1.25/1.27 tff(3886,plain,
% 1.25/1.27 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s42, c_1)) | (~m_main_v_turn(s42, c_2)))),
% 1.25/1.27 inference(quant_inst,[status(thm)],[])).
% 1.25/1.27 tff(3887,plain,
% 1.25/1.27 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s42, c_1)) | (~m_main_v_turn(s42, c_2))),
% 1.25/1.27 inference(modus_ponens,[status(thm)],[3886, 3885])).
% 1.25/1.27 tff(3888,plain,
% 1.25/1.27 (~m_main_v_turn(s42, c_2)),
% 1.25/1.27 inference(unit_resolution,[status(thm)],[3887, 156, 3884])).
% 1.25/1.28 tff(3889,plain,
% 1.25/1.28 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s42, c_2) | (~node12(s42)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s42, c_2) | (~node12(s42)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3890,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s42, c_2) | (~node12(s42)))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3891,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s42, c_2) | (~node12(s42))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3890, 3889])).
% 1.25/1.28 tff(3892,plain,
% 1.25/1.28 (~node12(s42)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3891, 184, 3888])).
% 1.25/1.28 tff(3893,plain,
% 1.25/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s42, c_n2) | (~node8(s42)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s42, c_n2) | (~node8(s42)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3894,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s42, c_n2) | (~node8(s42)))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3895,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s42, c_n2) | (~node8(s42))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 1.25/1.28 tff(3896,plain,
% 1.25/1.28 (~node8(s42)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3895, 271, 3825])).
% 1.25/1.28 tff(3897,plain,
% 1.25/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s42, c_n2) | (~node9(s42)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s42, c_n2) | (~node9(s42)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3898,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s42, c_n2) | (~node9(s42)))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3899,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s42, c_n2) | (~node9(s42))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 1.25/1.28 tff(3900,plain,
% 1.25/1.28 (~node9(s42)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3899, 88, 3825])).
% 1.25/1.28 tff(3901,plain,
% 1.25/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s42, c_n2) | (~node10(s42)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s42, c_n2) | (~node10(s42)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3902,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s42, c_n2) | (~node10(s42)))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3903,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s42, c_n2) | (~node10(s42))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3902, 3901])).
% 1.25/1.28 tff(3904,plain,
% 1.25/1.28 (~node10(s42)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3903, 249, 3825])).
% 1.25/1.28 tff(3905,plain,
% 1.25/1.28 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s42, c_n1) | (~node11(s42)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s42, c_n1) | (~node11(s42)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3906,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s42, c_n1) | (~node11(s42)))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3907,plain,
% 1.25/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s42, c_n1) | (~node11(s42))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3906, 3905])).
% 1.25/1.28 tff(3908,plain,
% 1.25/1.28 (~node11(s42)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3907, 238, 3845])).
% 1.25/1.28 tff(3909,plain,
% 1.25/1.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s42, s43)) | node14(s42, s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s42, s43)) | node14(s42, s43))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3910,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s42, s43)) | node14(s42, s43))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3911,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s42, s43)) | node14(s42, s43)),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3910, 3909])).
% 1.25/1.28 tff(3912,plain,
% 1.25/1.28 (node14(s42, s43)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3911, 46, 3856])).
% 1.25/1.28 tff(3913,plain,
% 1.25/1.28 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43) | (~node14(s42, s43)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43) | (~node14(s42, s43)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3914,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43) | (~node14(s42, s43)))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3915,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43) | (~node14(s42, s43))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3914, 3913])).
% 1.25/1.28 tff(3916,plain,
% 1.25/1.28 (m_main_v_state2(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3915, 296, 3912])).
% 1.25/1.28 tff(3917,plain,
% 1.25/1.28 (node13(s42, s43)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3916, 3908, 3833, 3904, 3900, 3896, 3892])).
% 1.25/1.28 tff(3918,plain,
% 1.25/1.28 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2) | (~node13(s42, s43)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2) | (~node13(s42, s43)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3919,plain,
% 1.25/1.28 (((~node13(s42, s43)) | (~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2)) <=> ((~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2) | (~node13(s42, s43)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3920,plain,
% 1.25/1.28 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s42, s43)) | (~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2) | (~node13(s42, s43))))),
% 1.25/1.28 inference(monotonicity,[status(thm)],[3919])).
% 1.25/1.28 tff(3921,plain,
% 1.25/1.28 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s42, s43)) | (~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2) | (~node13(s42, s43)))),
% 1.25/1.28 inference(transitivity,[status(thm)],[3920, 3918])).
% 1.25/1.28 tff(3922,plain,
% 1.25/1.28 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s42, s43)) | (~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3923,plain,
% 1.25/1.28 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s42, c_t2)) | m_main_v_state2(s43, c_t2) | (~node13(s42, s43))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 1.25/1.28 tff(3924,plain,
% 1.25/1.28 (m_main_v_state2(s43, c_t2)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3923, 518, 3821, 3917])).
% 1.25/1.28 tff(3925,plain,
% 1.25/1.28 (succ(s43, s44) <=> succ(s43, s44)),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3926,axiom,(succ(s43, s44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound44')).
% 1.25/1.28 tff(3927,plain,
% 1.25/1.28 (succ(s43, s44)),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3926, 3925])).
% 1.25/1.28 tff(3928,plain,
% 1.25/1.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3929,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3930,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44)),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 1.25/1.28 tff(3931,plain,
% 1.25/1.28 (trans(s43, s44)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3930, 3927, 32])).
% 1.25/1.28 tff(3932,plain,
% 1.25/1.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s43, s44)) | node7(s43, s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s43, s44)) | node7(s43, s44))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3933,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s43, s44)) | node7(s43, s44))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3934,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s43, s44)) | node7(s43, s44)),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3933, 3932])).
% 1.25/1.28 tff(3935,plain,
% 1.25/1.28 (node7(s43, s44)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3934, 206, 3931])).
% 1.25/1.28 tff(3936,plain,
% 1.25/1.28 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node7(s43, s44)) | m_main_v_state1(s44, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node7(s43, s44)) | m_main_v_state1(s44, c_t1))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3937,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node7(s43, s44)) | m_main_v_state1(s44, c_t1))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3938,plain,
% 1.25/1.28 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node7(s43, s44)) | m_main_v_state1(s44, c_t1)),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3937, 3936])).
% 1.25/1.28 tff(3939,plain,
% 1.25/1.28 ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | m_main_v_state1(s44, c_t1)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3938, 651, 3935])).
% 1.25/1.28 tff(3940,plain,
% 1.25/1.28 (m_main_v_state1(s44, c_t1)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3939, 3924, 3868])).
% 1.25/1.28 tff(3941,plain,
% 1.25/1.28 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s44, c_n1)) | (~m_main_v_state1(s44, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s44, c_n1)) | (~m_main_v_state1(s44, c_t1)))),
% 1.25/1.28 inference(rewrite,[status(thm)],[])).
% 1.25/1.28 tff(3942,plain,
% 1.25/1.28 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s44, c_n1)) | (~m_main_v_state1(s44, c_t1)))),
% 1.25/1.28 inference(quant_inst,[status(thm)],[])).
% 1.25/1.28 tff(3943,plain,
% 1.25/1.28 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s44, c_n1)) | (~m_main_v_state1(s44, c_t1))),
% 1.25/1.28 inference(modus_ponens,[status(thm)],[3942, 3941])).
% 1.25/1.28 tff(3944,plain,
% 1.25/1.28 (~m_main_v_state1(s44, c_n1)),
% 1.25/1.28 inference(unit_resolution,[status(thm)],[3943, 10, 3940])).
% 1.25/1.28 tff(3945,plain,
% 1.25/1.28 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s44, c_n1) | (~node1(s44)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s44, c_n1) | (~node1(s44)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3946,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s44, c_n1) | (~node1(s44)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3947,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s44, c_n1) | (~node1(s44))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 1.25/1.29 tff(3948,plain,
% 1.25/1.29 (~node1(s44)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3947, 421, 3944])).
% 1.25/1.29 tff(3949,plain,
% 1.25/1.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s43, s44)) | node18(s43, s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s43, s44)) | node18(s43, s44))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3950,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s43, s44)) | node18(s43, s44))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3951,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s43, s44)) | node18(s43, s44)),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3950, 3949])).
% 1.25/1.29 tff(3952,plain,
% 1.25/1.29 (node18(s43, s44)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3951, 125, 3931])).
% 1.25/1.29 tff(3953,plain,
% 1.25/1.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node18(s43, s44)) | m_main_v_turn(s44, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node18(s43, s44)) | m_main_v_turn(s44, c_2))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3954,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node18(s43, s44)) | m_main_v_turn(s44, c_2))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3955,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node18(s43, s44)) | m_main_v_turn(s44, c_2)),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 1.25/1.29 tff(3956,plain,
% 1.25/1.29 ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | m_main_v_turn(s44, c_2)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3955, 760, 3952])).
% 1.25/1.29 tff(3957,plain,
% 1.25/1.29 (m_main_v_turn(s44, c_2)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3956, 3924, 3868])).
% 1.25/1.29 tff(3958,plain,
% 1.25/1.29 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s44, c_1)) | (~m_main_v_turn(s44, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s44, c_1)) | (~m_main_v_turn(s44, c_2)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3959,plain,
% 1.25/1.29 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s44, c_1)) | (~m_main_v_turn(s44, c_2)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3960,plain,
% 1.25/1.29 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s44, c_1)) | (~m_main_v_turn(s44, c_2))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3959, 3958])).
% 1.25/1.29 tff(3961,plain,
% 1.25/1.29 (~m_main_v_turn(s44, c_1)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3960, 156, 3957])).
% 1.25/1.29 tff(3962,plain,
% 1.25/1.29 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s44, c_1) | (~node5(s44)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s44, c_1) | (~node5(s44)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3963,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s44, c_1) | (~node5(s44)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3964,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s44, c_1) | (~node5(s44))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3963, 3962])).
% 1.25/1.29 tff(3965,plain,
% 1.25/1.29 (~node5(s44)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3964, 776, 3961])).
% 1.25/1.29 tff(3966,plain,
% 1.25/1.29 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s44, c_n1) | (~node2(s44)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s44, c_n1) | (~node2(s44)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3967,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s44, c_n1) | (~node2(s44)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3968,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s44, c_n1) | (~node2(s44))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3967, 3966])).
% 1.25/1.29 tff(3969,plain,
% 1.25/1.29 (~node2(s44)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3968, 787, 3944])).
% 1.25/1.29 tff(3970,plain,
% 1.25/1.29 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s44, c_n1) | (~node3(s44)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s44, c_n1) | (~node3(s44)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3971,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s44, c_n1) | (~node3(s44)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3972,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s44, c_n1) | (~node3(s44))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3971, 3970])).
% 1.25/1.29 tff(3973,plain,
% 1.25/1.29 (~node3(s44)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3972, 798, 3944])).
% 1.25/1.29 tff(3974,plain,
% 1.25/1.29 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s44, c_t1)) | (~m_main_v_state1(s44, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s44, c_t1)) | (~m_main_v_state1(s44, c_c1)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3975,plain,
% 1.25/1.29 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s44, c_t1)) | (~m_main_v_state1(s44, c_c1)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3976,plain,
% 1.25/1.29 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s44, c_t1)) | (~m_main_v_state1(s44, c_c1))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 1.25/1.29 tff(3977,plain,
% 1.25/1.29 (~m_main_v_state1(s44, c_c1)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3976, 539, 3940])).
% 1.25/1.29 tff(3978,plain,
% 1.25/1.29 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)) | (~node13(s42, s43)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)) | (~node13(s42, s43)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3979,plain,
% 1.25/1.29 (((~node13(s42, s43)) | m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2))) <=> (m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)) | (~node13(s42, s43)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3980,plain,
% 1.25/1.29 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s42, s43)) | m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)) | (~node13(s42, s43))))),
% 1.25/1.29 inference(monotonicity,[status(thm)],[3979])).
% 1.25/1.29 tff(3981,plain,
% 1.25/1.29 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s42, s43)) | m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)) | (~node13(s42, s43)))),
% 1.25/1.29 inference(transitivity,[status(thm)],[3980, 3978])).
% 1.25/1.29 tff(3982,plain,
% 1.25/1.29 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s42, s43)) | m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3983,plain,
% 1.25/1.29 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s42, c_n2) | (~m_main_v_state2(s43, c_n2)) | (~node13(s42, s43))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 1.25/1.29 tff(3984,plain,
% 1.25/1.29 (~m_main_v_state2(s43, c_n2)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3983, 311, 3825, 3917])).
% 1.25/1.29 tff(3985,plain,
% 1.25/1.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s43, c_n2) | (~node9(s43)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s43, c_n2) | (~node9(s43)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3986,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s43, c_n2) | (~node9(s43)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3987,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s43, c_n2) | (~node9(s43))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3986, 3985])).
% 1.25/1.29 tff(3988,plain,
% 1.25/1.29 (~node9(s43)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3987, 88, 3984])).
% 1.25/1.29 tff(3989,plain,
% 1.25/1.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s43, c_n2) | (~node10(s43)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s43, c_n2) | (~node10(s43)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3990,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s43, c_n2) | (~node10(s43)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3991,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s43, c_n2) | (~node10(s43))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3990, 3989])).
% 1.25/1.29 tff(3992,plain,
% 1.25/1.29 (~node10(s43)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3991, 249, 3984])).
% 1.25/1.29 tff(3993,plain,
% 1.25/1.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s43, c_n2) | (~node8(s43)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s43, c_n2) | (~node8(s43)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3994,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s43, c_n2) | (~node8(s43)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3995,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s43, c_n2) | (~node8(s43))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3994, 3993])).
% 1.25/1.29 tff(3996,plain,
% 1.25/1.29 (~node8(s43)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3995, 271, 3984])).
% 1.25/1.29 tff(3997,plain,
% 1.25/1.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s43, s44)) | node14(s43, s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s43, s44)) | node14(s43, s44))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(3998,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s43, s44)) | node14(s43, s44))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(3999,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s43, s44)) | node14(s43, s44)),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 1.25/1.29 tff(4000,plain,
% 1.25/1.29 (node14(s43, s44)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[3999, 46, 3931])).
% 1.25/1.29 tff(4001,plain,
% 1.25/1.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | node9(s43) | node8(s43) | node10(s43) | (~node14(s43, s44)) | m_main_v_state2(s44, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | node9(s43) | node8(s43) | node10(s43) | (~node14(s43, s44)) | m_main_v_state2(s44, c_c2))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(4002,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | node9(s43) | node8(s43) | node10(s43) | (~node14(s43, s44)) | m_main_v_state2(s44, c_c2))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(4003,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | node9(s43) | node8(s43) | node10(s43) | (~node14(s43, s44)) | m_main_v_state2(s44, c_c2)),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[4002, 4001])).
% 1.25/1.29 tff(4004,plain,
% 1.25/1.29 ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | node9(s43) | node8(s43) | node10(s43) | m_main_v_state2(s44, c_c2)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[4003, 617, 4000])).
% 1.25/1.29 tff(4005,plain,
% 1.25/1.29 (m_main_v_state2(s44, c_c2)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[4004, 3996, 3868, 3924, 3992, 3988])).
% 1.25/1.29 tff(4006,plain,
% 1.25/1.29 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s44, c_n2)) | (~m_main_v_state2(s44, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s44, c_n2)) | (~m_main_v_state2(s44, c_c2)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(4007,plain,
% 1.25/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s44, c_n2)) | (~m_main_v_state2(s44, c_c2)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(4008,plain,
% 1.25/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s44, c_n2)) | (~m_main_v_state2(s44, c_c2))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[4007, 4006])).
% 1.25/1.29 tff(4009,plain,
% 1.25/1.29 (~m_main_v_state2(s44, c_n2)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[4008, 697, 4005])).
% 1.25/1.29 tff(4010,plain,
% 1.25/1.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s44, c_n2) | (~node4(s44)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s44, c_n2) | (~node4(s44)))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(4011,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s44, c_n2) | (~node4(s44)))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(4012,plain,
% 1.25/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s44, c_n2) | (~node4(s44))),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[4011, 4010])).
% 1.25/1.29 tff(4013,plain,
% 1.25/1.29 (~node4(s44)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[4012, 388, 4009])).
% 1.25/1.29 tff(4014,plain,
% 1.25/1.29 (succ(s44, s45) <=> succ(s44, s45)),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(4015,axiom,(succ(s44, s45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound45')).
% 1.25/1.29 tff(4016,plain,
% 1.25/1.29 (succ(s44, s45)),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 1.25/1.29 tff(4017,plain,
% 1.25/1.29 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45))),
% 1.25/1.29 inference(rewrite,[status(thm)],[])).
% 1.25/1.29 tff(4018,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))),
% 1.25/1.29 inference(quant_inst,[status(thm)],[])).
% 1.25/1.29 tff(4019,plain,
% 1.25/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45)),
% 1.25/1.29 inference(modus_ponens,[status(thm)],[4018, 4017])).
% 1.25/1.29 tff(4020,plain,
% 1.25/1.29 (trans(s44, s45)),
% 1.25/1.29 inference(unit_resolution,[status(thm)],[4019, 4016, 32])).
% 1.25/1.29 tff(4021,plain,
% 1.25/1.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s44, s45)) | node7(s44, s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s44, s45)) | node7(s44, s45))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4022,plain,
% 1.25/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s44, s45)) | node7(s44, s45))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4023,plain,
% 1.25/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s44, s45)) | node7(s44, s45)),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4022, 4021])).
% 1.25/1.30 tff(4024,plain,
% 1.25/1.30 (node7(s44, s45)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4023, 206, 4020])).
% 1.25/1.30 tff(4025,plain,
% 1.25/1.30 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45) | (~node7(s44, s45)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45) | (~node7(s44, s45)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4026,plain,
% 1.25/1.30 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45) | (~node7(s44, s45)))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4027,plain,
% 1.25/1.30 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45) | (~node7(s44, s45))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4026, 4025])).
% 1.25/1.30 tff(4028,plain,
% 1.25/1.30 (m_main_v_state1(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4027, 820, 4024])).
% 1.25/1.30 tff(4029,plain,
% 1.25/1.30 (node6(s44, s45)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4028, 4013, 3977, 3973, 3969, 3965, 3948])).
% 1.25/1.30 tff(4030,plain,
% 1.25/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1) | (~node6(s44, s45)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1) | (~node6(s44, s45)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4031,plain,
% 1.25/1.30 (((~node6(s44, s45)) | (~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1)) <=> ((~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1) | (~node6(s44, s45)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4032,plain,
% 1.25/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s44, s45)) | (~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1) | (~node6(s44, s45))))),
% 1.25/1.30 inference(monotonicity,[status(thm)],[4031])).
% 1.25/1.30 tff(4033,plain,
% 1.25/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s44, s45)) | (~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1) | (~node6(s44, s45)))),
% 1.25/1.30 inference(transitivity,[status(thm)],[4032, 4030])).
% 1.25/1.30 tff(4034,plain,
% 1.25/1.30 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s44, s45)) | (~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4035,plain,
% 1.25/1.30 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s44, c_t1)) | m_main_v_state1(s45, c_t1) | (~node6(s44, s45))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4034, 4033])).
% 1.25/1.30 tff(4036,plain,
% 1.25/1.30 (m_main_v_state1(s45, c_t1)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4035, 856, 3940, 4029])).
% 1.25/1.30 tff(4037,plain,
% 1.25/1.30 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s44, c_t2)) | (~m_main_v_state2(s44, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s44, c_t2)) | (~m_main_v_state2(s44, c_c2)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4038,plain,
% 1.25/1.30 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s44, c_t2)) | (~m_main_v_state2(s44, c_c2)))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4039,plain,
% 1.25/1.30 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s44, c_t2)) | (~m_main_v_state2(s44, c_c2))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4038, 4037])).
% 1.25/1.30 tff(4040,plain,
% 1.25/1.30 (~m_main_v_state2(s44, c_t2)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4039, 260, 4005])).
% 1.25/1.30 tff(4041,plain,
% 1.25/1.30 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s44, c_t2) | (~node12(s44)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s44, c_t2) | (~node12(s44)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4042,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s44, c_t2) | (~node12(s44)))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4043,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s44, c_t2) | (~node12(s44))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4042, 4041])).
% 1.25/1.30 tff(4044,plain,
% 1.25/1.30 (~node12(s44)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4043, 633, 4040])).
% 1.25/1.30 tff(4045,plain,
% 1.25/1.30 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s44, c_n1) | (~node11(s44)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s44, c_n1) | (~node11(s44)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4046,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s44, c_n1) | (~node11(s44)))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4047,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s44, c_n1) | (~node11(s44))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 1.25/1.30 tff(4048,plain,
% 1.25/1.30 (~node11(s44)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4047, 238, 3944])).
% 1.25/1.30 tff(4049,plain,
% 1.25/1.30 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s44, c_c1) | (~node10(s44)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s44, c_c1) | (~node10(s44)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4050,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s44, c_c1) | (~node10(s44)))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4051,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s44, c_c1) | (~node10(s44))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4050, 4049])).
% 1.25/1.30 tff(4052,plain,
% 1.25/1.30 (~node10(s44)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4051, 675, 3977])).
% 1.25/1.30 tff(4053,plain,
% 1.25/1.30 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s44, c_n1) | (~node9(s44)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s44, c_n1) | (~node9(s44)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4054,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s44, c_n1) | (~node9(s44)))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4055,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s44, c_n1) | (~node9(s44))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 1.25/1.30 tff(4056,plain,
% 1.25/1.30 (~node9(s44)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4055, 686, 3944])).
% 1.25/1.30 tff(4057,plain,
% 1.25/1.30 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s44, c_n2) | (~node8(s44)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s44, c_n2) | (~node8(s44)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4058,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s44, c_n2) | (~node8(s44)))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4059,plain,
% 1.25/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s44, c_n2) | (~node8(s44))),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4058, 4057])).
% 1.25/1.30 tff(4060,plain,
% 1.25/1.30 (~node8(s44)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4059, 271, 4009])).
% 1.25/1.30 tff(4061,plain,
% 1.25/1.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s44, s45)) | node14(s44, s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s44, s45)) | node14(s44, s45))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4062,plain,
% 1.25/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s44, s45)) | node14(s44, s45))),
% 1.25/1.30 inference(quant_inst,[status(thm)],[])).
% 1.25/1.30 tff(4063,plain,
% 1.25/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s44, s45)) | node14(s44, s45)),
% 1.25/1.30 inference(modus_ponens,[status(thm)],[4062, 4061])).
% 1.25/1.30 tff(4064,plain,
% 1.25/1.30 (node14(s44, s45)),
% 1.25/1.30 inference(unit_resolution,[status(thm)],[4063, 46, 4020])).
% 1.25/1.30 tff(4065,plain,
% 1.25/1.30 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | (~m_main_v_state2(s44, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | (~m_main_v_state2(s44, c_c2)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4066,plain,
% 1.25/1.30 (((~m_main_v_state2(s44, c_c2)) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | m_main_v_state2(s45, c_n2)) <=> (m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | (~m_main_v_state2(s44, c_c2)))),
% 1.25/1.30 inference(rewrite,[status(thm)],[])).
% 1.25/1.30 tff(4067,plain,
% 1.25/1.30 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s44, c_c2)) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | m_main_v_state2(s45, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | (~m_main_v_state2(s44, c_c2))))),
% 1.25/1.30 inference(monotonicity,[status(thm)],[4066])).
% 1.25/1.30 tff(4068,plain,
% 1.25/1.30 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s44, c_c2)) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | m_main_v_state2(s45, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | (~m_main_v_state2(s44, c_c2)))),
% 1.25/1.30 inference(transitivity,[status(thm)],[4067, 4065])).
% 1.25/1.30 tff(4069,plain,
% 1.25/1.30 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s44, c_c2)) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | m_main_v_state2(s45, c_n2))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4070,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~node14(s44, s45)) | (~m_main_v_state2(s44, c_c2))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4069, 4068])).
% 1.25/1.31 tff(4071,plain,
% 1.25/1.31 (m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~m_main_v_state2(s44, c_c2))),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4070, 726, 4064])).
% 1.25/1.31 tff(4072,plain,
% 1.25/1.31 (m_main_v_state2(s45, c_n2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4071, 4060, 4005, 4056, 4052, 4048, 4044])).
% 1.25/1.31 tff(4073,plain,
% 1.25/1.31 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_t2)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4074,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_t2)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4075,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_t2))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4074, 4073])).
% 1.25/1.31 tff(4076,plain,
% 1.25/1.31 (~m_main_v_state2(s45, c_t2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4075, 77, 4072])).
% 1.25/1.31 tff(4077,plain,
% 1.25/1.31 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s45, c_t2) | (~node15(s45)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s45, c_t2) | (~node15(s45)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4078,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s45, c_t2) | (~node15(s45)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4079,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s45, c_t2) | (~node15(s45))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4078, 4077])).
% 1.25/1.31 tff(4080,plain,
% 1.25/1.31 (~node15(s45)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4079, 103, 4076])).
% 1.25/1.31 tff(4081,plain,
% 1.25/1.31 (succ(s45, s46) <=> succ(s45, s46)),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4082,axiom,(succ(s45, s46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound46')).
% 1.25/1.31 tff(4083,plain,
% 1.25/1.31 (succ(s45, s46)),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4082, 4081])).
% 1.25/1.31 tff(4084,plain,
% 1.25/1.31 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4085,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4086,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46)),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4085, 4084])).
% 1.25/1.31 tff(4087,plain,
% 1.25/1.31 (trans(s45, s46)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4086, 4083, 32])).
% 1.25/1.31 tff(4088,plain,
% 1.25/1.31 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s45, s46)) | node18(s45, s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s45, s46)) | node18(s45, s46))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4089,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s45, s46)) | node18(s45, s46))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4090,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s45, s46)) | node18(s45, s46)),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 1.25/1.31 tff(4091,plain,
% 1.25/1.31 (node18(s45, s46)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4090, 125, 4087])).
% 1.25/1.31 tff(4092,plain,
% 1.25/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s45) | (~node18(s45, s46)) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s45) | (~node18(s45, s46)) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4093,plain,
% 1.25/1.31 (((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node15(s45) | (~node18(s45, s46)) | m_main_v_turn(s46, c_1)) <=> (node15(s45) | (~node18(s45, s46)) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4094,plain,
% 1.25/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node15(s45) | (~node18(s45, s46)) | m_main_v_turn(s46, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s45) | (~node18(s45, s46)) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1)))),
% 1.25/1.31 inference(monotonicity,[status(thm)],[4093])).
% 1.25/1.31 tff(4095,plain,
% 1.25/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node15(s45) | (~node18(s45, s46)) | m_main_v_turn(s46, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s45) | (~node18(s45, s46)) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1))),
% 1.25/1.31 inference(transitivity,[status(thm)],[4094, 4092])).
% 1.25/1.31 tff(4096,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node15(s45) | (~node18(s45, s46)) | m_main_v_turn(s46, c_1))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4097,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s45) | (~node18(s45, s46)) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1)),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4096, 4095])).
% 1.25/1.31 tff(4098,plain,
% 1.25/1.31 (node15(s45) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4097, 992, 4091])).
% 1.25/1.31 tff(4099,plain,
% 1.25/1.31 (m_main_v_turn(s46, c_1)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4098, 4080, 4072, 4036])).
% 1.25/1.31 tff(4100,plain,
% 1.25/1.31 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s46, c_1)) | (~m_main_v_turn(s46, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s46, c_1)) | (~m_main_v_turn(s46, c_2)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4101,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s46, c_1)) | (~m_main_v_turn(s46, c_2)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4102,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s46, c_1)) | (~m_main_v_turn(s46, c_2))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4101, 4100])).
% 1.25/1.31 tff(4103,plain,
% 1.25/1.31 (~m_main_v_turn(s46, c_2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4102, 156, 4099])).
% 1.25/1.31 tff(4104,plain,
% 1.25/1.31 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s46, c_2) | (~node12(s46)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s46, c_2) | (~node12(s46)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4105,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s46, c_2) | (~node12(s46)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4106,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s46, c_2) | (~node12(s46))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4105, 4104])).
% 1.25/1.31 tff(4107,plain,
% 1.25/1.31 (~node12(s46)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4106, 184, 4103])).
% 1.25/1.31 tff(4108,plain,
% 1.25/1.31 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s45, s46)) | node14(s45, s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s45, s46)) | node14(s45, s46))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4109,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s45, s46)) | node14(s45, s46))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4110,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s45, s46)) | node14(s45, s46)),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 1.25/1.31 tff(4111,plain,
% 1.25/1.31 (node14(s45, s46)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4110, 46, 4087])).
% 1.25/1.31 tff(4112,plain,
% 1.25/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | (~node14(s45, s46)) | m_main_v_state2(s46, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | (~node14(s45, s46)) | m_main_v_state2(s46, c_t2))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4113,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | (~node14(s45, s46)) | m_main_v_state2(s46, c_t2))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4114,plain,
% 1.25/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | (~node14(s45, s46)) | m_main_v_state2(s46, c_t2)),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4113, 4112])).
% 1.25/1.31 tff(4115,plain,
% 1.25/1.31 ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state2(s46, c_t2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4114, 922, 4111])).
% 1.25/1.31 tff(4116,plain,
% 1.25/1.31 (m_main_v_state2(s46, c_t2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4115, 4036, 4072])).
% 1.25/1.31 tff(4117,plain,
% 1.25/1.31 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s46, c_n2)) | (~m_main_v_state2(s46, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s46, c_n2)) | (~m_main_v_state2(s46, c_t2)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4118,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s46, c_n2)) | (~m_main_v_state2(s46, c_t2)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4119,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s46, c_n2)) | (~m_main_v_state2(s46, c_t2))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4118, 4117])).
% 1.25/1.31 tff(4120,plain,
% 1.25/1.31 (~m_main_v_state2(s46, c_n2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4119, 77, 4116])).
% 1.25/1.31 tff(4121,plain,
% 1.25/1.31 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s46, c_n2) | (~node8(s46)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s46, c_n2) | (~node8(s46)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4122,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s46, c_n2) | (~node8(s46)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4123,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s46, c_n2) | (~node8(s46))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4122, 4121])).
% 1.25/1.31 tff(4124,plain,
% 1.25/1.31 (~node8(s46)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4123, 271, 4120])).
% 1.25/1.31 tff(4125,plain,
% 1.25/1.31 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s46, c_n2) | (~node9(s46)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s46, c_n2) | (~node9(s46)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4126,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s46, c_n2) | (~node9(s46)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4127,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s46, c_n2) | (~node9(s46))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4126, 4125])).
% 1.25/1.31 tff(4128,plain,
% 1.25/1.31 (~node9(s46)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4127, 88, 4120])).
% 1.25/1.31 tff(4129,plain,
% 1.25/1.31 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s46, c_n2) | (~node10(s46)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s46, c_n2) | (~node10(s46)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4130,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s46, c_n2) | (~node10(s46)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4131,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s46, c_n2) | (~node10(s46))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4130, 4129])).
% 1.25/1.31 tff(4132,plain,
% 1.25/1.31 (~node10(s46)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4131, 249, 4120])).
% 1.25/1.31 tff(4133,plain,
% 1.25/1.31 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s46, c_t2)) | (~m_main_v_state2(s46, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s46, c_t2)) | (~m_main_v_state2(s46, c_c2)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4134,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s46, c_t2)) | (~m_main_v_state2(s46, c_c2)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4135,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s46, c_t2)) | (~m_main_v_state2(s46, c_c2))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4134, 4133])).
% 1.25/1.31 tff(4136,plain,
% 1.25/1.31 (~m_main_v_state2(s46, c_c2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4135, 260, 4116])).
% 1.25/1.31 tff(4137,plain,
% 1.25/1.31 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_c2)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4138,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_c2)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4139,plain,
% 1.25/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s45, c_n2)) | (~m_main_v_state2(s45, c_c2))),
% 1.25/1.31 inference(modus_ponens,[status(thm)],[4138, 4137])).
% 1.25/1.31 tff(4140,plain,
% 1.25/1.31 (~m_main_v_state2(s45, c_c2)),
% 1.25/1.31 inference(unit_resolution,[status(thm)],[4139, 697, 4072])).
% 1.25/1.31 tff(4141,plain,
% 1.25/1.31 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s45, c_c2) | (~node3(s45)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s45, c_c2) | (~node3(s45)))),
% 1.25/1.31 inference(rewrite,[status(thm)],[])).
% 1.25/1.31 tff(4142,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s45, c_c2) | (~node3(s45)))),
% 1.25/1.31 inference(quant_inst,[status(thm)],[])).
% 1.25/1.31 tff(4143,plain,
% 1.25/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s45, c_c2) | (~node3(s45))),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4142, 4141])).
% 1.25/1.32 tff(4144,plain,
% 1.25/1.32 (~node3(s45)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4143, 399, 4140])).
% 1.25/1.32 tff(4145,plain,
% 1.25/1.32 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)) | (~node6(s44, s45)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)) | (~node6(s44, s45)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4146,plain,
% 1.25/1.32 (((~node6(s44, s45)) | m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1))) <=> (m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)) | (~node6(s44, s45)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4147,plain,
% 1.25/1.32 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s44, s45)) | m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)) | (~node6(s44, s45))))),
% 1.25/1.32 inference(monotonicity,[status(thm)],[4146])).
% 1.25/1.32 tff(4148,plain,
% 1.25/1.32 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s44, s45)) | m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)) | (~node6(s44, s45)))),
% 1.25/1.32 inference(transitivity,[status(thm)],[4147, 4145])).
% 1.25/1.32 tff(4149,plain,
% 1.25/1.32 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s44, s45)) | m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4150,plain,
% 1.25/1.32 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s44, c_n1) | (~m_main_v_state1(s45, c_n1)) | (~node6(s44, s45))),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4149, 4148])).
% 1.25/1.32 tff(4151,plain,
% 1.25/1.32 (~m_main_v_state1(s45, c_n1)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4150, 835, 3944, 4029])).
% 1.25/1.32 tff(4152,plain,
% 1.25/1.32 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s45, c_n1) | (~node2(s45)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s45, c_n1) | (~node2(s45)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4153,plain,
% 1.25/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s45, c_n1) | (~node2(s45)))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4154,plain,
% 1.25/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s45, c_n1) | (~node2(s45))),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4153, 4152])).
% 1.25/1.32 tff(4155,plain,
% 1.25/1.32 (~node2(s45)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4154, 787, 4151])).
% 1.25/1.32 tff(4156,plain,
% 1.25/1.32 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s45, c_t2) | (~node1(s45)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s45, c_t2) | (~node1(s45)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4157,plain,
% 1.25/1.32 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s45, c_t2) | (~node1(s45)))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4158,plain,
% 1.25/1.32 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s45, c_t2) | (~node1(s45))),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4157, 4156])).
% 1.25/1.32 tff(4159,plain,
% 1.25/1.32 (~node1(s45)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4158, 195, 4076])).
% 1.25/1.32 tff(4160,plain,
% 1.25/1.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s45, s46)) | node7(s45, s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s45, s46)) | node7(s45, s46))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4161,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s45, s46)) | node7(s45, s46))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4162,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s45, s46)) | node7(s45, s46)),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 1.25/1.32 tff(4163,plain,
% 1.25/1.32 (node7(s45, s46)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4162, 206, 4087])).
% 1.25/1.32 tff(4164,plain,
% 1.25/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state1(s46, c_c1) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state1(s46, c_c1) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4165,plain,
% 1.25/1.32 (((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)) | m_main_v_state1(s46, c_c1)) <=> ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state1(s46, c_c1) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4166,plain,
% 1.25/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)) | m_main_v_state1(s46, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state1(s46, c_c1) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46))))),
% 1.25/1.32 inference(monotonicity,[status(thm)],[4165])).
% 1.25/1.32 tff(4167,plain,
% 1.25/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)) | m_main_v_state1(s46, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state1(s46, c_c1) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)))),
% 1.25/1.32 inference(transitivity,[status(thm)],[4166, 4164])).
% 1.25/1.32 tff(4168,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46)) | m_main_v_state1(s46, c_c1))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4169,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state1(s46, c_c1) | node1(s45) | node2(s45) | node3(s45) | (~node7(s45, s46))),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4168, 4167])).
% 1.25/1.32 tff(4170,plain,
% 1.25/1.32 ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state1(s46, c_c1) | node1(s45) | node2(s45) | node3(s45)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4169, 892, 4163])).
% 1.25/1.32 tff(4171,plain,
% 1.25/1.32 (m_main_v_state1(s46, c_c1)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4170, 4159, 4072, 4036, 4155, 4144])).
% 1.25/1.32 tff(4172,plain,
% 1.25/1.32 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s46, c_n1)) | (~m_main_v_state1(s46, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s46, c_n1)) | (~m_main_v_state1(s46, c_c1)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4173,plain,
% 1.25/1.32 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s46, c_n1)) | (~m_main_v_state1(s46, c_c1)))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4174,plain,
% 1.25/1.32 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s46, c_n1)) | (~m_main_v_state1(s46, c_c1))),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4173, 4172])).
% 1.25/1.32 tff(4175,plain,
% 1.25/1.32 (~m_main_v_state1(s46, c_n1)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4174, 454, 4171])).
% 1.25/1.32 tff(4176,plain,
% 1.25/1.32 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s46, c_n1) | (~node11(s46)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s46, c_n1) | (~node11(s46)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4177,plain,
% 1.25/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s46, c_n1) | (~node11(s46)))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4178,plain,
% 1.25/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s46, c_n1) | (~node11(s46))),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 1.25/1.32 tff(4179,plain,
% 1.25/1.32 (~node11(s46)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4178, 238, 4175])).
% 1.25/1.32 tff(4180,plain,
% 1.25/1.32 (succ(s46, s47) <=> succ(s46, s47)),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4181,axiom,(succ(s46, s47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound47')).
% 1.25/1.32 tff(4182,plain,
% 1.25/1.32 (succ(s46, s47)),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4181, 4180])).
% 1.25/1.32 tff(4183,plain,
% 1.25/1.32 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4184,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4185,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47)),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4184, 4183])).
% 1.25/1.32 tff(4186,plain,
% 1.25/1.32 (trans(s46, s47)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4185, 4182, 32])).
% 1.25/1.32 tff(4187,plain,
% 1.25/1.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s46, s47)) | node14(s46, s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s46, s47)) | node14(s46, s47))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4188,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s46, s47)) | node14(s46, s47))),
% 1.25/1.32 inference(quant_inst,[status(thm)],[])).
% 1.25/1.32 tff(4189,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s46, s47)) | node14(s46, s47)),
% 1.25/1.32 inference(modus_ponens,[status(thm)],[4188, 4187])).
% 1.25/1.32 tff(4190,plain,
% 1.25/1.32 (node14(s46, s47)),
% 1.25/1.32 inference(unit_resolution,[status(thm)],[4189, 46, 4186])).
% 1.25/1.32 tff(4191,plain,
% 1.25/1.32 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47)))),
% 1.25/1.32 inference(rewrite,[status(thm)],[])).
% 1.25/1.32 tff(4192,plain,
% 1.25/1.32 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4193,plain,
% 1.25/1.33 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 1.25/1.33 tff(4194,plain,
% 1.25/1.33 (m_main_v_state2(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4193, 296, 4190])).
% 1.25/1.33 tff(4195,plain,
% 1.25/1.33 (node13(s46, s47)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4194, 4179, 4136, 4132, 4128, 4124, 4107])).
% 1.25/1.33 tff(4196,plain,
% 1.25/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4197,plain,
% 1.25/1.33 (((~node13(s46, s47)) | m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2))) <=> (m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4198,plain,
% 1.25/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s46, s47)) | m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47))))),
% 1.25/1.33 inference(monotonicity,[status(thm)],[4197])).
% 1.25/1.33 tff(4199,plain,
% 1.25/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s46, s47)) | m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47)))),
% 1.25/1.33 inference(transitivity,[status(thm)],[4198, 4196])).
% 1.25/1.33 tff(4200,plain,
% 1.25/1.33 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s46, s47)) | m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4201,plain,
% 1.25/1.33 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4200, 4199])).
% 1.25/1.33 tff(4202,plain,
% 1.25/1.33 (~m_main_v_state2(s47, c_n2)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4201, 311, 4120, 4195])).
% 1.25/1.33 tff(4203,plain,
% 1.25/1.33 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s47, c_n2) | (~node9(s47)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s47, c_n2) | (~node9(s47)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4204,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s47, c_n2) | (~node9(s47)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4205,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s47, c_n2) | (~node9(s47))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4204, 4203])).
% 1.25/1.33 tff(4206,plain,
% 1.25/1.33 (~node9(s47)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4205, 88, 4202])).
% 1.25/1.33 tff(4207,plain,
% 1.25/1.33 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s47, c_n2) | (~node10(s47)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s47, c_n2) | (~node10(s47)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4208,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s47, c_n2) | (~node10(s47)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4209,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s47, c_n2) | (~node10(s47))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 1.25/1.33 tff(4210,plain,
% 1.25/1.33 (~node10(s47)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4209, 249, 4202])).
% 1.25/1.33 tff(4211,plain,
% 1.25/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4212,plain,
% 1.25/1.33 (((~node13(s46, s47)) | (~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2)) <=> ((~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4213,plain,
% 1.25/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s46, s47)) | (~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47))))),
% 1.25/1.33 inference(monotonicity,[status(thm)],[4212])).
% 1.25/1.33 tff(4214,plain,
% 1.25/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s46, s47)) | (~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47)))),
% 1.25/1.33 inference(transitivity,[status(thm)],[4213, 4211])).
% 1.25/1.33 tff(4215,plain,
% 1.25/1.33 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s46, s47)) | (~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4216,plain,
% 1.25/1.33 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4215, 4214])).
% 1.25/1.33 tff(4217,plain,
% 1.25/1.33 (m_main_v_state2(s47, c_t2)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4216, 518, 4116, 4195])).
% 1.25/1.33 tff(4218,plain,
% 1.25/1.33 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s46, c_t1)) | (~m_main_v_state1(s46, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s46, c_t1)) | (~m_main_v_state1(s46, c_c1)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4219,plain,
% 1.25/1.33 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s46, c_t1)) | (~m_main_v_state1(s46, c_c1)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4220,plain,
% 1.25/1.33 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s46, c_t1)) | (~m_main_v_state1(s46, c_c1))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4219, 4218])).
% 1.25/1.33 tff(4221,plain,
% 1.25/1.33 (~m_main_v_state1(s46, c_t1)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4220, 539, 4171])).
% 1.25/1.33 tff(4222,plain,
% 1.25/1.33 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s46, c_t1) | (~node5(s46)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s46, c_t1) | (~node5(s46)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4223,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s46, c_t1) | (~node5(s46)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4224,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s46, c_t1) | (~node5(s46))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4223, 4222])).
% 1.25/1.33 tff(4225,plain,
% 1.25/1.33 (~node5(s46)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4224, 550, 4221])).
% 1.25/1.33 tff(4226,plain,
% 1.25/1.33 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s46, c_n2) | (~node4(s46)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s46, c_n2) | (~node4(s46)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4227,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s46, c_n2) | (~node4(s46)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4228,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s46, c_n2) | (~node4(s46))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4227, 4226])).
% 1.25/1.33 tff(4229,plain,
% 1.25/1.33 (~node4(s46)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4228, 388, 4120])).
% 1.25/1.33 tff(4230,plain,
% 1.25/1.33 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s46, c_c2) | (~node3(s46)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s46, c_c2) | (~node3(s46)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4231,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s46, c_c2) | (~node3(s46)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4232,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s46, c_c2) | (~node3(s46))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4231, 4230])).
% 1.25/1.33 tff(4233,plain,
% 1.25/1.33 (~node3(s46)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4232, 399, 4136])).
% 1.25/1.33 tff(4234,plain,
% 1.25/1.33 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s46, c_n2) | (~node2(s46)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s46, c_n2) | (~node2(s46)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4235,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s46, c_n2) | (~node2(s46)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4236,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s46, c_n2) | (~node2(s46))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4235, 4234])).
% 1.25/1.33 tff(4237,plain,
% 1.25/1.33 (~node2(s46)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4236, 410, 4120])).
% 1.25/1.33 tff(4238,plain,
% 1.25/1.33 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s46, c_n1) | (~node1(s46)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s46, c_n1) | (~node1(s46)))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4239,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s46, c_n1) | (~node1(s46)))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4240,plain,
% 1.25/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s46, c_n1) | (~node1(s46))),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4239, 4238])).
% 1.25/1.33 tff(4241,plain,
% 1.25/1.33 (~node1(s46)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4240, 421, 4175])).
% 1.25/1.33 tff(4242,plain,
% 1.25/1.33 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s46, s47)) | node7(s46, s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s46, s47)) | node7(s46, s47))),
% 1.25/1.33 inference(rewrite,[status(thm)],[])).
% 1.25/1.33 tff(4243,plain,
% 1.25/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s46, s47)) | node7(s46, s47))),
% 1.25/1.33 inference(quant_inst,[status(thm)],[])).
% 1.25/1.33 tff(4244,plain,
% 1.25/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s46, s47)) | node7(s46, s47)),
% 1.25/1.33 inference(modus_ponens,[status(thm)],[4243, 4242])).
% 1.25/1.33 tff(4245,plain,
% 1.25/1.33 (node7(s46, s47)),
% 1.25/1.33 inference(unit_resolution,[status(thm)],[4244, 206, 4186])).
% 1.25/1.33 tff(4246,plain,
% 1.25/1.33 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)))),
% 1.25/1.34 inference(rewrite,[status(thm)],[])).
% 1.25/1.34 tff(4247,plain,
% 1.25/1.34 (((~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)) | m_main_v_state1(s47, c_n1)) <=> (m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)))),
% 1.25/1.34 inference(rewrite,[status(thm)],[])).
% 1.25/1.34 tff(4248,plain,
% 1.25/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)) | m_main_v_state1(s47, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47))))),
% 1.25/1.34 inference(monotonicity,[status(thm)],[4247])).
% 1.25/1.34 tff(4249,plain,
% 1.25/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)) | m_main_v_state1(s47, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)))),
% 1.25/1.34 inference(transitivity,[status(thm)],[4248, 4246])).
% 1.25/1.34 tff(4250,plain,
% 1.25/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)) | m_main_v_state1(s47, c_n1))),
% 1.25/1.34 inference(quant_inst,[status(thm)],[])).
% 1.25/1.34 tff(4251,plain,
% 1.25/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47))),
% 1.25/1.34 inference(modus_ponens,[status(thm)],[4250, 4249])).
% 1.25/1.34 tff(4252,plain,
% 1.25/1.34 (m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46)),
% 1.25/1.34 inference(unit_resolution,[status(thm)],[4251, 584, 4245])).
% 1.25/1.34 tff(4253,plain,
% 1.25/1.34 (m_main_v_state1(s47, c_n1)),
% 1.25/1.34 inference(unit_resolution,[status(thm)],[4252, 4241, 4171, 4237, 4233, 4229, 4225])).
% 1.25/1.34 tff(4254,plain,
% 1.25/1.34 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s47, c_n2) | (~node8(s47)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s47, c_n2) | (~node8(s47)))),
% 1.25/1.34 inference(rewrite,[status(thm)],[])).
% 1.25/1.34 tff(4255,plain,
% 1.25/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s47, c_n2) | (~node8(s47)))),
% 1.25/1.34 inference(quant_inst,[status(thm)],[])).
% 1.25/1.34 tff(4256,plain,
% 1.25/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s47, c_n2) | (~node8(s47))),
% 1.25/1.34 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 1.25/1.34 tff(4257,plain,
% 1.25/1.34 (~node8(s47)),
% 1.25/1.34 inference(unit_resolution,[status(thm)],[4256, 271, 4202])).
% 1.25/1.34 tff(4258,plain,
% 1.25/1.34 (succ(s47, s48) <=> succ(s47, s48)),
% 1.25/1.34 inference(rewrite,[status(thm)],[])).
% 1.25/1.34 tff(4259,axiom,(succ(s47, s48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound48')).
% 1.25/1.34 tff(4260,plain,
% 1.25/1.34 (succ(s47, s48)),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4259, 4258])).
% 1.32/1.34 tff(4261,plain,
% 1.32/1.34 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4262,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4263,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48)),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4262, 4261])).
% 1.32/1.34 tff(4264,plain,
% 1.32/1.34 (trans(s47, s48)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4263, 4260, 32])).
% 1.32/1.34 tff(4265,plain,
% 1.32/1.34 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s47, s48)) | node14(s47, s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s47, s48)) | node14(s47, s48))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4266,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s47, s48)) | node14(s47, s48))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4267,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s47, s48)) | node14(s47, s48)),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 1.32/1.34 tff(4268,plain,
% 1.32/1.34 (node14(s47, s48)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4267, 46, 4264])).
% 1.32/1.34 tff(4269,plain,
% 1.32/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | node9(s47) | node8(s47) | node10(s47) | (~node14(s47, s48)) | m_main_v_state2(s48, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | node9(s47) | node8(s47) | node10(s47) | (~node14(s47, s48)) | m_main_v_state2(s48, c_c2))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4270,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | node9(s47) | node8(s47) | node10(s47) | (~node14(s47, s48)) | m_main_v_state2(s48, c_c2))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4271,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | node9(s47) | node8(s47) | node10(s47) | (~node14(s47, s48)) | m_main_v_state2(s48, c_c2)),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4270, 4269])).
% 1.32/1.34 tff(4272,plain,
% 1.32/1.34 ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | node9(s47) | node8(s47) | node10(s47) | m_main_v_state2(s48, c_c2)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4271, 617, 4268])).
% 1.32/1.34 tff(4273,plain,
% 1.32/1.34 (m_main_v_state2(s48, c_c2)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4272, 4257, 4253, 4217, 4210, 4206])).
% 1.32/1.34 tff(4274,plain,
% 1.32/1.34 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s48, c_t2)) | (~m_main_v_state2(s48, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s48, c_t2)) | (~m_main_v_state2(s48, c_c2)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4275,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s48, c_t2)) | (~m_main_v_state2(s48, c_c2)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4276,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s48, c_t2)) | (~m_main_v_state2(s48, c_c2))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4275, 4274])).
% 1.32/1.34 tff(4277,plain,
% 1.32/1.34 (~m_main_v_state2(s48, c_t2)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4276, 260, 4273])).
% 1.32/1.34 tff(4278,plain,
% 1.32/1.34 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s48, c_t2) | (~node12(s48)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s48, c_t2) | (~node12(s48)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4279,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s48, c_t2) | (~node12(s48)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4280,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s48, c_t2) | (~node12(s48))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4279, 4278])).
% 1.32/1.34 tff(4281,plain,
% 1.32/1.34 (~node12(s48)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4280, 633, 4277])).
% 1.32/1.34 tff(4282,plain,
% 1.32/1.34 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s47, s48)) | node7(s47, s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s47, s48)) | node7(s47, s48))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4283,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s47, s48)) | node7(s47, s48))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4284,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s47, s48)) | node7(s47, s48)),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4283, 4282])).
% 1.32/1.34 tff(4285,plain,
% 1.32/1.34 (node7(s47, s48)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4284, 206, 4264])).
% 1.32/1.34 tff(4286,plain,
% 1.32/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4287,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4288,plain,
% 1.32/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1)),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4287, 4286])).
% 1.32/1.34 tff(4289,plain,
% 1.32/1.34 ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | m_main_v_state1(s48, c_t1)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4288, 651, 4285])).
% 1.32/1.34 tff(4290,plain,
% 1.32/1.34 (m_main_v_state1(s48, c_t1)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4289, 4217, 4253])).
% 1.32/1.34 tff(4291,plain,
% 1.32/1.34 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s48, c_n1)) | (~m_main_v_state1(s48, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s48, c_n1)) | (~m_main_v_state1(s48, c_t1)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4292,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s48, c_n1)) | (~m_main_v_state1(s48, c_t1)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4293,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s48, c_n1)) | (~m_main_v_state1(s48, c_t1))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4292, 4291])).
% 1.32/1.34 tff(4294,plain,
% 1.32/1.34 (~m_main_v_state1(s48, c_n1)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4293, 10, 4290])).
% 1.32/1.34 tff(4295,plain,
% 1.32/1.34 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s48, c_n1) | (~node11(s48)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s48, c_n1) | (~node11(s48)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4296,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s48, c_n1) | (~node11(s48)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4297,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s48, c_n1) | (~node11(s48))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 1.32/1.34 tff(4298,plain,
% 1.32/1.34 (~node11(s48)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4297, 238, 4294])).
% 1.32/1.34 tff(4299,plain,
% 1.32/1.34 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s48, c_t1)) | (~m_main_v_state1(s48, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s48, c_t1)) | (~m_main_v_state1(s48, c_c1)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4300,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s48, c_t1)) | (~m_main_v_state1(s48, c_c1)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4301,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s48, c_t1)) | (~m_main_v_state1(s48, c_c1))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 1.32/1.34 tff(4302,plain,
% 1.32/1.34 (~m_main_v_state1(s48, c_c1)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4301, 539, 4290])).
% 1.32/1.34 tff(4303,plain,
% 1.32/1.34 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s48, c_c1) | (~node10(s48)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s48, c_c1) | (~node10(s48)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4304,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s48, c_c1) | (~node10(s48)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4305,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s48, c_c1) | (~node10(s48))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4304, 4303])).
% 1.32/1.34 tff(4306,plain,
% 1.32/1.34 (~node10(s48)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4305, 675, 4302])).
% 1.32/1.34 tff(4307,plain,
% 1.32/1.34 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s48, c_n1) | (~node9(s48)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s48, c_n1) | (~node9(s48)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4308,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s48, c_n1) | (~node9(s48)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4309,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s48, c_n1) | (~node9(s48))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4308, 4307])).
% 1.32/1.34 tff(4310,plain,
% 1.32/1.34 (~node9(s48)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4309, 686, 4294])).
% 1.32/1.34 tff(4311,plain,
% 1.32/1.34 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s48, c_n2)) | (~m_main_v_state2(s48, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s48, c_n2)) | (~m_main_v_state2(s48, c_c2)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4312,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s48, c_n2)) | (~m_main_v_state2(s48, c_c2)))),
% 1.32/1.34 inference(quant_inst,[status(thm)],[])).
% 1.32/1.34 tff(4313,plain,
% 1.32/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s48, c_n2)) | (~m_main_v_state2(s48, c_c2))),
% 1.32/1.34 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 1.32/1.34 tff(4314,plain,
% 1.32/1.34 (~m_main_v_state2(s48, c_n2)),
% 1.32/1.34 inference(unit_resolution,[status(thm)],[4313, 697, 4273])).
% 1.32/1.34 tff(4315,plain,
% 1.32/1.34 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s48, c_n2) | (~node8(s48)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s48, c_n2) | (~node8(s48)))),
% 1.32/1.34 inference(rewrite,[status(thm)],[])).
% 1.32/1.34 tff(4316,plain,
% 1.32/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s48, c_n2) | (~node8(s48)))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4317,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s48, c_n2) | (~node8(s48))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4316, 4315])).
% 1.32/1.35 tff(4318,plain,
% 1.32/1.35 (~node8(s48)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4317, 271, 4314])).
% 1.32/1.35 tff(4319,plain,
% 1.32/1.35 (succ(s48, s49) <=> succ(s48, s49)),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4320,axiom,(succ(s48, s49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound49')).
% 1.32/1.35 tff(4321,plain,
% 1.32/1.35 (succ(s48, s49)),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4320, 4319])).
% 1.32/1.35 tff(4322,plain,
% 1.32/1.35 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4323,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4324,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49)),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4323, 4322])).
% 1.32/1.35 tff(4325,plain,
% 1.32/1.35 (trans(s48, s49)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4324, 4321, 32])).
% 1.32/1.35 tff(4326,plain,
% 1.32/1.35 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s48, s49)) | node14(s48, s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s48, s49)) | node14(s48, s49))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4327,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s48, s49)) | node14(s48, s49))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4328,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s48, s49)) | node14(s48, s49)),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4327, 4326])).
% 1.32/1.35 tff(4329,plain,
% 1.32/1.35 (node14(s48, s49)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4328, 46, 4325])).
% 1.32/1.35 tff(4330,plain,
% 1.32/1.35 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | (~m_main_v_state2(s48, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | (~m_main_v_state2(s48, c_c2)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4331,plain,
% 1.32/1.35 (((~m_main_v_state2(s48, c_c2)) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | m_main_v_state2(s49, c_n2)) <=> (m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | (~m_main_v_state2(s48, c_c2)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4332,plain,
% 1.32/1.35 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s48, c_c2)) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | m_main_v_state2(s49, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | (~m_main_v_state2(s48, c_c2))))),
% 1.32/1.35 inference(monotonicity,[status(thm)],[4331])).
% 1.32/1.35 tff(4333,plain,
% 1.32/1.35 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s48, c_c2)) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | m_main_v_state2(s49, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | (~m_main_v_state2(s48, c_c2)))),
% 1.32/1.35 inference(transitivity,[status(thm)],[4332, 4330])).
% 1.32/1.35 tff(4334,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s48, c_c2)) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | m_main_v_state2(s49, c_n2))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4335,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | (~m_main_v_state2(s48, c_c2))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4334, 4333])).
% 1.32/1.35 tff(4336,plain,
% 1.32/1.35 (m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~m_main_v_state2(s48, c_c2))),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4335, 726, 4329])).
% 1.32/1.35 tff(4337,plain,
% 1.32/1.35 (m_main_v_state2(s49, c_n2)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4336, 4318, 4273, 4310, 4306, 4298, 4281])).
% 1.32/1.35 tff(4338,plain,
% 1.32/1.35 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_c2)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4339,plain,
% 1.32/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_c2)))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4340,plain,
% 1.32/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_c2))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4339, 4338])).
% 1.32/1.35 tff(4341,plain,
% 1.32/1.35 (~m_main_v_state2(s49, c_c2)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4340, 697, 4337])).
% 1.32/1.35 tff(4342,plain,
% 1.32/1.35 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s49, c_c2) | (~node3(s49)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s49, c_c2) | (~node3(s49)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4343,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s49, c_c2) | (~node3(s49)))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4344,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s49, c_c2) | (~node3(s49))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 1.32/1.35 tff(4345,plain,
% 1.32/1.35 (~node3(s49)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4344, 399, 4341])).
% 1.32/1.35 tff(4346,plain,
% 1.32/1.35 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s48, c_n1) | (~node1(s48)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s48, c_n1) | (~node1(s48)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4347,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s48, c_n1) | (~node1(s48)))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4348,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s48, c_n1) | (~node1(s48))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4347, 4346])).
% 1.32/1.35 tff(4349,plain,
% 1.32/1.35 (~node1(s48)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4348, 421, 4294])).
% 1.32/1.35 tff(4350,plain,
% 1.32/1.35 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s47, s48)) | node18(s47, s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s47, s48)) | node18(s47, s48))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4351,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s47, s48)) | node18(s47, s48))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4352,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s47, s48)) | node18(s47, s48)),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4351, 4350])).
% 1.32/1.35 tff(4353,plain,
% 1.32/1.35 (node18(s47, s48)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4352, 125, 4264])).
% 1.32/1.35 tff(4354,plain,
% 1.32/1.35 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node18(s47, s48)) | m_main_v_turn(s48, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node18(s47, s48)) | m_main_v_turn(s48, c_2))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4355,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node18(s47, s48)) | m_main_v_turn(s48, c_2))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4356,plain,
% 1.32/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node18(s47, s48)) | m_main_v_turn(s48, c_2)),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4355, 4354])).
% 1.32/1.35 tff(4357,plain,
% 1.32/1.35 ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | m_main_v_turn(s48, c_2)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4356, 760, 4353])).
% 1.32/1.35 tff(4358,plain,
% 1.32/1.35 (m_main_v_turn(s48, c_2)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4357, 4217, 4253])).
% 1.32/1.35 tff(4359,plain,
% 1.32/1.35 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s48, c_1)) | (~m_main_v_turn(s48, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s48, c_1)) | (~m_main_v_turn(s48, c_2)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4360,plain,
% 1.32/1.35 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s48, c_1)) | (~m_main_v_turn(s48, c_2)))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4361,plain,
% 1.32/1.35 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s48, c_1)) | (~m_main_v_turn(s48, c_2))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4360, 4359])).
% 1.32/1.35 tff(4362,plain,
% 1.32/1.35 (~m_main_v_turn(s48, c_1)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4361, 156, 4358])).
% 1.32/1.35 tff(4363,plain,
% 1.32/1.35 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s48, c_1) | (~node5(s48)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s48, c_1) | (~node5(s48)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4364,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s48, c_1) | (~node5(s48)))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4365,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s48, c_1) | (~node5(s48))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4364, 4363])).
% 1.32/1.35 tff(4366,plain,
% 1.32/1.35 (~node5(s48)),
% 1.32/1.35 inference(unit_resolution,[status(thm)],[4365, 776, 4362])).
% 1.32/1.35 tff(4367,plain,
% 1.32/1.35 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s48, c_n1) | (~node2(s48)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s48, c_n1) | (~node2(s48)))),
% 1.32/1.35 inference(rewrite,[status(thm)],[])).
% 1.32/1.35 tff(4368,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s48, c_n1) | (~node2(s48)))),
% 1.32/1.35 inference(quant_inst,[status(thm)],[])).
% 1.32/1.35 tff(4369,plain,
% 1.32/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s48, c_n1) | (~node2(s48))),
% 1.32/1.35 inference(modus_ponens,[status(thm)],[4368, 4367])).
% 1.32/1.36 tff(4370,plain,
% 1.32/1.36 (~node2(s48)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4369, 787, 4294])).
% 1.32/1.36 tff(4371,plain,
% 1.32/1.36 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s48, c_n1) | (~node3(s48)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s48, c_n1) | (~node3(s48)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4372,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s48, c_n1) | (~node3(s48)))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4373,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s48, c_n1) | (~node3(s48))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4372, 4371])).
% 1.32/1.36 tff(4374,plain,
% 1.32/1.36 (~node3(s48)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4373, 798, 4294])).
% 1.32/1.36 tff(4375,plain,
% 1.32/1.36 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s48, c_n2) | (~node4(s48)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s48, c_n2) | (~node4(s48)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4376,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s48, c_n2) | (~node4(s48)))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4377,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s48, c_n2) | (~node4(s48))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4376, 4375])).
% 1.32/1.36 tff(4378,plain,
% 1.32/1.36 (~node4(s48)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4377, 388, 4314])).
% 1.32/1.36 tff(4379,plain,
% 1.32/1.36 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s48, s49)) | node7(s48, s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s48, s49)) | node7(s48, s49))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4380,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s48, s49)) | node7(s48, s49))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4381,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s48, s49)) | node7(s48, s49)),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4380, 4379])).
% 1.32/1.36 tff(4382,plain,
% 1.32/1.36 (node7(s48, s49)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4381, 206, 4325])).
% 1.32/1.36 tff(4383,plain,
% 1.32/1.36 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49) | (~node7(s48, s49)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49) | (~node7(s48, s49)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4384,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49) | (~node7(s48, s49)))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4385,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49) | (~node7(s48, s49))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4384, 4383])).
% 1.32/1.36 tff(4386,plain,
% 1.32/1.36 (m_main_v_state1(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4385, 820, 4382])).
% 1.32/1.36 tff(4387,plain,
% 1.32/1.36 (node6(s48, s49)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4386, 4378, 4302, 4374, 4370, 4366, 4349])).
% 1.32/1.36 tff(4388,plain,
% 1.32/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4389,plain,
% 1.32/1.36 (((~node6(s48, s49)) | m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1))) <=> (m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4390,plain,
% 1.32/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s48, s49)) | m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49))))),
% 1.32/1.36 inference(monotonicity,[status(thm)],[4389])).
% 1.32/1.36 tff(4391,plain,
% 1.32/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s48, s49)) | m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49)))),
% 1.32/1.36 inference(transitivity,[status(thm)],[4390, 4388])).
% 1.32/1.36 tff(4392,plain,
% 1.32/1.36 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s48, s49)) | m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4393,plain,
% 1.32/1.36 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4392, 4391])).
% 1.32/1.36 tff(4394,plain,
% 1.32/1.36 (~m_main_v_state1(s49, c_n1)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4393, 835, 4294, 4387])).
% 1.32/1.36 tff(4395,plain,
% 1.32/1.36 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s49, c_n1) | (~node2(s49)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s49, c_n1) | (~node2(s49)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4396,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s49, c_n1) | (~node2(s49)))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4397,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s49, c_n1) | (~node2(s49))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4396, 4395])).
% 1.32/1.36 tff(4398,plain,
% 1.32/1.36 (~node2(s49)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4397, 787, 4394])).
% 1.32/1.36 tff(4399,plain,
% 1.32/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1) | (~node6(s48, s49)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1) | (~node6(s48, s49)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4400,plain,
% 1.32/1.36 (((~node6(s48, s49)) | (~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1)) <=> ((~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1) | (~node6(s48, s49)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4401,plain,
% 1.32/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s48, s49)) | (~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1) | (~node6(s48, s49))))),
% 1.32/1.36 inference(monotonicity,[status(thm)],[4400])).
% 1.32/1.36 tff(4402,plain,
% 1.32/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s48, s49)) | (~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1) | (~node6(s48, s49)))),
% 1.32/1.36 inference(transitivity,[status(thm)],[4401, 4399])).
% 1.32/1.36 tff(4403,plain,
% 1.32/1.36 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s48, s49)) | (~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4404,plain,
% 1.32/1.36 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s48, c_t1)) | m_main_v_state1(s49, c_t1) | (~node6(s48, s49))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4403, 4402])).
% 1.32/1.36 tff(4405,plain,
% 1.32/1.36 (m_main_v_state1(s49, c_t1)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4404, 856, 4290, 4387])).
% 1.32/1.36 tff(4406,plain,
% 1.32/1.36 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_t2)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4407,plain,
% 1.32/1.36 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_t2)))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4408,plain,
% 1.32/1.36 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s49, c_n2)) | (~m_main_v_state2(s49, c_t2))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4407, 4406])).
% 1.32/1.36 tff(4409,plain,
% 1.32/1.36 (~m_main_v_state2(s49, c_t2)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4408, 77, 4337])).
% 1.32/1.36 tff(4410,plain,
% 1.32/1.36 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s49, c_t2) | (~node1(s49)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s49, c_t2) | (~node1(s49)))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4411,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s49, c_t2) | (~node1(s49)))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4412,plain,
% 1.32/1.36 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s49, c_t2) | (~node1(s49))),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4411, 4410])).
% 1.32/1.36 tff(4413,plain,
% 1.32/1.36 (~node1(s49)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4412, 195, 4409])).
% 1.32/1.36 tff(4414,plain,
% 1.32/1.36 (succ(s49, s50) <=> succ(s49, s50)),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4415,axiom,(succ(s49, s50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound50')).
% 1.32/1.36 tff(4416,plain,
% 1.32/1.36 (succ(s49, s50)),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4415, 4414])).
% 1.32/1.36 tff(4417,plain,
% 1.32/1.36 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4418,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4419,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50)),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4418, 4417])).
% 1.32/1.36 tff(4420,plain,
% 1.32/1.36 (trans(s49, s50)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4419, 4416, 32])).
% 1.32/1.36 tff(4421,plain,
% 1.32/1.36 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s49, s50)) | node7(s49, s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s49, s50)) | node7(s49, s50))),
% 1.32/1.36 inference(rewrite,[status(thm)],[])).
% 1.32/1.36 tff(4422,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s49, s50)) | node7(s49, s50))),
% 1.32/1.36 inference(quant_inst,[status(thm)],[])).
% 1.32/1.36 tff(4423,plain,
% 1.32/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s49, s50)) | node7(s49, s50)),
% 1.32/1.36 inference(modus_ponens,[status(thm)],[4422, 4421])).
% 1.32/1.36 tff(4424,plain,
% 1.32/1.36 (node7(s49, s50)),
% 1.32/1.36 inference(unit_resolution,[status(thm)],[4423, 206, 4420])).
% 1.32/1.36 tff(4425,plain,
% 1.32/1.36 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state1(s50, c_c1) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state1(s50, c_c1) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)))),
% 1.32/1.37 inference(rewrite,[status(thm)],[])).
% 1.32/1.37 tff(4426,plain,
% 1.32/1.37 (((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)) | m_main_v_state1(s50, c_c1)) <=> ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state1(s50, c_c1) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)))),
% 1.32/1.37 inference(rewrite,[status(thm)],[])).
% 1.32/1.37 tff(4427,plain,
% 1.32/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)) | m_main_v_state1(s50, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state1(s50, c_c1) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50))))),
% 1.32/1.37 inference(monotonicity,[status(thm)],[4426])).
% 1.32/1.37 tff(4428,plain,
% 1.32/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)) | m_main_v_state1(s50, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state1(s50, c_c1) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)))),
% 1.32/1.37 inference(transitivity,[status(thm)],[4427, 4425])).
% 1.32/1.37 tff(4429,plain,
% 1.32/1.37 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50)) | m_main_v_state1(s50, c_c1))),
% 1.32/1.37 inference(quant_inst,[status(thm)],[])).
% 1.32/1.37 tff(4430,plain,
% 1.32/1.37 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state1(s50, c_c1) | node1(s49) | node2(s49) | node3(s49) | (~node7(s49, s50))),
% 1.32/1.37 inference(modus_ponens,[status(thm)],[4429, 4428])).
% 1.32/1.37 tff(4431,plain,
% 1.32/1.37 ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state1(s50, c_c1) | node1(s49) | node2(s49) | node3(s49)),
% 1.32/1.37 inference(unit_resolution,[status(thm)],[4430, 892, 4424])).
% 1.32/1.37 tff(4432,plain,
% 1.32/1.37 (m_main_v_state1(s50, c_c1)),
% 1.32/1.37 inference(unit_resolution,[status(thm)],[4431, 4413, 4337, 4405, 4398, 4345])).
% 1.32/1.37 tff(4433,plain,
% 1.32/1.37 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s50, c_t1)) | (~m_main_v_state1(s50, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s50, c_t1)) | (~m_main_v_state1(s50, c_c1)))),
% 1.32/1.37 inference(rewrite,[status(thm)],[])).
% 1.32/1.37 tff(4434,plain,
% 1.32/1.37 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s50, c_t1)) | (~m_main_v_state1(s50, c_c1)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4435,plain,
% 1.35/1.37 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s50, c_t1)) | (~m_main_v_state1(s50, c_c1))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4434, 4433])).
% 1.35/1.37 tff(4436,plain,
% 1.35/1.37 (~m_main_v_state1(s50, c_t1)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4435, 539, 4432])).
% 1.35/1.37 tff(4437,plain,
% 1.35/1.37 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s50, c_t1) | (~node5(s50)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s50, c_t1) | (~node5(s50)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4438,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s50, c_t1) | (~node5(s50)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4439,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s50, c_t1) | (~node5(s50))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4438, 4437])).
% 1.35/1.37 tff(4440,plain,
% 1.35/1.37 (~node5(s50)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4439, 550, 4436])).
% 1.35/1.37 tff(4441,plain,
% 1.35/1.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s49, s50)) | node14(s49, s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s49, s50)) | node14(s49, s50))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4442,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s49, s50)) | node14(s49, s50))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4443,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s49, s50)) | node14(s49, s50)),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4442, 4441])).
% 1.35/1.37 tff(4444,plain,
% 1.35/1.37 (node14(s49, s50)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4443, 46, 4420])).
% 1.35/1.37 tff(4445,plain,
% 1.35/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | (~node14(s49, s50)) | m_main_v_state2(s50, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | (~node14(s49, s50)) | m_main_v_state2(s50, c_t2))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4446,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | (~node14(s49, s50)) | m_main_v_state2(s50, c_t2))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4447,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | (~node14(s49, s50)) | m_main_v_state2(s50, c_t2)),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4446, 4445])).
% 1.35/1.37 tff(4448,plain,
% 1.35/1.37 ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state2(s50, c_t2)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4447, 922, 4444])).
% 1.35/1.37 tff(4449,plain,
% 1.35/1.37 (m_main_v_state2(s50, c_t2)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4448, 4405, 4337])).
% 1.35/1.37 tff(4450,plain,
% 1.35/1.37 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s50, c_n2)) | (~m_main_v_state2(s50, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s50, c_n2)) | (~m_main_v_state2(s50, c_t2)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4451,plain,
% 1.35/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s50, c_n2)) | (~m_main_v_state2(s50, c_t2)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4452,plain,
% 1.35/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s50, c_n2)) | (~m_main_v_state2(s50, c_t2))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4451, 4450])).
% 1.35/1.37 tff(4453,plain,
% 1.35/1.37 (~m_main_v_state2(s50, c_n2)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4452, 77, 4449])).
% 1.35/1.37 tff(4454,plain,
% 1.35/1.37 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s50, c_n2) | (~node4(s50)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s50, c_n2) | (~node4(s50)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4455,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s50, c_n2) | (~node4(s50)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4456,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s50, c_n2) | (~node4(s50))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4455, 4454])).
% 1.35/1.37 tff(4457,plain,
% 1.35/1.37 (~node4(s50)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4456, 388, 4453])).
% 1.35/1.37 tff(4458,plain,
% 1.35/1.37 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s50, c_t2)) | (~m_main_v_state2(s50, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s50, c_t2)) | (~m_main_v_state2(s50, c_c2)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4459,plain,
% 1.35/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s50, c_t2)) | (~m_main_v_state2(s50, c_c2)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4460,plain,
% 1.35/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s50, c_t2)) | (~m_main_v_state2(s50, c_c2))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 1.35/1.37 tff(4461,plain,
% 1.35/1.37 (~m_main_v_state2(s50, c_c2)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4460, 260, 4449])).
% 1.35/1.37 tff(4462,plain,
% 1.35/1.37 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s50, c_c2) | (~node3(s50)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s50, c_c2) | (~node3(s50)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4463,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s50, c_c2) | (~node3(s50)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4464,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s50, c_c2) | (~node3(s50))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 1.35/1.37 tff(4465,plain,
% 1.35/1.37 (~node3(s50)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4464, 399, 4461])).
% 1.35/1.37 tff(4466,plain,
% 1.35/1.37 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s50, c_n2) | (~node2(s50)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s50, c_n2) | (~node2(s50)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4467,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s50, c_n2) | (~node2(s50)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4468,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s50, c_n2) | (~node2(s50))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4467, 4466])).
% 1.35/1.37 tff(4469,plain,
% 1.35/1.37 (~node2(s50)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4468, 410, 4453])).
% 1.35/1.37 tff(4470,plain,
% 1.35/1.37 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s50, c_n1)) | (~m_main_v_state1(s50, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s50, c_n1)) | (~m_main_v_state1(s50, c_c1)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4471,plain,
% 1.35/1.37 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s50, c_n1)) | (~m_main_v_state1(s50, c_c1)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4472,plain,
% 1.35/1.37 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s50, c_n1)) | (~m_main_v_state1(s50, c_c1))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4471, 4470])).
% 1.35/1.37 tff(4473,plain,
% 1.35/1.37 (~m_main_v_state1(s50, c_n1)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4472, 454, 4432])).
% 1.35/1.37 tff(4474,plain,
% 1.35/1.37 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s50, c_n1) | (~node1(s50)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s50, c_n1) | (~node1(s50)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4475,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s50, c_n1) | (~node1(s50)))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4476,plain,
% 1.35/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s50, c_n1) | (~node1(s50))),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4475, 4474])).
% 1.35/1.37 tff(4477,plain,
% 1.35/1.37 (~node1(s50)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4476, 421, 4473])).
% 1.35/1.37 tff(4478,plain,
% 1.35/1.37 (succ(s50, s51) <=> succ(s50, s51)),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4479,axiom,(succ(s50, s51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound51')).
% 1.35/1.37 tff(4480,plain,
% 1.35/1.37 (succ(s50, s51)),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4479, 4478])).
% 1.35/1.37 tff(4481,plain,
% 1.35/1.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4482,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4483,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51)),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4482, 4481])).
% 1.35/1.37 tff(4484,plain,
% 1.35/1.37 (trans(s50, s51)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4483, 4480, 32])).
% 1.35/1.37 tff(4485,plain,
% 1.35/1.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s50, s51)) | node7(s50, s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s50, s51)) | node7(s50, s51))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4486,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s50, s51)) | node7(s50, s51))),
% 1.35/1.37 inference(quant_inst,[status(thm)],[])).
% 1.35/1.37 tff(4487,plain,
% 1.35/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s50, s51)) | node7(s50, s51)),
% 1.35/1.37 inference(modus_ponens,[status(thm)],[4486, 4485])).
% 1.35/1.37 tff(4488,plain,
% 1.35/1.37 (node7(s50, s51)),
% 1.35/1.37 inference(unit_resolution,[status(thm)],[4487, 206, 4484])).
% 1.35/1.37 tff(4489,plain,
% 1.35/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4490,plain,
% 1.35/1.37 (((~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)) | m_main_v_state1(s51, c_n1)) <=> (m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)))),
% 1.35/1.37 inference(rewrite,[status(thm)],[])).
% 1.35/1.37 tff(4491,plain,
% 1.35/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)) | m_main_v_state1(s51, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51))))),
% 1.35/1.37 inference(monotonicity,[status(thm)],[4490])).
% 1.35/1.37 tff(4492,plain,
% 1.35/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)) | m_main_v_state1(s51, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)))),
% 1.35/1.38 inference(transitivity,[status(thm)],[4491, 4489])).
% 1.35/1.38 tff(4493,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51)) | m_main_v_state1(s51, c_n1))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4494,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50) | (~node7(s50, s51))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4493, 4492])).
% 1.35/1.38 tff(4495,plain,
% 1.35/1.38 (m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4494, 584, 4488])).
% 1.35/1.38 tff(4496,plain,
% 1.35/1.38 (m_main_v_state1(s51, c_n1)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4495, 4477, 4432, 4469, 4465, 4457, 4440])).
% 1.35/1.38 tff(4497,plain,
% 1.35/1.38 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s49, c_t2) | (~node15(s49)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s49, c_t2) | (~node15(s49)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4498,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s49, c_t2) | (~node15(s49)))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4499,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s49, c_t2) | (~node15(s49))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4498, 4497])).
% 1.35/1.38 tff(4500,plain,
% 1.35/1.38 (~node15(s49)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4499, 103, 4409])).
% 1.35/1.38 tff(4501,plain,
% 1.35/1.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s49, s50)) | node18(s49, s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s49, s50)) | node18(s49, s50))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4502,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s49, s50)) | node18(s49, s50))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4503,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s49, s50)) | node18(s49, s50)),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 1.35/1.38 tff(4504,plain,
% 1.35/1.38 (node18(s49, s50)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4503, 125, 4420])).
% 1.35/1.38 tff(4505,plain,
% 1.35/1.38 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s49) | (~node18(s49, s50)) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s49) | (~node18(s49, s50)) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4506,plain,
% 1.35/1.38 (((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node15(s49) | (~node18(s49, s50)) | m_main_v_turn(s50, c_1)) <=> (node15(s49) | (~node18(s49, s50)) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4507,plain,
% 1.35/1.38 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node15(s49) | (~node18(s49, s50)) | m_main_v_turn(s50, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s49) | (~node18(s49, s50)) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1)))),
% 1.35/1.38 inference(monotonicity,[status(thm)],[4506])).
% 1.35/1.38 tff(4508,plain,
% 1.35/1.38 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node15(s49) | (~node18(s49, s50)) | m_main_v_turn(s50, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s49) | (~node18(s49, s50)) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1))),
% 1.35/1.38 inference(transitivity,[status(thm)],[4507, 4505])).
% 1.35/1.38 tff(4509,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | node15(s49) | (~node18(s49, s50)) | m_main_v_turn(s50, c_1))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4510,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s49) | (~node18(s49, s50)) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1)),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4509, 4508])).
% 1.35/1.38 tff(4511,plain,
% 1.35/1.38 (node15(s49) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4510, 992, 4504])).
% 1.35/1.38 tff(4512,plain,
% 1.35/1.38 (m_main_v_turn(s50, c_1)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4511, 4500, 4337, 4405])).
% 1.35/1.38 tff(4513,plain,
% 1.35/1.38 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s50, c_1)) | (~m_main_v_turn(s50, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s50, c_1)) | (~m_main_v_turn(s50, c_2)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4514,plain,
% 1.35/1.38 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s50, c_1)) | (~m_main_v_turn(s50, c_2)))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4515,plain,
% 1.35/1.38 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s50, c_1)) | (~m_main_v_turn(s50, c_2))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 1.35/1.38 tff(4516,plain,
% 1.35/1.38 (~m_main_v_turn(s50, c_2)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4515, 156, 4512])).
% 1.35/1.38 tff(4517,plain,
% 1.35/1.38 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s50, c_2) | (~node12(s50)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s50, c_2) | (~node12(s50)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4518,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s50, c_2) | (~node12(s50)))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4519,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s50, c_2) | (~node12(s50))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4518, 4517])).
% 1.35/1.38 tff(4520,plain,
% 1.35/1.38 (~node12(s50)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4519, 184, 4516])).
% 1.35/1.38 tff(4521,plain,
% 1.35/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s50, c_n2) | (~node8(s50)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s50, c_n2) | (~node8(s50)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4522,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s50, c_n2) | (~node8(s50)))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4523,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s50, c_n2) | (~node8(s50))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4522, 4521])).
% 1.35/1.38 tff(4524,plain,
% 1.35/1.38 (~node8(s50)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4523, 271, 4453])).
% 1.35/1.38 tff(4525,plain,
% 1.35/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s50, c_n2) | (~node9(s50)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s50, c_n2) | (~node9(s50)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4526,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s50, c_n2) | (~node9(s50)))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4527,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s50, c_n2) | (~node9(s50))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4526, 4525])).
% 1.35/1.38 tff(4528,plain,
% 1.35/1.38 (~node9(s50)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4527, 88, 4453])).
% 1.35/1.38 tff(4529,plain,
% 1.35/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s50, c_n2) | (~node10(s50)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s50, c_n2) | (~node10(s50)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4530,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s50, c_n2) | (~node10(s50)))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4531,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s50, c_n2) | (~node10(s50))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4530, 4529])).
% 1.35/1.38 tff(4532,plain,
% 1.35/1.38 (~node10(s50)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4531, 249, 4453])).
% 1.35/1.38 tff(4533,plain,
% 1.35/1.38 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s50, c_n1) | (~node11(s50)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s50, c_n1) | (~node11(s50)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4534,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s50, c_n1) | (~node11(s50)))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4535,plain,
% 1.35/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s50, c_n1) | (~node11(s50))),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4534, 4533])).
% 1.35/1.38 tff(4536,plain,
% 1.35/1.38 (~node11(s50)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4535, 238, 4473])).
% 1.35/1.38 tff(4537,plain,
% 1.35/1.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s50, s51)) | node14(s50, s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s50, s51)) | node14(s50, s51))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4538,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s50, s51)) | node14(s50, s51))),
% 1.35/1.38 inference(quant_inst,[status(thm)],[])).
% 1.35/1.38 tff(4539,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s50, s51)) | node14(s50, s51)),
% 1.35/1.38 inference(modus_ponens,[status(thm)],[4538, 4537])).
% 1.35/1.38 tff(4540,plain,
% 1.35/1.38 (node14(s50, s51)),
% 1.35/1.38 inference(unit_resolution,[status(thm)],[4539, 46, 4484])).
% 1.35/1.38 tff(4541,plain,
% 1.35/1.38 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s50, c_c2) | node9(s50) | node8(s50) | node10(s50) | node11(s50) | node12(s50) | node13(s50, s51) | (~node14(s50, s51)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s50, c_c2) | node9(s50) | node8(s50) | node10(s50) | node11(s50) | node12(s50) | node13(s50, s51) | (~node14(s50, s51)))),
% 1.35/1.38 inference(rewrite,[status(thm)],[])).
% 1.35/1.38 tff(4542,plain,
% 1.35/1.38 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s50, c_c2) | node9(s50) | node8(s50) | node10(s50) | node11(s50) | node12(s50) | node13(s50, s51) | (~node14(s50, s51)))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4543,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s50, c_c2) | node9(s50) | node8(s50) | node10(s50) | node11(s50) | node12(s50) | node13(s50, s51) | (~node14(s50, s51))),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4542, 4541])).
% 1.35/1.39 tff(4544,plain,
% 1.35/1.39 (m_main_v_state2(s50, c_c2) | node9(s50) | node8(s50) | node10(s50) | node11(s50) | node12(s50) | node13(s50, s51)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4543, 296, 4540])).
% 1.35/1.39 tff(4545,plain,
% 1.35/1.39 (node13(s50, s51)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4544, 4536, 4461, 4532, 4528, 4524, 4520])).
% 1.35/1.39 tff(4546,plain,
% 1.35/1.39 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2) | (~node13(s50, s51)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2) | (~node13(s50, s51)))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4547,plain,
% 1.35/1.39 (((~node13(s50, s51)) | (~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2)) <=> ((~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2) | (~node13(s50, s51)))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4548,plain,
% 1.35/1.39 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s50, s51)) | (~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2) | (~node13(s50, s51))))),
% 1.35/1.39 inference(monotonicity,[status(thm)],[4547])).
% 1.35/1.39 tff(4549,plain,
% 1.35/1.39 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s50, s51)) | (~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2) | (~node13(s50, s51)))),
% 1.35/1.39 inference(transitivity,[status(thm)],[4548, 4546])).
% 1.35/1.39 tff(4550,plain,
% 1.35/1.39 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s50, s51)) | (~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4551,plain,
% 1.35/1.39 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s50, c_t2)) | m_main_v_state2(s51, c_t2) | (~node13(s50, s51))),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4550, 4549])).
% 1.35/1.39 tff(4552,plain,
% 1.35/1.39 (m_main_v_state2(s51, c_t2)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4551, 518, 4449, 4545])).
% 1.35/1.39 tff(4553,plain,
% 1.35/1.39 (succ(s51, s52) <=> succ(s51, s52)),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4554,axiom,(succ(s51, s52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound52')).
% 1.35/1.39 tff(4555,plain,
% 1.35/1.39 (succ(s51, s52)),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4554, 4553])).
% 1.35/1.39 tff(4556,plain,
% 1.35/1.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4557,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4558,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52)),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4557, 4556])).
% 1.35/1.39 tff(4559,plain,
% 1.35/1.39 (trans(s51, s52)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4558, 4555, 32])).
% 1.35/1.39 tff(4560,plain,
% 1.35/1.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s51, s52)) | node7(s51, s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s51, s52)) | node7(s51, s52))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4561,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s51, s52)) | node7(s51, s52))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4562,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s51, s52)) | node7(s51, s52)),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4561, 4560])).
% 1.35/1.39 tff(4563,plain,
% 1.35/1.39 (node7(s51, s52)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4562, 206, 4559])).
% 1.35/1.39 tff(4564,plain,
% 1.35/1.39 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node7(s51, s52)) | m_main_v_state1(s52, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node7(s51, s52)) | m_main_v_state1(s52, c_t1))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4565,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node7(s51, s52)) | m_main_v_state1(s52, c_t1))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4566,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node7(s51, s52)) | m_main_v_state1(s52, c_t1)),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4565, 4564])).
% 1.35/1.39 tff(4567,plain,
% 1.35/1.39 ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | m_main_v_state1(s52, c_t1)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4566, 651, 4563])).
% 1.35/1.39 tff(4568,plain,
% 1.35/1.39 (m_main_v_state1(s52, c_t1)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4567, 4552, 4496])).
% 1.35/1.39 tff(4569,plain,
% 1.35/1.39 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s52, c_n1)) | (~m_main_v_state1(s52, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s52, c_n1)) | (~m_main_v_state1(s52, c_t1)))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4570,plain,
% 1.35/1.39 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s52, c_n1)) | (~m_main_v_state1(s52, c_t1)))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4571,plain,
% 1.35/1.39 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s52, c_n1)) | (~m_main_v_state1(s52, c_t1))),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4570, 4569])).
% 1.35/1.39 tff(4572,plain,
% 1.35/1.39 (~m_main_v_state1(s52, c_n1)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4571, 10, 4568])).
% 1.35/1.39 tff(4573,plain,
% 1.35/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s52, c_n1) | (~node1(s52)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s52, c_n1) | (~node1(s52)))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4574,plain,
% 1.35/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s52, c_n1) | (~node1(s52)))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4575,plain,
% 1.35/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s52, c_n1) | (~node1(s52))),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4574, 4573])).
% 1.35/1.39 tff(4576,plain,
% 1.35/1.39 (~node1(s52)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4575, 421, 4572])).
% 1.35/1.39 tff(4577,plain,
% 1.35/1.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s51, s52)) | node18(s51, s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s51, s52)) | node18(s51, s52))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4578,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s51, s52)) | node18(s51, s52))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4579,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s51, s52)) | node18(s51, s52)),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4578, 4577])).
% 1.35/1.39 tff(4580,plain,
% 1.35/1.39 (node18(s51, s52)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4579, 125, 4559])).
% 1.35/1.39 tff(4581,plain,
% 1.35/1.39 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node18(s51, s52)) | m_main_v_turn(s52, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node18(s51, s52)) | m_main_v_turn(s52, c_2))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4582,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node18(s51, s52)) | m_main_v_turn(s52, c_2))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4583,plain,
% 1.35/1.39 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node18(s51, s52)) | m_main_v_turn(s52, c_2)),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4582, 4581])).
% 1.35/1.39 tff(4584,plain,
% 1.35/1.39 ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | m_main_v_turn(s52, c_2)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4583, 760, 4580])).
% 1.35/1.39 tff(4585,plain,
% 1.35/1.39 (m_main_v_turn(s52, c_2)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4584, 4552, 4496])).
% 1.35/1.39 tff(4586,plain,
% 1.35/1.39 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s52, c_1)) | (~m_main_v_turn(s52, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s52, c_1)) | (~m_main_v_turn(s52, c_2)))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4587,plain,
% 1.35/1.39 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s52, c_1)) | (~m_main_v_turn(s52, c_2)))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4588,plain,
% 1.35/1.39 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s52, c_1)) | (~m_main_v_turn(s52, c_2))),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4587, 4586])).
% 1.35/1.39 tff(4589,plain,
% 1.35/1.39 (~m_main_v_turn(s52, c_1)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4588, 156, 4585])).
% 1.35/1.39 tff(4590,plain,
% 1.35/1.39 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s52, c_1) | (~node5(s52)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s52, c_1) | (~node5(s52)))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4591,plain,
% 1.35/1.39 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s52, c_1) | (~node5(s52)))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4592,plain,
% 1.35/1.39 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s52, c_1) | (~node5(s52))),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4591, 4590])).
% 1.35/1.39 tff(4593,plain,
% 1.35/1.39 (~node5(s52)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4592, 776, 4589])).
% 1.35/1.39 tff(4594,plain,
% 1.35/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s52, c_n1) | (~node2(s52)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s52, c_n1) | (~node2(s52)))),
% 1.35/1.39 inference(rewrite,[status(thm)],[])).
% 1.35/1.39 tff(4595,plain,
% 1.35/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s52, c_n1) | (~node2(s52)))),
% 1.35/1.39 inference(quant_inst,[status(thm)],[])).
% 1.35/1.39 tff(4596,plain,
% 1.35/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s52, c_n1) | (~node2(s52))),
% 1.35/1.39 inference(modus_ponens,[status(thm)],[4595, 4594])).
% 1.35/1.39 tff(4597,plain,
% 1.35/1.39 (~node2(s52)),
% 1.35/1.39 inference(unit_resolution,[status(thm)],[4596, 787, 4572])).
% 1.35/1.39 tff(4598,plain,
% 1.35/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s52, c_n1) | (~node3(s52)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s52, c_n1) | (~node3(s52)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4599,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s52, c_n1) | (~node3(s52)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4600,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s52, c_n1) | (~node3(s52))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4599, 4598])).
% 1.35/1.40 tff(4601,plain,
% 1.35/1.40 (~node3(s52)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4600, 798, 4572])).
% 1.35/1.40 tff(4602,plain,
% 1.35/1.40 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s52, c_t1)) | (~m_main_v_state1(s52, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s52, c_t1)) | (~m_main_v_state1(s52, c_c1)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4603,plain,
% 1.35/1.40 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s52, c_t1)) | (~m_main_v_state1(s52, c_c1)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4604,plain,
% 1.35/1.40 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s52, c_t1)) | (~m_main_v_state1(s52, c_c1))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4603, 4602])).
% 1.35/1.40 tff(4605,plain,
% 1.35/1.40 (~m_main_v_state1(s52, c_c1)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4604, 539, 4568])).
% 1.35/1.40 tff(4606,plain,
% 1.35/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)) | (~node13(s50, s51)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)) | (~node13(s50, s51)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4607,plain,
% 1.35/1.40 (((~node13(s50, s51)) | m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2))) <=> (m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)) | (~node13(s50, s51)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4608,plain,
% 1.35/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s50, s51)) | m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)) | (~node13(s50, s51))))),
% 1.35/1.40 inference(monotonicity,[status(thm)],[4607])).
% 1.35/1.40 tff(4609,plain,
% 1.35/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s50, s51)) | m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)) | (~node13(s50, s51)))),
% 1.35/1.40 inference(transitivity,[status(thm)],[4608, 4606])).
% 1.35/1.40 tff(4610,plain,
% 1.35/1.40 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s50, s51)) | m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4611,plain,
% 1.35/1.40 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s50, c_n2) | (~m_main_v_state2(s51, c_n2)) | (~node13(s50, s51))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4610, 4609])).
% 1.35/1.40 tff(4612,plain,
% 1.35/1.40 (~m_main_v_state2(s51, c_n2)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4611, 311, 4453, 4545])).
% 1.35/1.40 tff(4613,plain,
% 1.35/1.40 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s51, c_n2) | (~node9(s51)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s51, c_n2) | (~node9(s51)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4614,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s51, c_n2) | (~node9(s51)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4615,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s51, c_n2) | (~node9(s51))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4614, 4613])).
% 1.35/1.40 tff(4616,plain,
% 1.35/1.40 (~node9(s51)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4615, 88, 4612])).
% 1.35/1.40 tff(4617,plain,
% 1.35/1.40 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s51, c_n2) | (~node10(s51)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s51, c_n2) | (~node10(s51)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4618,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s51, c_n2) | (~node10(s51)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4619,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s51, c_n2) | (~node10(s51))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 1.35/1.40 tff(4620,plain,
% 1.35/1.40 (~node10(s51)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4619, 249, 4612])).
% 1.35/1.40 tff(4621,plain,
% 1.35/1.40 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s51, c_n2) | (~node8(s51)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s51, c_n2) | (~node8(s51)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4622,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s51, c_n2) | (~node8(s51)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4623,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s51, c_n2) | (~node8(s51))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4622, 4621])).
% 1.35/1.40 tff(4624,plain,
% 1.35/1.40 (~node8(s51)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4623, 271, 4612])).
% 1.35/1.40 tff(4625,plain,
% 1.35/1.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s51, s52)) | node14(s51, s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s51, s52)) | node14(s51, s52))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4626,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s51, s52)) | node14(s51, s52))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4627,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s51, s52)) | node14(s51, s52)),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4626, 4625])).
% 1.35/1.40 tff(4628,plain,
% 1.35/1.40 (node14(s51, s52)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4627, 46, 4559])).
% 1.35/1.40 tff(4629,plain,
% 1.35/1.40 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | node9(s51) | node8(s51) | node10(s51) | (~node14(s51, s52)) | m_main_v_state2(s52, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | node9(s51) | node8(s51) | node10(s51) | (~node14(s51, s52)) | m_main_v_state2(s52, c_c2))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4630,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | node9(s51) | node8(s51) | node10(s51) | (~node14(s51, s52)) | m_main_v_state2(s52, c_c2))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4631,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | node9(s51) | node8(s51) | node10(s51) | (~node14(s51, s52)) | m_main_v_state2(s52, c_c2)),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4630, 4629])).
% 1.35/1.40 tff(4632,plain,
% 1.35/1.40 ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | node9(s51) | node8(s51) | node10(s51) | m_main_v_state2(s52, c_c2)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4631, 617, 4628])).
% 1.35/1.40 tff(4633,plain,
% 1.35/1.40 (m_main_v_state2(s52, c_c2)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4632, 4624, 4496, 4552, 4620, 4616])).
% 1.35/1.40 tff(4634,plain,
% 1.35/1.40 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s52, c_n2)) | (~m_main_v_state2(s52, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s52, c_n2)) | (~m_main_v_state2(s52, c_c2)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4635,plain,
% 1.35/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s52, c_n2)) | (~m_main_v_state2(s52, c_c2)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4636,plain,
% 1.35/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s52, c_n2)) | (~m_main_v_state2(s52, c_c2))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4635, 4634])).
% 1.35/1.40 tff(4637,plain,
% 1.35/1.40 (~m_main_v_state2(s52, c_n2)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4636, 697, 4633])).
% 1.35/1.40 tff(4638,plain,
% 1.35/1.40 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s52, c_n2) | (~node4(s52)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s52, c_n2) | (~node4(s52)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4639,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s52, c_n2) | (~node4(s52)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4640,plain,
% 1.35/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s52, c_n2) | (~node4(s52))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4639, 4638])).
% 1.35/1.40 tff(4641,plain,
% 1.35/1.40 (~node4(s52)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4640, 388, 4637])).
% 1.35/1.40 tff(4642,plain,
% 1.35/1.40 (succ(s52, s53) <=> succ(s52, s53)),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4643,axiom,(succ(s52, s53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound53')).
% 1.35/1.40 tff(4644,plain,
% 1.35/1.40 (succ(s52, s53)),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4643, 4642])).
% 1.35/1.40 tff(4645,plain,
% 1.35/1.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4646,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4647,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53)),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4646, 4645])).
% 1.35/1.40 tff(4648,plain,
% 1.35/1.40 (trans(s52, s53)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4647, 4644, 32])).
% 1.35/1.40 tff(4649,plain,
% 1.35/1.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s52, s53)) | node7(s52, s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s52, s53)) | node7(s52, s53))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4650,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s52, s53)) | node7(s52, s53))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4651,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s52, s53)) | node7(s52, s53)),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4650, 4649])).
% 1.35/1.40 tff(4652,plain,
% 1.35/1.40 (node7(s52, s53)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4651, 206, 4648])).
% 1.35/1.40 tff(4653,plain,
% 1.35/1.40 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s52, c_c1) | node1(s52) | node2(s52) | node3(s52) | node4(s52) | node5(s52) | node6(s52, s53) | (~node7(s52, s53)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s52, c_c1) | node1(s52) | node2(s52) | node3(s52) | node4(s52) | node5(s52) | node6(s52, s53) | (~node7(s52, s53)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4654,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s52, c_c1) | node1(s52) | node2(s52) | node3(s52) | node4(s52) | node5(s52) | node6(s52, s53) | (~node7(s52, s53)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4655,plain,
% 1.35/1.40 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s52, c_c1) | node1(s52) | node2(s52) | node3(s52) | node4(s52) | node5(s52) | node6(s52, s53) | (~node7(s52, s53))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4654, 4653])).
% 1.35/1.40 tff(4656,plain,
% 1.35/1.40 (m_main_v_state1(s52, c_c1) | node1(s52) | node2(s52) | node3(s52) | node4(s52) | node5(s52) | node6(s52, s53)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4655, 820, 4652])).
% 1.35/1.40 tff(4657,plain,
% 1.35/1.40 (node6(s52, s53)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4656, 4641, 4605, 4601, 4597, 4593, 4576])).
% 1.35/1.40 tff(4658,plain,
% 1.35/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1) | (~node6(s52, s53)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1) | (~node6(s52, s53)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4659,plain,
% 1.35/1.40 (((~node6(s52, s53)) | (~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1)) <=> ((~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1) | (~node6(s52, s53)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4660,plain,
% 1.35/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s52, s53)) | (~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1) | (~node6(s52, s53))))),
% 1.35/1.40 inference(monotonicity,[status(thm)],[4659])).
% 1.35/1.40 tff(4661,plain,
% 1.35/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s52, s53)) | (~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1) | (~node6(s52, s53)))),
% 1.35/1.40 inference(transitivity,[status(thm)],[4660, 4658])).
% 1.35/1.40 tff(4662,plain,
% 1.35/1.40 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s52, s53)) | (~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4663,plain,
% 1.35/1.40 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s52, c_t1)) | m_main_v_state1(s53, c_t1) | (~node6(s52, s53))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4662, 4661])).
% 1.35/1.40 tff(4664,plain,
% 1.35/1.40 (m_main_v_state1(s53, c_t1)),
% 1.35/1.40 inference(unit_resolution,[status(thm)],[4663, 856, 4568, 4657])).
% 1.35/1.40 tff(4665,plain,
% 1.35/1.40 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s52, c_t2)) | (~m_main_v_state2(s52, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s52, c_t2)) | (~m_main_v_state2(s52, c_c2)))),
% 1.35/1.40 inference(rewrite,[status(thm)],[])).
% 1.35/1.40 tff(4666,plain,
% 1.35/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s52, c_t2)) | (~m_main_v_state2(s52, c_c2)))),
% 1.35/1.40 inference(quant_inst,[status(thm)],[])).
% 1.35/1.40 tff(4667,plain,
% 1.35/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s52, c_t2)) | (~m_main_v_state2(s52, c_c2))),
% 1.35/1.40 inference(modus_ponens,[status(thm)],[4666, 4665])).
% 1.35/1.40 tff(4668,plain,
% 1.35/1.40 (~m_main_v_state2(s52, c_t2)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4667, 260, 4633])).
% 1.35/1.41 tff(4669,plain,
% 1.35/1.41 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s52, c_t2) | (~node12(s52)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s52, c_t2) | (~node12(s52)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4670,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s52, c_t2) | (~node12(s52)))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4671,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s52, c_t2) | (~node12(s52))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4670, 4669])).
% 1.35/1.41 tff(4672,plain,
% 1.35/1.41 (~node12(s52)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4671, 633, 4668])).
% 1.35/1.41 tff(4673,plain,
% 1.35/1.41 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s52, c_n1) | (~node11(s52)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s52, c_n1) | (~node11(s52)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4674,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s52, c_n1) | (~node11(s52)))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4675,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s52, c_n1) | (~node11(s52))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 1.35/1.41 tff(4676,plain,
% 1.35/1.41 (~node11(s52)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4675, 238, 4572])).
% 1.35/1.41 tff(4677,plain,
% 1.35/1.41 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s52, c_c1) | (~node10(s52)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s52, c_c1) | (~node10(s52)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4678,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s52, c_c1) | (~node10(s52)))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4679,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s52, c_c1) | (~node10(s52))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4678, 4677])).
% 1.35/1.41 tff(4680,plain,
% 1.35/1.41 (~node10(s52)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4679, 675, 4605])).
% 1.35/1.41 tff(4681,plain,
% 1.35/1.41 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s52, c_n1) | (~node9(s52)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s52, c_n1) | (~node9(s52)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4682,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s52, c_n1) | (~node9(s52)))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4683,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s52, c_n1) | (~node9(s52))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4682, 4681])).
% 1.35/1.41 tff(4684,plain,
% 1.35/1.41 (~node9(s52)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4683, 686, 4572])).
% 1.35/1.41 tff(4685,plain,
% 1.35/1.41 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s52, c_n2) | (~node8(s52)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s52, c_n2) | (~node8(s52)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4686,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s52, c_n2) | (~node8(s52)))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4687,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s52, c_n2) | (~node8(s52))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4686, 4685])).
% 1.35/1.41 tff(4688,plain,
% 1.35/1.41 (~node8(s52)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4687, 271, 4637])).
% 1.35/1.41 tff(4689,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s52, s53)) | node14(s52, s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s52, s53)) | node14(s52, s53))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4690,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s52, s53)) | node14(s52, s53))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4691,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s52, s53)) | node14(s52, s53)),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4690, 4689])).
% 1.35/1.41 tff(4692,plain,
% 1.35/1.41 (node14(s52, s53)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4691, 46, 4648])).
% 1.35/1.41 tff(4693,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | (~m_main_v_state2(s52, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | (~m_main_v_state2(s52, c_c2)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4694,plain,
% 1.35/1.41 (((~m_main_v_state2(s52, c_c2)) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | m_main_v_state2(s53, c_n2)) <=> (m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | (~m_main_v_state2(s52, c_c2)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4695,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s52, c_c2)) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | m_main_v_state2(s53, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | (~m_main_v_state2(s52, c_c2))))),
% 1.35/1.41 inference(monotonicity,[status(thm)],[4694])).
% 1.35/1.41 tff(4696,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s52, c_c2)) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | m_main_v_state2(s53, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | (~m_main_v_state2(s52, c_c2)))),
% 1.35/1.41 inference(transitivity,[status(thm)],[4695, 4693])).
% 1.35/1.41 tff(4697,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s52, c_c2)) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | m_main_v_state2(s53, c_n2))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4698,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~node14(s52, s53)) | (~m_main_v_state2(s52, c_c2))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4697, 4696])).
% 1.35/1.41 tff(4699,plain,
% 1.35/1.41 (m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~m_main_v_state2(s52, c_c2))),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4698, 726, 4692])).
% 1.35/1.41 tff(4700,plain,
% 1.35/1.41 (m_main_v_state2(s53, c_n2)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4699, 4688, 4633, 4684, 4680, 4676, 4672])).
% 1.35/1.41 tff(4701,plain,
% 1.35/1.41 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_t2)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4702,plain,
% 1.35/1.41 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_t2)))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4703,plain,
% 1.35/1.41 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_t2))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4702, 4701])).
% 1.35/1.41 tff(4704,plain,
% 1.35/1.41 (~m_main_v_state2(s53, c_t2)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4703, 77, 4700])).
% 1.35/1.41 tff(4705,plain,
% 1.35/1.41 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s53, c_t2) | (~node15(s53)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s53, c_t2) | (~node15(s53)))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4706,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s53, c_t2) | (~node15(s53)))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4707,plain,
% 1.35/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s53, c_t2) | (~node15(s53))),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4706, 4705])).
% 1.35/1.41 tff(4708,plain,
% 1.35/1.41 (~node15(s53)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4707, 103, 4704])).
% 1.35/1.41 tff(4709,plain,
% 1.35/1.41 (succ(s53, s54) <=> succ(s53, s54)),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4710,axiom,(succ(s53, s54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound54')).
% 1.35/1.41 tff(4711,plain,
% 1.35/1.41 (succ(s53, s54)),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 1.35/1.41 tff(4712,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4713,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4714,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54)),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4713, 4712])).
% 1.35/1.41 tff(4715,plain,
% 1.35/1.41 (trans(s53, s54)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4714, 4711, 32])).
% 1.35/1.41 tff(4716,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s53, s54)) | node18(s53, s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s53, s54)) | node18(s53, s54))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4717,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s53, s54)) | node18(s53, s54))),
% 1.35/1.41 inference(quant_inst,[status(thm)],[])).
% 1.35/1.41 tff(4718,plain,
% 1.35/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s53, s54)) | node18(s53, s54)),
% 1.35/1.41 inference(modus_ponens,[status(thm)],[4717, 4716])).
% 1.35/1.41 tff(4719,plain,
% 1.35/1.41 (node18(s53, s54)),
% 1.35/1.41 inference(unit_resolution,[status(thm)],[4718, 125, 4715])).
% 1.35/1.41 tff(4720,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s53) | (~node18(s53, s54)) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s53) | (~node18(s53, s54)) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4721,plain,
% 1.35/1.41 (((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node15(s53) | (~node18(s53, s54)) | m_main_v_turn(s54, c_1)) <=> (node15(s53) | (~node18(s53, s54)) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1))),
% 1.35/1.41 inference(rewrite,[status(thm)],[])).
% 1.35/1.41 tff(4722,plain,
% 1.35/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node15(s53) | (~node18(s53, s54)) | m_main_v_turn(s54, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s53) | (~node18(s53, s54)) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1)))),
% 1.35/1.42 inference(monotonicity,[status(thm)],[4721])).
% 1.35/1.42 tff(4723,plain,
% 1.35/1.42 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node15(s53) | (~node18(s53, s54)) | m_main_v_turn(s54, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s53) | (~node18(s53, s54)) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1))),
% 1.35/1.42 inference(transitivity,[status(thm)],[4722, 4720])).
% 1.35/1.42 tff(4724,plain,
% 1.35/1.42 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node15(s53) | (~node18(s53, s54)) | m_main_v_turn(s54, c_1))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4725,plain,
% 1.35/1.42 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s53) | (~node18(s53, s54)) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1)),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4724, 4723])).
% 1.35/1.42 tff(4726,plain,
% 1.35/1.42 (node15(s53) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4725, 992, 4719])).
% 1.35/1.42 tff(4727,plain,
% 1.35/1.42 (m_main_v_turn(s54, c_1)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4726, 4708, 4700, 4664])).
% 1.35/1.42 tff(4728,plain,
% 1.35/1.42 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s54, c_1)) | (~m_main_v_turn(s54, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s54, c_1)) | (~m_main_v_turn(s54, c_2)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4729,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s54, c_1)) | (~m_main_v_turn(s54, c_2)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4730,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s54, c_1)) | (~m_main_v_turn(s54, c_2))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4729, 4728])).
% 1.35/1.42 tff(4731,plain,
% 1.35/1.42 (~m_main_v_turn(s54, c_2)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4730, 156, 4727])).
% 1.35/1.42 tff(4732,plain,
% 1.35/1.42 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s54, c_2) | (~node12(s54)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s54, c_2) | (~node12(s54)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4733,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s54, c_2) | (~node12(s54)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4734,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s54, c_2) | (~node12(s54))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4733, 4732])).
% 1.35/1.42 tff(4735,plain,
% 1.35/1.42 (~node12(s54)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4734, 184, 4731])).
% 1.35/1.42 tff(4736,plain,
% 1.35/1.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s53, s54)) | node14(s53, s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s53, s54)) | node14(s53, s54))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4737,plain,
% 1.35/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s53, s54)) | node14(s53, s54))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4738,plain,
% 1.35/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s53, s54)) | node14(s53, s54)),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4737, 4736])).
% 1.35/1.42 tff(4739,plain,
% 1.35/1.42 (node14(s53, s54)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4738, 46, 4715])).
% 1.35/1.42 tff(4740,plain,
% 1.35/1.42 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | (~node14(s53, s54)) | m_main_v_state2(s54, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | (~node14(s53, s54)) | m_main_v_state2(s54, c_t2))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4741,plain,
% 1.35/1.42 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | (~node14(s53, s54)) | m_main_v_state2(s54, c_t2))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4742,plain,
% 1.35/1.42 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | (~node14(s53, s54)) | m_main_v_state2(s54, c_t2)),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4741, 4740])).
% 1.35/1.42 tff(4743,plain,
% 1.35/1.42 ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state2(s54, c_t2)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4742, 922, 4739])).
% 1.35/1.42 tff(4744,plain,
% 1.35/1.42 (m_main_v_state2(s54, c_t2)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4743, 4664, 4700])).
% 1.35/1.42 tff(4745,plain,
% 1.35/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s54, c_n2)) | (~m_main_v_state2(s54, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s54, c_n2)) | (~m_main_v_state2(s54, c_t2)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4746,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s54, c_n2)) | (~m_main_v_state2(s54, c_t2)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4747,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s54, c_n2)) | (~m_main_v_state2(s54, c_t2))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4746, 4745])).
% 1.35/1.42 tff(4748,plain,
% 1.35/1.42 (~m_main_v_state2(s54, c_n2)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4747, 77, 4744])).
% 1.35/1.42 tff(4749,plain,
% 1.35/1.42 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s54, c_n2) | (~node8(s54)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s54, c_n2) | (~node8(s54)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4750,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s54, c_n2) | (~node8(s54)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4751,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s54, c_n2) | (~node8(s54))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4750, 4749])).
% 1.35/1.42 tff(4752,plain,
% 1.35/1.42 (~node8(s54)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4751, 271, 4748])).
% 1.35/1.42 tff(4753,plain,
% 1.35/1.42 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s54, c_n2) | (~node9(s54)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s54, c_n2) | (~node9(s54)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4754,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s54, c_n2) | (~node9(s54)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4755,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s54, c_n2) | (~node9(s54))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4754, 4753])).
% 1.35/1.42 tff(4756,plain,
% 1.35/1.42 (~node9(s54)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4755, 88, 4748])).
% 1.35/1.42 tff(4757,plain,
% 1.35/1.42 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s54, c_n2) | (~node10(s54)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s54, c_n2) | (~node10(s54)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4758,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s54, c_n2) | (~node10(s54)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4759,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s54, c_n2) | (~node10(s54))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4758, 4757])).
% 1.35/1.42 tff(4760,plain,
% 1.35/1.42 (~node10(s54)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4759, 249, 4748])).
% 1.35/1.42 tff(4761,plain,
% 1.35/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s54, c_t2)) | (~m_main_v_state2(s54, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s54, c_t2)) | (~m_main_v_state2(s54, c_c2)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4762,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s54, c_t2)) | (~m_main_v_state2(s54, c_c2)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4763,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s54, c_t2)) | (~m_main_v_state2(s54, c_c2))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4762, 4761])).
% 1.35/1.42 tff(4764,plain,
% 1.35/1.42 (~m_main_v_state2(s54, c_c2)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4763, 260, 4744])).
% 1.35/1.42 tff(4765,plain,
% 1.35/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_c2)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4766,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_c2)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4767,plain,
% 1.35/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s53, c_n2)) | (~m_main_v_state2(s53, c_c2))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4766, 4765])).
% 1.35/1.42 tff(4768,plain,
% 1.35/1.42 (~m_main_v_state2(s53, c_c2)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4767, 697, 4700])).
% 1.35/1.42 tff(4769,plain,
% 1.35/1.42 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s53, c_c2) | (~node3(s53)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s53, c_c2) | (~node3(s53)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4770,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s53, c_c2) | (~node3(s53)))),
% 1.35/1.42 inference(quant_inst,[status(thm)],[])).
% 1.35/1.42 tff(4771,plain,
% 1.35/1.42 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s53, c_c2) | (~node3(s53))),
% 1.35/1.42 inference(modus_ponens,[status(thm)],[4770, 4769])).
% 1.35/1.42 tff(4772,plain,
% 1.35/1.42 (~node3(s53)),
% 1.35/1.42 inference(unit_resolution,[status(thm)],[4771, 399, 4768])).
% 1.35/1.42 tff(4773,plain,
% 1.35/1.42 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4774,plain,
% 1.35/1.42 (((~node6(s52, s53)) | m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1))) <=> (m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53)))),
% 1.35/1.42 inference(rewrite,[status(thm)],[])).
% 1.35/1.42 tff(4775,plain,
% 1.35/1.42 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s52, s53)) | m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53))))),
% 1.41/1.43 inference(monotonicity,[status(thm)],[4774])).
% 1.41/1.43 tff(4776,plain,
% 1.41/1.43 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s52, s53)) | m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53)))),
% 1.41/1.43 inference(transitivity,[status(thm)],[4775, 4773])).
% 1.41/1.43 tff(4777,plain,
% 1.41/1.43 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s52, s53)) | m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4778,plain,
% 1.41/1.43 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4777, 4776])).
% 1.41/1.43 tff(4779,plain,
% 1.41/1.43 (~m_main_v_state1(s53, c_n1)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4778, 835, 4572, 4657])).
% 1.41/1.43 tff(4780,plain,
% 1.41/1.43 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s53, c_n1) | (~node2(s53)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s53, c_n1) | (~node2(s53)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4781,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s53, c_n1) | (~node2(s53)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4782,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s53, c_n1) | (~node2(s53))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4781, 4780])).
% 1.41/1.43 tff(4783,plain,
% 1.41/1.43 (~node2(s53)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4782, 787, 4779])).
% 1.41/1.43 tff(4784,plain,
% 1.41/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s53, c_t2) | (~node1(s53)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s53, c_t2) | (~node1(s53)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4785,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s53, c_t2) | (~node1(s53)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4786,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s53, c_t2) | (~node1(s53))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4785, 4784])).
% 1.41/1.43 tff(4787,plain,
% 1.41/1.43 (~node1(s53)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4786, 195, 4704])).
% 1.41/1.43 tff(4788,plain,
% 1.41/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s53, s54)) | node7(s53, s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s53, s54)) | node7(s53, s54))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4789,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s53, s54)) | node7(s53, s54))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4790,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s53, s54)) | node7(s53, s54)),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4789, 4788])).
% 1.41/1.43 tff(4791,plain,
% 1.41/1.43 (node7(s53, s54)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4790, 206, 4715])).
% 1.41/1.43 tff(4792,plain,
% 1.41/1.43 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state1(s54, c_c1) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state1(s54, c_c1) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4793,plain,
% 1.41/1.43 (((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)) | m_main_v_state1(s54, c_c1)) <=> ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state1(s54, c_c1) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4794,plain,
% 1.41/1.43 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)) | m_main_v_state1(s54, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state1(s54, c_c1) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54))))),
% 1.41/1.43 inference(monotonicity,[status(thm)],[4793])).
% 1.41/1.43 tff(4795,plain,
% 1.41/1.43 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)) | m_main_v_state1(s54, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state1(s54, c_c1) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)))),
% 1.41/1.43 inference(transitivity,[status(thm)],[4794, 4792])).
% 1.41/1.43 tff(4796,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54)) | m_main_v_state1(s54, c_c1))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4797,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state1(s54, c_c1) | node1(s53) | node2(s53) | node3(s53) | (~node7(s53, s54))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4796, 4795])).
% 1.41/1.43 tff(4798,plain,
% 1.41/1.43 ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state1(s54, c_c1) | node1(s53) | node2(s53) | node3(s53)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4797, 892, 4791])).
% 1.41/1.43 tff(4799,plain,
% 1.41/1.43 (m_main_v_state1(s54, c_c1)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4798, 4787, 4700, 4664, 4783, 4772])).
% 1.41/1.43 tff(4800,plain,
% 1.41/1.43 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s54, c_n1)) | (~m_main_v_state1(s54, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s54, c_n1)) | (~m_main_v_state1(s54, c_c1)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4801,plain,
% 1.41/1.43 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s54, c_n1)) | (~m_main_v_state1(s54, c_c1)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4802,plain,
% 1.41/1.43 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s54, c_n1)) | (~m_main_v_state1(s54, c_c1))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4801, 4800])).
% 1.41/1.43 tff(4803,plain,
% 1.41/1.43 (~m_main_v_state1(s54, c_n1)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4802, 454, 4799])).
% 1.41/1.43 tff(4804,plain,
% 1.41/1.43 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s54, c_n1) | (~node11(s54)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s54, c_n1) | (~node11(s54)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4805,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s54, c_n1) | (~node11(s54)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4806,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s54, c_n1) | (~node11(s54))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4805, 4804])).
% 1.41/1.43 tff(4807,plain,
% 1.41/1.43 (~node11(s54)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4806, 238, 4803])).
% 1.41/1.43 tff(4808,plain,
% 1.41/1.43 (succ(s54, s55) <=> succ(s54, s55)),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4809,axiom,(succ(s54, s55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound55')).
% 1.41/1.43 tff(4810,plain,
% 1.41/1.43 (succ(s54, s55)),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4809, 4808])).
% 1.41/1.43 tff(4811,plain,
% 1.41/1.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4812,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4813,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55)),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4812, 4811])).
% 1.41/1.43 tff(4814,plain,
% 1.41/1.43 (trans(s54, s55)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4813, 4810, 32])).
% 1.41/1.43 tff(4815,plain,
% 1.41/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s54, s55)) | node14(s54, s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s54, s55)) | node14(s54, s55))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4816,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s54, s55)) | node14(s54, s55))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4817,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s54, s55)) | node14(s54, s55)),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 1.41/1.43 tff(4818,plain,
% 1.41/1.43 (node14(s54, s55)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4817, 46, 4814])).
% 1.41/1.43 tff(4819,plain,
% 1.41/1.43 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4820,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4821,plain,
% 1.41/1.43 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4820, 4819])).
% 1.41/1.43 tff(4822,plain,
% 1.41/1.43 (m_main_v_state2(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4821, 296, 4818])).
% 1.41/1.43 tff(4823,plain,
% 1.41/1.43 (node13(s54, s55)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4822, 4807, 4764, 4760, 4756, 4752, 4735])).
% 1.41/1.43 tff(4824,plain,
% 1.41/1.43 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)) | (~node13(s54, s55)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)) | (~node13(s54, s55)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4825,plain,
% 1.41/1.43 (((~node13(s54, s55)) | m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2))) <=> (m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)) | (~node13(s54, s55)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4826,plain,
% 1.41/1.43 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s54, s55)) | m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)) | (~node13(s54, s55))))),
% 1.41/1.43 inference(monotonicity,[status(thm)],[4825])).
% 1.41/1.43 tff(4827,plain,
% 1.41/1.43 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s54, s55)) | m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)) | (~node13(s54, s55)))),
% 1.41/1.43 inference(transitivity,[status(thm)],[4826, 4824])).
% 1.41/1.43 tff(4828,plain,
% 1.41/1.43 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s54, s55)) | m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4829,plain,
% 1.41/1.43 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s54, c_n2) | (~m_main_v_state2(s55, c_n2)) | (~node13(s54, s55))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4828, 4827])).
% 1.41/1.43 tff(4830,plain,
% 1.41/1.43 (~m_main_v_state2(s55, c_n2)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4829, 311, 4748, 4823])).
% 1.41/1.43 tff(4831,plain,
% 1.41/1.43 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s55, c_n2) | (~node9(s55)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s55, c_n2) | (~node9(s55)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4832,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s55, c_n2) | (~node9(s55)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4833,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s55, c_n2) | (~node9(s55))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4832, 4831])).
% 1.41/1.43 tff(4834,plain,
% 1.41/1.43 (~node9(s55)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4833, 88, 4830])).
% 1.41/1.43 tff(4835,plain,
% 1.41/1.43 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s55, c_n2) | (~node10(s55)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s55, c_n2) | (~node10(s55)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4836,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s55, c_n2) | (~node10(s55)))),
% 1.41/1.43 inference(quant_inst,[status(thm)],[])).
% 1.41/1.43 tff(4837,plain,
% 1.41/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s55, c_n2) | (~node10(s55))),
% 1.41/1.43 inference(modus_ponens,[status(thm)],[4836, 4835])).
% 1.41/1.43 tff(4838,plain,
% 1.41/1.43 (~node10(s55)),
% 1.41/1.43 inference(unit_resolution,[status(thm)],[4837, 249, 4830])).
% 1.41/1.43 tff(4839,plain,
% 1.41/1.43 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55)))),
% 1.41/1.43 inference(rewrite,[status(thm)],[])).
% 1.41/1.43 tff(4840,plain,
% 1.41/1.43 (((~node13(s54, s55)) | (~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2)) <=> ((~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4841,plain,
% 1.41/1.44 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s54, s55)) | (~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55))))),
% 1.41/1.44 inference(monotonicity,[status(thm)],[4840])).
% 1.41/1.44 tff(4842,plain,
% 1.41/1.44 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s54, s55)) | (~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55)))),
% 1.41/1.44 inference(transitivity,[status(thm)],[4841, 4839])).
% 1.41/1.44 tff(4843,plain,
% 1.41/1.44 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s54, s55)) | (~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4844,plain,
% 1.41/1.44 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4843, 4842])).
% 1.41/1.44 tff(4845,plain,
% 1.41/1.44 (m_main_v_state2(s55, c_t2)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4844, 518, 4744, 4823])).
% 1.41/1.44 tff(4846,plain,
% 1.41/1.44 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s54, c_t1)) | (~m_main_v_state1(s54, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s54, c_t1)) | (~m_main_v_state1(s54, c_c1)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4847,plain,
% 1.41/1.44 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s54, c_t1)) | (~m_main_v_state1(s54, c_c1)))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4848,plain,
% 1.41/1.44 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s54, c_t1)) | (~m_main_v_state1(s54, c_c1))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4847, 4846])).
% 1.41/1.44 tff(4849,plain,
% 1.41/1.44 (~m_main_v_state1(s54, c_t1)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4848, 539, 4799])).
% 1.41/1.44 tff(4850,plain,
% 1.41/1.44 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s54, c_t1) | (~node5(s54)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s54, c_t1) | (~node5(s54)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4851,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s54, c_t1) | (~node5(s54)))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4852,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s54, c_t1) | (~node5(s54))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4851, 4850])).
% 1.41/1.44 tff(4853,plain,
% 1.41/1.44 (~node5(s54)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4852, 550, 4849])).
% 1.41/1.44 tff(4854,plain,
% 1.41/1.44 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s54, c_n2) | (~node4(s54)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s54, c_n2) | (~node4(s54)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4855,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s54, c_n2) | (~node4(s54)))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4856,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s54, c_n2) | (~node4(s54))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4855, 4854])).
% 1.41/1.44 tff(4857,plain,
% 1.41/1.44 (~node4(s54)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4856, 388, 4748])).
% 1.41/1.44 tff(4858,plain,
% 1.41/1.44 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s54, c_c2) | (~node3(s54)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s54, c_c2) | (~node3(s54)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4859,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s54, c_c2) | (~node3(s54)))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4860,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s54, c_c2) | (~node3(s54))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4859, 4858])).
% 1.41/1.44 tff(4861,plain,
% 1.41/1.44 (~node3(s54)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4860, 399, 4764])).
% 1.41/1.44 tff(4862,plain,
% 1.41/1.44 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s54, c_n2) | (~node2(s54)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s54, c_n2) | (~node2(s54)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4863,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s54, c_n2) | (~node2(s54)))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4864,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s54, c_n2) | (~node2(s54))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4863, 4862])).
% 1.41/1.44 tff(4865,plain,
% 1.41/1.44 (~node2(s54)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4864, 410, 4748])).
% 1.41/1.44 tff(4866,plain,
% 1.41/1.44 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s54, c_n1) | (~node1(s54)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s54, c_n1) | (~node1(s54)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4867,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s54, c_n1) | (~node1(s54)))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4868,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s54, c_n1) | (~node1(s54))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4867, 4866])).
% 1.41/1.44 tff(4869,plain,
% 1.41/1.44 (~node1(s54)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4868, 421, 4803])).
% 1.41/1.44 tff(4870,plain,
% 1.41/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s54, s55)) | node7(s54, s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s54, s55)) | node7(s54, s55))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4871,plain,
% 1.41/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s54, s55)) | node7(s54, s55))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4872,plain,
% 1.41/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s54, s55)) | node7(s54, s55)),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4871, 4870])).
% 1.41/1.44 tff(4873,plain,
% 1.41/1.44 (node7(s54, s55)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4872, 206, 4814])).
% 1.41/1.44 tff(4874,plain,
% 1.41/1.44 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4875,plain,
% 1.41/1.44 (((~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)) | m_main_v_state1(s55, c_n1)) <=> (m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4876,plain,
% 1.41/1.44 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)) | m_main_v_state1(s55, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55))))),
% 1.41/1.44 inference(monotonicity,[status(thm)],[4875])).
% 1.41/1.44 tff(4877,plain,
% 1.41/1.44 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)) | m_main_v_state1(s55, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)))),
% 1.41/1.44 inference(transitivity,[status(thm)],[4876, 4874])).
% 1.41/1.44 tff(4878,plain,
% 1.41/1.44 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)) | m_main_v_state1(s55, c_n1))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4879,plain,
% 1.41/1.44 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4878, 4877])).
% 1.41/1.44 tff(4880,plain,
% 1.41/1.44 (m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4879, 584, 4873])).
% 1.41/1.44 tff(4881,plain,
% 1.41/1.44 (m_main_v_state1(s55, c_n1)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4880, 4869, 4799, 4865, 4861, 4857, 4853])).
% 1.41/1.44 tff(4882,plain,
% 1.41/1.44 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s55, c_n2) | (~node8(s55)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s55, c_n2) | (~node8(s55)))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4883,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s55, c_n2) | (~node8(s55)))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4884,plain,
% 1.41/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s55, c_n2) | (~node8(s55))),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4883, 4882])).
% 1.41/1.44 tff(4885,plain,
% 1.41/1.44 (~node8(s55)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4884, 271, 4830])).
% 1.41/1.44 tff(4886,plain,
% 1.41/1.44 (succ(s55, s56) <=> succ(s55, s56)),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4887,axiom,(succ(s55, s56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound56')).
% 1.41/1.44 tff(4888,plain,
% 1.41/1.44 (succ(s55, s56)),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4887, 4886])).
% 1.41/1.44 tff(4889,plain,
% 1.41/1.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4890,plain,
% 1.41/1.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))),
% 1.41/1.44 inference(quant_inst,[status(thm)],[])).
% 1.41/1.44 tff(4891,plain,
% 1.41/1.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56)),
% 1.41/1.44 inference(modus_ponens,[status(thm)],[4890, 4889])).
% 1.41/1.44 tff(4892,plain,
% 1.41/1.44 (trans(s55, s56)),
% 1.41/1.44 inference(unit_resolution,[status(thm)],[4891, 4888, 32])).
% 1.41/1.44 tff(4893,plain,
% 1.41/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s55, s56)) | node14(s55, s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s55, s56)) | node14(s55, s56))),
% 1.41/1.44 inference(rewrite,[status(thm)],[])).
% 1.41/1.44 tff(4894,plain,
% 1.41/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s55, s56)) | node14(s55, s56))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4895,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s55, s56)) | node14(s55, s56)),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4894, 4893])).
% 1.41/1.45 tff(4896,plain,
% 1.41/1.45 (node14(s55, s56)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4895, 46, 4892])).
% 1.41/1.45 tff(4897,plain,
% 1.41/1.45 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | node9(s55) | node8(s55) | node10(s55) | (~node14(s55, s56)) | m_main_v_state2(s56, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | node9(s55) | node8(s55) | node10(s55) | (~node14(s55, s56)) | m_main_v_state2(s56, c_c2))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4898,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | node9(s55) | node8(s55) | node10(s55) | (~node14(s55, s56)) | m_main_v_state2(s56, c_c2))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4899,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | node9(s55) | node8(s55) | node10(s55) | (~node14(s55, s56)) | m_main_v_state2(s56, c_c2)),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4898, 4897])).
% 1.41/1.45 tff(4900,plain,
% 1.41/1.45 ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | node9(s55) | node8(s55) | node10(s55) | m_main_v_state2(s56, c_c2)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4899, 617, 4896])).
% 1.41/1.45 tff(4901,plain,
% 1.41/1.45 (m_main_v_state2(s56, c_c2)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4900, 4885, 4881, 4845, 4838, 4834])).
% 1.41/1.45 tff(4902,plain,
% 1.41/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s56, c_t2)) | (~m_main_v_state2(s56, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s56, c_t2)) | (~m_main_v_state2(s56, c_c2)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4903,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s56, c_t2)) | (~m_main_v_state2(s56, c_c2)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4904,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s56, c_t2)) | (~m_main_v_state2(s56, c_c2))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4903, 4902])).
% 1.41/1.45 tff(4905,plain,
% 1.41/1.45 (~m_main_v_state2(s56, c_t2)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4904, 260, 4901])).
% 1.41/1.45 tff(4906,plain,
% 1.41/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s56, c_t2) | (~node12(s56)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s56, c_t2) | (~node12(s56)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4907,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s56, c_t2) | (~node12(s56)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4908,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s56, c_t2) | (~node12(s56))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4907, 4906])).
% 1.41/1.45 tff(4909,plain,
% 1.41/1.45 (~node12(s56)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4908, 633, 4905])).
% 1.41/1.45 tff(4910,plain,
% 1.41/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s55, s56)) | node7(s55, s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s55, s56)) | node7(s55, s56))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4911,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s55, s56)) | node7(s55, s56))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4912,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s55, s56)) | node7(s55, s56)),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 1.41/1.45 tff(4913,plain,
% 1.41/1.45 (node7(s55, s56)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4912, 206, 4892])).
% 1.41/1.45 tff(4914,plain,
% 1.41/1.45 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node7(s55, s56)) | m_main_v_state1(s56, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node7(s55, s56)) | m_main_v_state1(s56, c_t1))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4915,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node7(s55, s56)) | m_main_v_state1(s56, c_t1))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4916,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node7(s55, s56)) | m_main_v_state1(s56, c_t1)),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4915, 4914])).
% 1.41/1.45 tff(4917,plain,
% 1.41/1.45 ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | m_main_v_state1(s56, c_t1)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4916, 651, 4913])).
% 1.41/1.45 tff(4918,plain,
% 1.41/1.45 (m_main_v_state1(s56, c_t1)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4917, 4845, 4881])).
% 1.41/1.45 tff(4919,plain,
% 1.41/1.45 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s56, c_n1)) | (~m_main_v_state1(s56, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s56, c_n1)) | (~m_main_v_state1(s56, c_t1)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4920,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s56, c_n1)) | (~m_main_v_state1(s56, c_t1)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4921,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s56, c_n1)) | (~m_main_v_state1(s56, c_t1))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4920, 4919])).
% 1.41/1.45 tff(4922,plain,
% 1.41/1.45 (~m_main_v_state1(s56, c_n1)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4921, 10, 4918])).
% 1.41/1.45 tff(4923,plain,
% 1.41/1.45 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s56, c_n1) | (~node11(s56)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s56, c_n1) | (~node11(s56)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4924,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s56, c_n1) | (~node11(s56)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4925,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s56, c_n1) | (~node11(s56))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4924, 4923])).
% 1.41/1.45 tff(4926,plain,
% 1.41/1.45 (~node11(s56)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4925, 238, 4922])).
% 1.41/1.45 tff(4927,plain,
% 1.41/1.45 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s56, c_t1)) | (~m_main_v_state1(s56, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s56, c_t1)) | (~m_main_v_state1(s56, c_c1)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4928,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s56, c_t1)) | (~m_main_v_state1(s56, c_c1)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4929,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s56, c_t1)) | (~m_main_v_state1(s56, c_c1))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4928, 4927])).
% 1.41/1.45 tff(4930,plain,
% 1.41/1.45 (~m_main_v_state1(s56, c_c1)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4929, 539, 4918])).
% 1.41/1.45 tff(4931,plain,
% 1.41/1.45 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s56, c_c1) | (~node10(s56)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s56, c_c1) | (~node10(s56)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4932,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s56, c_c1) | (~node10(s56)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4933,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s56, c_c1) | (~node10(s56))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4932, 4931])).
% 1.41/1.45 tff(4934,plain,
% 1.41/1.45 (~node10(s56)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4933, 675, 4930])).
% 1.41/1.45 tff(4935,plain,
% 1.41/1.45 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s56, c_n1) | (~node9(s56)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s56, c_n1) | (~node9(s56)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4936,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s56, c_n1) | (~node9(s56)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4937,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s56, c_n1) | (~node9(s56))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4936, 4935])).
% 1.41/1.45 tff(4938,plain,
% 1.41/1.45 (~node9(s56)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4937, 686, 4922])).
% 1.41/1.45 tff(4939,plain,
% 1.41/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s56, c_n2)) | (~m_main_v_state2(s56, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s56, c_n2)) | (~m_main_v_state2(s56, c_c2)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4940,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s56, c_n2)) | (~m_main_v_state2(s56, c_c2)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4941,plain,
% 1.41/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s56, c_n2)) | (~m_main_v_state2(s56, c_c2))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4940, 4939])).
% 1.41/1.45 tff(4942,plain,
% 1.41/1.45 (~m_main_v_state2(s56, c_n2)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4941, 697, 4901])).
% 1.41/1.45 tff(4943,plain,
% 1.41/1.45 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s56, c_n2) | (~node8(s56)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s56, c_n2) | (~node8(s56)))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4944,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s56, c_n2) | (~node8(s56)))),
% 1.41/1.45 inference(quant_inst,[status(thm)],[])).
% 1.41/1.45 tff(4945,plain,
% 1.41/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s56, c_n2) | (~node8(s56))),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 1.41/1.45 tff(4946,plain,
% 1.41/1.45 (~node8(s56)),
% 1.41/1.45 inference(unit_resolution,[status(thm)],[4945, 271, 4942])).
% 1.41/1.45 tff(4947,plain,
% 1.41/1.45 (succ(s56, s57) <=> succ(s56, s57)),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4948,axiom,(succ(s56, s57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound57')).
% 1.41/1.45 tff(4949,plain,
% 1.41/1.45 (succ(s56, s57)),
% 1.41/1.45 inference(modus_ponens,[status(thm)],[4948, 4947])).
% 1.41/1.45 tff(4950,plain,
% 1.41/1.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57))),
% 1.41/1.45 inference(rewrite,[status(thm)],[])).
% 1.41/1.45 tff(4951,plain,
% 1.41/1.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4952,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57)),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4951, 4950])).
% 1.44/1.46 tff(4953,plain,
% 1.44/1.46 (trans(s56, s57)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4952, 4949, 32])).
% 1.44/1.46 tff(4954,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s56, s57)) | node14(s56, s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s56, s57)) | node14(s56, s57))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4955,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s56, s57)) | node14(s56, s57))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4956,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s56, s57)) | node14(s56, s57)),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4955, 4954])).
% 1.44/1.46 tff(4957,plain,
% 1.44/1.46 (node14(s56, s57)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4956, 46, 4953])).
% 1.44/1.46 tff(4958,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4959,plain,
% 1.44/1.46 (((~m_main_v_state2(s56, c_c2)) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | m_main_v_state2(s57, c_n2)) <=> (m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4960,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s56, c_c2)) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | m_main_v_state2(s57, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2))))),
% 1.44/1.46 inference(monotonicity,[status(thm)],[4959])).
% 1.44/1.46 tff(4961,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s56, c_c2)) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | m_main_v_state2(s57, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2)))),
% 1.44/1.46 inference(transitivity,[status(thm)],[4960, 4958])).
% 1.44/1.46 tff(4962,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s56, c_c2)) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | m_main_v_state2(s57, c_n2))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4963,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4962, 4961])).
% 1.44/1.46 tff(4964,plain,
% 1.44/1.46 (m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~m_main_v_state2(s56, c_c2))),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4963, 726, 4957])).
% 1.44/1.46 tff(4965,plain,
% 1.44/1.46 (m_main_v_state2(s57, c_n2)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4964, 4946, 4901, 4938, 4934, 4926, 4909])).
% 1.44/1.46 tff(4966,plain,
% 1.44/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_t2)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4967,plain,
% 1.44/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_t2)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4968,plain,
% 1.44/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_t2))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4967, 4966])).
% 1.44/1.46 tff(4969,plain,
% 1.44/1.46 (~m_main_v_state2(s57, c_t2)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4968, 77, 4965])).
% 1.44/1.46 tff(4970,plain,
% 1.44/1.46 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node26(X))) <=> (m_main_v_state2(X, c_t2) | (~node26(X))))),
% 1.44/1.46 inference(bind,[status(th)],[])).
% 1.44/1.46 tff(4971,plain,
% 1.44/1.46 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.44/1.46 inference(quant_intro,[status(thm)],[4970])).
% 1.44/1.46 tff(4972,plain,
% 1.44/1.46 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4973,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty17')).
% 1.44/1.46 tff(4974,plain,
% 1.44/1.46 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4973, 4972])).
% 1.44/1.46 tff(4975,plain,(
% 1.44/1.46 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.44/1.46 inference(skolemize,[status(sab)],[4974])).
% 1.44/1.46 tff(4976,plain,
% 1.44/1.46 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4975, 4971])).
% 1.44/1.46 tff(4977,plain,
% 1.44/1.46 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s57, c_t2) | (~node26(s57)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s57, c_t2) | (~node26(s57)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4978,plain,
% 1.44/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s57, c_t2) | (~node26(s57)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4979,plain,
% 1.44/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s57, c_t2) | (~node26(s57))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4978, 4977])).
% 1.44/1.46 tff(4980,plain,
% 1.44/1.46 (~node26(s57)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4979, 4976, 4969])).
% 1.44/1.46 tff(4981,plain,
% 1.44/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s56)) | (~m_main_v_state2(s56, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s56)) | (~m_main_v_state2(s56, c_c2)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4982,plain,
% 1.44/1.46 (((~m_main_v_state2(s56, c_c2)) | (~always25(s56))) <=> ((~always25(s56)) | (~m_main_v_state2(s56, c_c2)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4983,plain,
% 1.44/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s56, c_c2)) | (~always25(s56)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s56)) | (~m_main_v_state2(s56, c_c2))))),
% 1.44/1.46 inference(monotonicity,[status(thm)],[4982])).
% 1.44/1.46 tff(4984,plain,
% 1.44/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s56, c_c2)) | (~always25(s56)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s56)) | (~m_main_v_state2(s56, c_c2)))),
% 1.44/1.46 inference(transitivity,[status(thm)],[4983, 4981])).
% 1.44/1.46 tff(4985,plain,
% 1.44/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s56, c_c2)) | (~always25(s56)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4986,plain,
% 1.44/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s56)) | (~m_main_v_state2(s56, c_c2))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4985, 4984])).
% 1.44/1.46 tff(4987,plain,
% 1.44/1.46 (~always25(s56)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4986, 2024, 4901])).
% 1.44/1.46 tff(4988,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s55, s56)) | (~always25(s55)) | always25(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s55, s56)) | (~always25(s55)) | always25(s56))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4989,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s55, s56)) | (~always25(s55)) | always25(s56))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4990,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s55, s56)) | (~always25(s55)) | always25(s56)),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4989, 4988])).
% 1.44/1.46 tff(4991,plain,
% 1.44/1.46 ((~always25(s55)) | always25(s56)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4990, 2041, 4892])).
% 1.44/1.46 tff(4992,plain,
% 1.44/1.46 (~always25(s55)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4991, 4987])).
% 1.44/1.46 tff(4993,plain,
% 1.44/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s55) | (~node26(s55)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s55) | (~node26(s55)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4994,plain,
% 1.44/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s55) | (~node26(s55)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4995,plain,
% 1.44/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s55) | (~node26(s55))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4994, 4993])).
% 1.44/1.46 tff(4996,plain,
% 1.44/1.46 (~node26(s55)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4995, 2069, 4992])).
% 1.44/1.46 tff(4997,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s54, s55)) | (~always25(s54)) | always25(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s54, s55)) | (~always25(s54)) | always25(s55))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(4998,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s54, s55)) | (~always25(s54)) | always25(s55))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(4999,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s54, s55)) | (~always25(s54)) | always25(s55)),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 1.44/1.46 tff(5000,plain,
% 1.44/1.46 ((~always25(s54)) | always25(s55)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[4999, 2041, 4814])).
% 1.44/1.46 tff(5001,plain,
% 1.44/1.46 (~always25(s54)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[5000, 4992])).
% 1.44/1.46 tff(5002,plain,
% 1.44/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s54) | (~node26(s54)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s54) | (~node26(s54)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(5003,plain,
% 1.44/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s54) | (~node26(s54)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(5004,plain,
% 1.44/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s54) | (~node26(s54))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[5003, 5002])).
% 1.44/1.46 tff(5005,plain,
% 1.44/1.46 (~node26(s54)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[5004, 2069, 5001])).
% 1.44/1.46 tff(5006,plain,
% 1.44/1.46 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s53, c_t2) | (~node26(s53)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s53, c_t2) | (~node26(s53)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(5007,plain,
% 1.44/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s53, c_t2) | (~node26(s53)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(5008,plain,
% 1.44/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s53, c_t2) | (~node26(s53))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[5007, 5006])).
% 1.44/1.46 tff(5009,plain,
% 1.44/1.46 (~node26(s53)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[5008, 4976, 4704])).
% 1.44/1.46 tff(5010,plain,
% 1.44/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s52)) | (~m_main_v_state2(s52, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s52)) | (~m_main_v_state2(s52, c_c2)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(5011,plain,
% 1.44/1.46 (((~m_main_v_state2(s52, c_c2)) | (~always25(s52))) <=> ((~always25(s52)) | (~m_main_v_state2(s52, c_c2)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(5012,plain,
% 1.44/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s52, c_c2)) | (~always25(s52)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s52)) | (~m_main_v_state2(s52, c_c2))))),
% 1.44/1.46 inference(monotonicity,[status(thm)],[5011])).
% 1.44/1.46 tff(5013,plain,
% 1.44/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s52, c_c2)) | (~always25(s52)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s52)) | (~m_main_v_state2(s52, c_c2)))),
% 1.44/1.46 inference(transitivity,[status(thm)],[5012, 5010])).
% 1.44/1.46 tff(5014,plain,
% 1.44/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s52, c_c2)) | (~always25(s52)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(5015,plain,
% 1.44/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s52)) | (~m_main_v_state2(s52, c_c2))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 1.44/1.46 tff(5016,plain,
% 1.44/1.46 (~always25(s52)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[5015, 2024, 4633])).
% 1.44/1.46 tff(5017,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s51, s52)) | (~always25(s51)) | always25(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s51, s52)) | (~always25(s51)) | always25(s52))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(5018,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s51, s52)) | (~always25(s51)) | always25(s52))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(5019,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s51, s52)) | (~always25(s51)) | always25(s52)),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[5018, 5017])).
% 1.44/1.46 tff(5020,plain,
% 1.44/1.46 ((~always25(s51)) | always25(s52)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[5019, 2041, 4559])).
% 1.44/1.46 tff(5021,plain,
% 1.44/1.46 (~always25(s51)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[5020, 5016])).
% 1.44/1.46 tff(5022,plain,
% 1.44/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s51) | (~node26(s51)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s51) | (~node26(s51)))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(5023,plain,
% 1.44/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s51) | (~node26(s51)))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.46 tff(5024,plain,
% 1.44/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s51) | (~node26(s51))),
% 1.44/1.46 inference(modus_ponens,[status(thm)],[5023, 5022])).
% 1.44/1.46 tff(5025,plain,
% 1.44/1.46 (~node26(s51)),
% 1.44/1.46 inference(unit_resolution,[status(thm)],[5024, 2069, 5021])).
% 1.44/1.46 tff(5026,plain,
% 1.44/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s50, s51)) | (~always25(s50)) | always25(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s50, s51)) | (~always25(s50)) | always25(s51))),
% 1.44/1.46 inference(rewrite,[status(thm)],[])).
% 1.44/1.46 tff(5027,plain,
% 1.44/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s50, s51)) | (~always25(s50)) | always25(s51))),
% 1.44/1.46 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5028,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s50, s51)) | (~always25(s50)) | always25(s51)),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5027, 5026])).
% 1.44/1.47 tff(5029,plain,
% 1.44/1.47 ((~always25(s50)) | always25(s51)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5028, 2041, 4484])).
% 1.44/1.47 tff(5030,plain,
% 1.44/1.47 (~always25(s50)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5029, 5021])).
% 1.44/1.47 tff(5031,plain,
% 1.44/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s50) | (~node26(s50)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s50) | (~node26(s50)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5032,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s50) | (~node26(s50)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5033,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s50) | (~node26(s50))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5032, 5031])).
% 1.44/1.47 tff(5034,plain,
% 1.44/1.47 (~node26(s50)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5033, 2069, 5030])).
% 1.44/1.47 tff(5035,plain,
% 1.44/1.47 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s49, c_t2) | (~node26(s49)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s49, c_t2) | (~node26(s49)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5036,plain,
% 1.44/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s49, c_t2) | (~node26(s49)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5037,plain,
% 1.44/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s49, c_t2) | (~node26(s49))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 1.44/1.47 tff(5038,plain,
% 1.44/1.47 (~node26(s49)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5037, 4976, 4409])).
% 1.44/1.47 tff(5039,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s48)) | (~m_main_v_state2(s48, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s48)) | (~m_main_v_state2(s48, c_c2)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5040,plain,
% 1.44/1.47 (((~m_main_v_state2(s48, c_c2)) | (~always25(s48))) <=> ((~always25(s48)) | (~m_main_v_state2(s48, c_c2)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5041,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s48, c_c2)) | (~always25(s48)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s48)) | (~m_main_v_state2(s48, c_c2))))),
% 1.44/1.47 inference(monotonicity,[status(thm)],[5040])).
% 1.44/1.47 tff(5042,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s48, c_c2)) | (~always25(s48)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s48)) | (~m_main_v_state2(s48, c_c2)))),
% 1.44/1.47 inference(transitivity,[status(thm)],[5041, 5039])).
% 1.44/1.47 tff(5043,plain,
% 1.44/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s48, c_c2)) | (~always25(s48)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5044,plain,
% 1.44/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s48)) | (~m_main_v_state2(s48, c_c2))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5043, 5042])).
% 1.44/1.47 tff(5045,plain,
% 1.44/1.47 (~always25(s48)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5044, 2024, 4273])).
% 1.44/1.47 tff(5046,plain,
% 1.44/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s47, s48)) | (~always25(s47)) | always25(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s47, s48)) | (~always25(s47)) | always25(s48))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5047,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s47, s48)) | (~always25(s47)) | always25(s48))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5048,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s47, s48)) | (~always25(s47)) | always25(s48)),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5047, 5046])).
% 1.44/1.47 tff(5049,plain,
% 1.44/1.47 ((~always25(s47)) | always25(s48)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5048, 2041, 4264])).
% 1.44/1.47 tff(5050,plain,
% 1.44/1.47 (~always25(s47)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5049, 5045])).
% 1.44/1.47 tff(5051,plain,
% 1.44/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s47) | (~node26(s47)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s47) | (~node26(s47)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5052,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s47) | (~node26(s47)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5053,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s47) | (~node26(s47))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5052, 5051])).
% 1.44/1.47 tff(5054,plain,
% 1.44/1.47 (~node26(s47)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5053, 2069, 5050])).
% 1.44/1.47 tff(5055,plain,
% 1.44/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s46, s47)) | (~always25(s46)) | always25(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s46, s47)) | (~always25(s46)) | always25(s47))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5056,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s46, s47)) | (~always25(s46)) | always25(s47))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5057,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s46, s47)) | (~always25(s46)) | always25(s47)),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5056, 5055])).
% 1.44/1.47 tff(5058,plain,
% 1.44/1.47 ((~always25(s46)) | always25(s47)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5057, 2041, 4186])).
% 1.44/1.47 tff(5059,plain,
% 1.44/1.47 (~always25(s46)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5058, 5050])).
% 1.44/1.47 tff(5060,plain,
% 1.44/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s46) | (~node26(s46)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s46) | (~node26(s46)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5061,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s46) | (~node26(s46)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5062,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s46) | (~node26(s46))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5061, 5060])).
% 1.44/1.47 tff(5063,plain,
% 1.44/1.47 (~node26(s46)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5062, 2069, 5059])).
% 1.44/1.47 tff(5064,plain,
% 1.44/1.47 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s45, c_t2) | (~node26(s45)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s45, c_t2) | (~node26(s45)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5065,plain,
% 1.44/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s45, c_t2) | (~node26(s45)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5066,plain,
% 1.44/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s45, c_t2) | (~node26(s45))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5065, 5064])).
% 1.44/1.47 tff(5067,plain,
% 1.44/1.47 (~node26(s45)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5066, 4976, 4076])).
% 1.44/1.47 tff(5068,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s44)) | (~m_main_v_state2(s44, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s44)) | (~m_main_v_state2(s44, c_c2)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5069,plain,
% 1.44/1.47 (((~m_main_v_state2(s44, c_c2)) | (~always25(s44))) <=> ((~always25(s44)) | (~m_main_v_state2(s44, c_c2)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5070,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s44, c_c2)) | (~always25(s44)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s44)) | (~m_main_v_state2(s44, c_c2))))),
% 1.44/1.47 inference(monotonicity,[status(thm)],[5069])).
% 1.44/1.47 tff(5071,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s44, c_c2)) | (~always25(s44)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s44)) | (~m_main_v_state2(s44, c_c2)))),
% 1.44/1.47 inference(transitivity,[status(thm)],[5070, 5068])).
% 1.44/1.47 tff(5072,plain,
% 1.44/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s44, c_c2)) | (~always25(s44)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5073,plain,
% 1.44/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s44)) | (~m_main_v_state2(s44, c_c2))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5072, 5071])).
% 1.44/1.47 tff(5074,plain,
% 1.44/1.47 (~always25(s44)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5073, 2024, 4005])).
% 1.44/1.47 tff(5075,plain,
% 1.44/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s43, s44)) | (~always25(s43)) | always25(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s43, s44)) | (~always25(s43)) | always25(s44))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5076,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s43, s44)) | (~always25(s43)) | always25(s44))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5077,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s43, s44)) | (~always25(s43)) | always25(s44)),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5076, 5075])).
% 1.44/1.47 tff(5078,plain,
% 1.44/1.47 ((~always25(s43)) | always25(s44)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5077, 2041, 3931])).
% 1.44/1.47 tff(5079,plain,
% 1.44/1.47 (~always25(s43)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5078, 5074])).
% 1.44/1.47 tff(5080,plain,
% 1.44/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s43) | (~node26(s43)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s43) | (~node26(s43)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5081,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s43) | (~node26(s43)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5082,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s43) | (~node26(s43))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5081, 5080])).
% 1.44/1.47 tff(5083,plain,
% 1.44/1.47 (~node26(s43)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5082, 2069, 5079])).
% 1.44/1.47 tff(5084,plain,
% 1.44/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s42, s43)) | (~always25(s42)) | always25(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s42, s43)) | (~always25(s42)) | always25(s43))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5085,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s42, s43)) | (~always25(s42)) | always25(s43))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5086,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s42, s43)) | (~always25(s42)) | always25(s43)),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5085, 5084])).
% 1.44/1.47 tff(5087,plain,
% 1.44/1.47 ((~always25(s42)) | always25(s43)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5086, 2041, 3856])).
% 1.44/1.47 tff(5088,plain,
% 1.44/1.47 (~always25(s42)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5087, 5079])).
% 1.44/1.47 tff(5089,plain,
% 1.44/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s42) | (~node26(s42)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s42) | (~node26(s42)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5090,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s42) | (~node26(s42)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5091,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s42) | (~node26(s42))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5090, 5089])).
% 1.44/1.47 tff(5092,plain,
% 1.44/1.47 (~node26(s42)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5091, 2069, 5088])).
% 1.44/1.47 tff(5093,plain,
% 1.44/1.47 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s41, c_t2) | (~node26(s41)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s41, c_t2) | (~node26(s41)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5094,plain,
% 1.44/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s41, c_t2) | (~node26(s41)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5095,plain,
% 1.44/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s41, c_t2) | (~node26(s41))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5094, 5093])).
% 1.44/1.47 tff(5096,plain,
% 1.44/1.47 (~node26(s41)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5095, 4976, 3781])).
% 1.44/1.47 tff(5097,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s40)) | (~m_main_v_state2(s40, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s40)) | (~m_main_v_state2(s40, c_c2)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5098,plain,
% 1.44/1.47 (((~m_main_v_state2(s40, c_c2)) | (~always25(s40))) <=> ((~always25(s40)) | (~m_main_v_state2(s40, c_c2)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5099,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s40, c_c2)) | (~always25(s40)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s40)) | (~m_main_v_state2(s40, c_c2))))),
% 1.44/1.47 inference(monotonicity,[status(thm)],[5098])).
% 1.44/1.47 tff(5100,plain,
% 1.44/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s40, c_c2)) | (~always25(s40)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s40)) | (~m_main_v_state2(s40, c_c2)))),
% 1.44/1.47 inference(transitivity,[status(thm)],[5099, 5097])).
% 1.44/1.47 tff(5101,plain,
% 1.44/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s40, c_c2)) | (~always25(s40)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5102,plain,
% 1.44/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s40)) | (~m_main_v_state2(s40, c_c2))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5101, 5100])).
% 1.44/1.47 tff(5103,plain,
% 1.44/1.47 (~always25(s40)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5102, 2024, 3645])).
% 1.44/1.47 tff(5104,plain,
% 1.44/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s39, s40)) | (~always25(s39)) | always25(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s39, s40)) | (~always25(s39)) | always25(s40))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5105,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s39, s40)) | (~always25(s39)) | always25(s40))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5106,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s39, s40)) | (~always25(s39)) | always25(s40)),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5105, 5104])).
% 1.44/1.47 tff(5107,plain,
% 1.44/1.47 ((~always25(s39)) | always25(s40)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5106, 2041, 3636])).
% 1.44/1.47 tff(5108,plain,
% 1.44/1.47 (~always25(s39)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5107, 5103])).
% 1.44/1.47 tff(5109,plain,
% 1.44/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s39) | (~node26(s39)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s39) | (~node26(s39)))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5110,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s39) | (~node26(s39)))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.47 tff(5111,plain,
% 1.44/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s39) | (~node26(s39))),
% 1.44/1.47 inference(modus_ponens,[status(thm)],[5110, 5109])).
% 1.44/1.47 tff(5112,plain,
% 1.44/1.47 (~node26(s39)),
% 1.44/1.47 inference(unit_resolution,[status(thm)],[5111, 2069, 5108])).
% 1.44/1.47 tff(5113,plain,
% 1.44/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s38, s39)) | (~always25(s38)) | always25(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s38, s39)) | (~always25(s38)) | always25(s39))),
% 1.44/1.47 inference(rewrite,[status(thm)],[])).
% 1.44/1.47 tff(5114,plain,
% 1.44/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s38, s39)) | (~always25(s38)) | always25(s39))),
% 1.44/1.47 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5115,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s38, s39)) | (~always25(s38)) | always25(s39)),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5114, 5113])).
% 1.44/1.48 tff(5116,plain,
% 1.44/1.48 ((~always25(s38)) | always25(s39)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5115, 2041, 3558])).
% 1.44/1.48 tff(5117,plain,
% 1.44/1.48 (~always25(s38)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5116, 5108])).
% 1.44/1.48 tff(5118,plain,
% 1.44/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s38) | (~node26(s38)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s38) | (~node26(s38)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5119,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s38) | (~node26(s38)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5120,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s38) | (~node26(s38))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 1.44/1.48 tff(5121,plain,
% 1.44/1.48 (~node26(s38)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5120, 2069, 5117])).
% 1.44/1.48 tff(5122,plain,
% 1.44/1.48 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s37, c_t2) | (~node26(s37)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s37, c_t2) | (~node26(s37)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5123,plain,
% 1.44/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s37, c_t2) | (~node26(s37)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5124,plain,
% 1.44/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s37, c_t2) | (~node26(s37))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5123, 5122])).
% 1.44/1.48 tff(5125,plain,
% 1.44/1.48 (~node26(s37)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5124, 4976, 3448])).
% 1.44/1.48 tff(5126,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s36)) | (~m_main_v_state2(s36, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s36)) | (~m_main_v_state2(s36, c_c2)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5127,plain,
% 1.44/1.48 (((~m_main_v_state2(s36, c_c2)) | (~always25(s36))) <=> ((~always25(s36)) | (~m_main_v_state2(s36, c_c2)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5128,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s36, c_c2)) | (~always25(s36)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s36)) | (~m_main_v_state2(s36, c_c2))))),
% 1.44/1.48 inference(monotonicity,[status(thm)],[5127])).
% 1.44/1.48 tff(5129,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s36, c_c2)) | (~always25(s36)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s36)) | (~m_main_v_state2(s36, c_c2)))),
% 1.44/1.48 inference(transitivity,[status(thm)],[5128, 5126])).
% 1.44/1.48 tff(5130,plain,
% 1.44/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s36, c_c2)) | (~always25(s36)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5131,plain,
% 1.44/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s36)) | (~m_main_v_state2(s36, c_c2))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5130, 5129])).
% 1.44/1.48 tff(5132,plain,
% 1.44/1.48 (~always25(s36)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5131, 2024, 3377])).
% 1.44/1.48 tff(5133,plain,
% 1.44/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s35, s36)) | (~always25(s35)) | always25(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s35, s36)) | (~always25(s35)) | always25(s36))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5134,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s35, s36)) | (~always25(s35)) | always25(s36))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5135,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s35, s36)) | (~always25(s35)) | always25(s36)),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5134, 5133])).
% 1.44/1.48 tff(5136,plain,
% 1.44/1.48 ((~always25(s35)) | always25(s36)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5135, 2041, 3303])).
% 1.44/1.48 tff(5137,plain,
% 1.44/1.48 (~always25(s35)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5136, 5132])).
% 1.44/1.48 tff(5138,plain,
% 1.44/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s35) | (~node26(s35)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s35) | (~node26(s35)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5139,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s35) | (~node26(s35)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5140,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s35) | (~node26(s35))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5139, 5138])).
% 1.44/1.48 tff(5141,plain,
% 1.44/1.48 (~node26(s35)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5140, 2069, 5137])).
% 1.44/1.48 tff(5142,plain,
% 1.44/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s34, s35)) | (~always25(s34)) | always25(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s34, s35)) | (~always25(s34)) | always25(s35))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5143,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s34, s35)) | (~always25(s34)) | always25(s35))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5144,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s34, s35)) | (~always25(s34)) | always25(s35)),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5143, 5142])).
% 1.44/1.48 tff(5145,plain,
% 1.44/1.48 ((~always25(s34)) | always25(s35)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5144, 2041, 3228])).
% 1.44/1.48 tff(5146,plain,
% 1.44/1.48 (~always25(s34)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5145, 5137])).
% 1.44/1.48 tff(5147,plain,
% 1.44/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s34) | (~node26(s34)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s34) | (~node26(s34)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5148,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s34) | (~node26(s34)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5149,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s34) | (~node26(s34))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5148, 5147])).
% 1.44/1.48 tff(5150,plain,
% 1.44/1.48 (~node26(s34)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5149, 2069, 5146])).
% 1.44/1.48 tff(5151,plain,
% 1.44/1.48 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s33, c_t2) | (~node26(s33)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s33, c_t2) | (~node26(s33)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5152,plain,
% 1.44/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s33, c_t2) | (~node26(s33)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5153,plain,
% 1.44/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s33, c_t2) | (~node26(s33))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5152, 5151])).
% 1.44/1.48 tff(5154,plain,
% 1.44/1.48 (~node26(s33)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5153, 4976, 3153])).
% 1.44/1.48 tff(5155,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s32)) | (~m_main_v_state2(s32, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s32)) | (~m_main_v_state2(s32, c_c2)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5156,plain,
% 1.44/1.48 (((~m_main_v_state2(s32, c_c2)) | (~always25(s32))) <=> ((~always25(s32)) | (~m_main_v_state2(s32, c_c2)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5157,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s32, c_c2)) | (~always25(s32)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s32)) | (~m_main_v_state2(s32, c_c2))))),
% 1.44/1.48 inference(monotonicity,[status(thm)],[5156])).
% 1.44/1.48 tff(5158,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s32, c_c2)) | (~always25(s32)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s32)) | (~m_main_v_state2(s32, c_c2)))),
% 1.44/1.48 inference(transitivity,[status(thm)],[5157, 5155])).
% 1.44/1.48 tff(5159,plain,
% 1.44/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s32, c_c2)) | (~always25(s32)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5160,plain,
% 1.44/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s32)) | (~m_main_v_state2(s32, c_c2))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5159, 5158])).
% 1.44/1.48 tff(5161,plain,
% 1.44/1.48 (~always25(s32)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5160, 2024, 3017])).
% 1.44/1.48 tff(5162,plain,
% 1.44/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s31, s32)) | (~always25(s31)) | always25(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s31, s32)) | (~always25(s31)) | always25(s32))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5163,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s31, s32)) | (~always25(s31)) | always25(s32))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5164,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s31, s32)) | (~always25(s31)) | always25(s32)),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5163, 5162])).
% 1.44/1.48 tff(5165,plain,
% 1.44/1.48 ((~always25(s31)) | always25(s32)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5164, 2041, 3008])).
% 1.44/1.48 tff(5166,plain,
% 1.44/1.48 (~always25(s31)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5165, 5161])).
% 1.44/1.48 tff(5167,plain,
% 1.44/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s31) | (~node26(s31)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s31) | (~node26(s31)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5168,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s31) | (~node26(s31)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5169,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s31) | (~node26(s31))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5168, 5167])).
% 1.44/1.48 tff(5170,plain,
% 1.44/1.48 (~node26(s31)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5169, 2069, 5166])).
% 1.44/1.48 tff(5171,plain,
% 1.44/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s30, s31)) | (~always25(s30)) | always25(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s30, s31)) | (~always25(s30)) | always25(s31))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5172,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s30, s31)) | (~always25(s30)) | always25(s31))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5173,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s30, s31)) | (~always25(s30)) | always25(s31)),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5172, 5171])).
% 1.44/1.48 tff(5174,plain,
% 1.44/1.48 ((~always25(s30)) | always25(s31)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5173, 2041, 2930])).
% 1.44/1.48 tff(5175,plain,
% 1.44/1.48 (~always25(s30)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5174, 5166])).
% 1.44/1.48 tff(5176,plain,
% 1.44/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s30) | (~node26(s30)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s30) | (~node26(s30)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5177,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s30) | (~node26(s30)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5178,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s30) | (~node26(s30))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5177, 5176])).
% 1.44/1.48 tff(5179,plain,
% 1.44/1.48 (~node26(s30)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5178, 2069, 5175])).
% 1.44/1.48 tff(5180,plain,
% 1.44/1.48 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s29, c_t2) | (~node26(s29)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s29, c_t2) | (~node26(s29)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5181,plain,
% 1.44/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s29, c_t2) | (~node26(s29)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5182,plain,
% 1.44/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s29, c_t2) | (~node26(s29))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5181, 5180])).
% 1.44/1.48 tff(5183,plain,
% 1.44/1.48 (~node26(s29)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5182, 4976, 2820])).
% 1.44/1.48 tff(5184,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s28)) | (~m_main_v_state2(s28, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s28)) | (~m_main_v_state2(s28, c_c2)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5185,plain,
% 1.44/1.48 (((~m_main_v_state2(s28, c_c2)) | (~always25(s28))) <=> ((~always25(s28)) | (~m_main_v_state2(s28, c_c2)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5186,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s28, c_c2)) | (~always25(s28)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s28)) | (~m_main_v_state2(s28, c_c2))))),
% 1.44/1.48 inference(monotonicity,[status(thm)],[5185])).
% 1.44/1.48 tff(5187,plain,
% 1.44/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s28, c_c2)) | (~always25(s28)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s28)) | (~m_main_v_state2(s28, c_c2)))),
% 1.44/1.48 inference(transitivity,[status(thm)],[5186, 5184])).
% 1.44/1.48 tff(5188,plain,
% 1.44/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s28, c_c2)) | (~always25(s28)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5189,plain,
% 1.44/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s28)) | (~m_main_v_state2(s28, c_c2))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5188, 5187])).
% 1.44/1.48 tff(5190,plain,
% 1.44/1.48 (~always25(s28)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5189, 2024, 2749])).
% 1.44/1.48 tff(5191,plain,
% 1.44/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s27, s28)) | (~always25(s27)) | always25(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s27, s28)) | (~always25(s27)) | always25(s28))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5192,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s27, s28)) | (~always25(s27)) | always25(s28))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5193,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s27, s28)) | (~always25(s27)) | always25(s28)),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5192, 5191])).
% 1.44/1.48 tff(5194,plain,
% 1.44/1.48 ((~always25(s27)) | always25(s28)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5193, 2041, 2675])).
% 1.44/1.48 tff(5195,plain,
% 1.44/1.48 (~always25(s27)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5194, 5190])).
% 1.44/1.48 tff(5196,plain,
% 1.44/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s27) | (~node26(s27)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s27) | (~node26(s27)))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5197,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s27) | (~node26(s27)))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.48 tff(5198,plain,
% 1.44/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s27) | (~node26(s27))),
% 1.44/1.48 inference(modus_ponens,[status(thm)],[5197, 5196])).
% 1.44/1.48 tff(5199,plain,
% 1.44/1.48 (~node26(s27)),
% 1.44/1.48 inference(unit_resolution,[status(thm)],[5198, 2069, 5195])).
% 1.44/1.48 tff(5200,plain,
% 1.44/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s26, s27)) | (~always25(s26)) | always25(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s26, s27)) | (~always25(s26)) | always25(s27))),
% 1.44/1.48 inference(rewrite,[status(thm)],[])).
% 1.44/1.48 tff(5201,plain,
% 1.44/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s26, s27)) | (~always25(s26)) | always25(s27))),
% 1.44/1.48 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5202,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s26, s27)) | (~always25(s26)) | always25(s27)),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5201, 5200])).
% 1.44/1.49 tff(5203,plain,
% 1.44/1.49 ((~always25(s26)) | always25(s27)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5202, 2041, 2600])).
% 1.44/1.49 tff(5204,plain,
% 1.44/1.49 (~always25(s26)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5203, 5195])).
% 1.44/1.49 tff(5205,plain,
% 1.44/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s26) | (~node26(s26)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s26) | (~node26(s26)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5206,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s26) | (~node26(s26)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5207,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s26) | (~node26(s26))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5206, 5205])).
% 1.44/1.49 tff(5208,plain,
% 1.44/1.49 (~node26(s26)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5207, 2069, 5204])).
% 1.44/1.49 tff(5209,plain,
% 1.44/1.49 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s25, c_t2) | (~node26(s25)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s25, c_t2) | (~node26(s25)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5210,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s25, c_t2) | (~node26(s25)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5211,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s25, c_t2) | (~node26(s25))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5210, 5209])).
% 1.44/1.49 tff(5212,plain,
% 1.44/1.49 (~node26(s25)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5211, 4976, 2525])).
% 1.44/1.49 tff(5213,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s24)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s24)) | (~m_main_v_state2(s24, c_c2)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5214,plain,
% 1.44/1.49 (((~m_main_v_state2(s24, c_c2)) | (~always25(s24))) <=> ((~always25(s24)) | (~m_main_v_state2(s24, c_c2)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5215,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s24, c_c2)) | (~always25(s24)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s24)) | (~m_main_v_state2(s24, c_c2))))),
% 1.44/1.49 inference(monotonicity,[status(thm)],[5214])).
% 1.44/1.49 tff(5216,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s24, c_c2)) | (~always25(s24)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s24)) | (~m_main_v_state2(s24, c_c2)))),
% 1.44/1.49 inference(transitivity,[status(thm)],[5215, 5213])).
% 1.44/1.49 tff(5217,plain,
% 1.44/1.49 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s24, c_c2)) | (~always25(s24)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5218,plain,
% 1.44/1.49 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s24)) | (~m_main_v_state2(s24, c_c2))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5217, 5216])).
% 1.44/1.49 tff(5219,plain,
% 1.44/1.49 (~always25(s24)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5218, 2024, 2389])).
% 1.44/1.49 tff(5220,plain,
% 1.44/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s23, s24)) | (~always25(s23)) | always25(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s23, s24)) | (~always25(s23)) | always25(s24))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5221,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s23, s24)) | (~always25(s23)) | always25(s24))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5222,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s23, s24)) | (~always25(s23)) | always25(s24)),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5221, 5220])).
% 1.44/1.49 tff(5223,plain,
% 1.44/1.49 ((~always25(s23)) | always25(s24)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5222, 2041, 2380])).
% 1.44/1.49 tff(5224,plain,
% 1.44/1.49 (~always25(s23)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5223, 5219])).
% 1.44/1.49 tff(5225,plain,
% 1.44/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s23) | (~node26(s23)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s23) | (~node26(s23)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5226,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s23) | (~node26(s23)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5227,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s23) | (~node26(s23))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5226, 5225])).
% 1.44/1.49 tff(5228,plain,
% 1.44/1.49 (~node26(s23)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5227, 2069, 5224])).
% 1.44/1.49 tff(5229,plain,
% 1.44/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s22, s23)) | (~always25(s22)) | always25(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s22, s23)) | (~always25(s22)) | always25(s23))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5230,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s22, s23)) | (~always25(s22)) | always25(s23))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5231,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s22, s23)) | (~always25(s22)) | always25(s23)),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5230, 5229])).
% 1.44/1.49 tff(5232,plain,
% 1.44/1.49 ((~always25(s22)) | always25(s23)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5231, 2041, 2302])).
% 1.44/1.49 tff(5233,plain,
% 1.44/1.49 (~always25(s22)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5232, 5224])).
% 1.44/1.49 tff(5234,plain,
% 1.44/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s22) | (~node26(s22)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s22) | (~node26(s22)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5235,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s22) | (~node26(s22)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5236,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s22) | (~node26(s22))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5235, 5234])).
% 1.44/1.49 tff(5237,plain,
% 1.44/1.49 (~node26(s22)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5236, 2069, 5233])).
% 1.44/1.49 tff(5238,plain,
% 1.44/1.49 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s21, c_t2) | (~node26(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s21, c_t2) | (~node26(s21)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5239,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s21, c_t2) | (~node26(s21)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5240,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s21, c_t2) | (~node26(s21))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5239, 5238])).
% 1.44/1.49 tff(5241,plain,
% 1.44/1.49 (~node26(s21)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5240, 4976, 2192])).
% 1.44/1.49 tff(5242,plain,
% 1.44/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s19) | (~node26(s19)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s19) | (~node26(s19)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5243,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s19) | (~node26(s19)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5244,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s19) | (~node26(s19))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 1.44/1.49 tff(5245,plain,
% 1.44/1.49 (~node26(s19)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5244, 2069, 2046])).
% 1.44/1.49 tff(5246,plain,
% 1.44/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s18, s19)) | (~always25(s18)) | always25(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s18, s19)) | (~always25(s18)) | always25(s19))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5247,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s18, s19)) | (~always25(s18)) | always25(s19))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5248,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s18, s19)) | (~always25(s18)) | always25(s19)),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5247, 5246])).
% 1.44/1.49 tff(5249,plain,
% 1.44/1.49 ((~always25(s18)) | always25(s19)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5248, 2041, 1930])).
% 1.44/1.49 tff(5250,plain,
% 1.44/1.49 (~always25(s18)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5249, 2046])).
% 1.44/1.49 tff(5251,plain,
% 1.44/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s18) | (~node26(s18)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s18) | (~node26(s18)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5252,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s18) | (~node26(s18)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5253,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s18) | (~node26(s18))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5252, 5251])).
% 1.44/1.49 tff(5254,plain,
% 1.44/1.49 (~node26(s18)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5253, 2069, 5250])).
% 1.44/1.49 tff(5255,plain,
% 1.44/1.49 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s17, c_t2) | (~node26(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s17, c_t2) | (~node26(s17)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5256,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s17, c_t2) | (~node26(s17)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5257,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s17, c_t2) | (~node26(s17))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5256, 5255])).
% 1.44/1.49 tff(5258,plain,
% 1.44/1.49 (~node26(s17)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5257, 4976, 1820])).
% 1.44/1.49 tff(5259,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s16)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s16)) | (~m_main_v_state2(s16, c_c2)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5260,plain,
% 1.44/1.49 (((~m_main_v_state2(s16, c_c2)) | (~always25(s16))) <=> ((~always25(s16)) | (~m_main_v_state2(s16, c_c2)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5261,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s16, c_c2)) | (~always25(s16)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s16)) | (~m_main_v_state2(s16, c_c2))))),
% 1.44/1.49 inference(monotonicity,[status(thm)],[5260])).
% 1.44/1.49 tff(5262,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s16, c_c2)) | (~always25(s16)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s16)) | (~m_main_v_state2(s16, c_c2)))),
% 1.44/1.49 inference(transitivity,[status(thm)],[5261, 5259])).
% 1.44/1.49 tff(5263,plain,
% 1.44/1.49 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s16, c_c2)) | (~always25(s16)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5264,plain,
% 1.44/1.49 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s16)) | (~m_main_v_state2(s16, c_c2))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5263, 5262])).
% 1.44/1.49 tff(5265,plain,
% 1.44/1.49 (~always25(s16)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5264, 2024, 1749])).
% 1.44/1.49 tff(5266,plain,
% 1.44/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s15, s16)) | (~always25(s15)) | always25(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s15, s16)) | (~always25(s15)) | always25(s16))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5267,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s15, s16)) | (~always25(s15)) | always25(s16))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5268,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s15, s16)) | (~always25(s15)) | always25(s16)),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5267, 5266])).
% 1.44/1.49 tff(5269,plain,
% 1.44/1.49 ((~always25(s15)) | always25(s16)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5268, 2041, 1675])).
% 1.44/1.49 tff(5270,plain,
% 1.44/1.49 (~always25(s15)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5269, 5265])).
% 1.44/1.49 tff(5271,plain,
% 1.44/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s15) | (~node26(s15)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s15) | (~node26(s15)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5272,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s15) | (~node26(s15)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5273,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s15) | (~node26(s15))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5272, 5271])).
% 1.44/1.49 tff(5274,plain,
% 1.44/1.49 (~node26(s15)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5273, 2069, 5270])).
% 1.44/1.49 tff(5275,plain,
% 1.44/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s14, s15)) | (~always25(s14)) | always25(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s14, s15)) | (~always25(s14)) | always25(s15))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5276,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s14, s15)) | (~always25(s14)) | always25(s15))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5277,plain,
% 1.44/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s14, s15)) | (~always25(s14)) | always25(s15)),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5276, 5275])).
% 1.44/1.49 tff(5278,plain,
% 1.44/1.49 ((~always25(s14)) | always25(s15)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5277, 2041, 1600])).
% 1.44/1.49 tff(5279,plain,
% 1.44/1.49 (~always25(s14)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5278, 5270])).
% 1.44/1.49 tff(5280,plain,
% 1.44/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s14) | (~node26(s14)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s14) | (~node26(s14)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5281,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s14) | (~node26(s14)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5282,plain,
% 1.44/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s14) | (~node26(s14))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5281, 5280])).
% 1.44/1.49 tff(5283,plain,
% 1.44/1.49 (~node26(s14)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5282, 2069, 5279])).
% 1.44/1.49 tff(5284,plain,
% 1.44/1.49 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s13, c_t2) | (~node26(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s13, c_t2) | (~node26(s13)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5285,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s13, c_t2) | (~node26(s13)))),
% 1.44/1.49 inference(quant_inst,[status(thm)],[])).
% 1.44/1.49 tff(5286,plain,
% 1.44/1.49 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s13, c_t2) | (~node26(s13))),
% 1.44/1.49 inference(modus_ponens,[status(thm)],[5285, 5284])).
% 1.44/1.49 tff(5287,plain,
% 1.44/1.49 (~node26(s13)),
% 1.44/1.49 inference(unit_resolution,[status(thm)],[5286, 4976, 1525])).
% 1.44/1.49 tff(5288,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s12)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s12)) | (~m_main_v_state2(s12, c_c2)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5289,plain,
% 1.44/1.49 (((~m_main_v_state2(s12, c_c2)) | (~always25(s12))) <=> ((~always25(s12)) | (~m_main_v_state2(s12, c_c2)))),
% 1.44/1.49 inference(rewrite,[status(thm)],[])).
% 1.44/1.49 tff(5290,plain,
% 1.44/1.49 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s12, c_c2)) | (~always25(s12)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s12)) | (~m_main_v_state2(s12, c_c2))))),
% 1.44/1.49 inference(monotonicity,[status(thm)],[5289])).
% 1.44/1.50 tff(5291,plain,
% 1.44/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s12, c_c2)) | (~always25(s12)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s12)) | (~m_main_v_state2(s12, c_c2)))),
% 1.44/1.50 inference(transitivity,[status(thm)],[5290, 5288])).
% 1.44/1.50 tff(5292,plain,
% 1.44/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s12, c_c2)) | (~always25(s12)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5293,plain,
% 1.44/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s12)) | (~m_main_v_state2(s12, c_c2))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5292, 5291])).
% 1.44/1.50 tff(5294,plain,
% 1.44/1.50 (~always25(s12)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5293, 2024, 1389])).
% 1.44/1.50 tff(5295,plain,
% 1.44/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s11, s12)) | (~always25(s11)) | always25(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s11, s12)) | (~always25(s11)) | always25(s12))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5296,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s11, s12)) | (~always25(s11)) | always25(s12))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5297,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s11, s12)) | (~always25(s11)) | always25(s12)),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5296, 5295])).
% 1.44/1.50 tff(5298,plain,
% 1.44/1.50 ((~always25(s11)) | always25(s12)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5297, 2041, 1380])).
% 1.44/1.50 tff(5299,plain,
% 1.44/1.50 (~always25(s11)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5298, 5294])).
% 1.44/1.50 tff(5300,plain,
% 1.44/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s11) | (~node26(s11)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s11) | (~node26(s11)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5301,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s11) | (~node26(s11)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5302,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s11) | (~node26(s11))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5301, 5300])).
% 1.44/1.50 tff(5303,plain,
% 1.44/1.50 (~node26(s11)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5302, 2069, 5299])).
% 1.44/1.50 tff(5304,plain,
% 1.44/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s10, s11)) | (~always25(s10)) | always25(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s10, s11)) | (~always25(s10)) | always25(s11))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5305,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s10, s11)) | (~always25(s10)) | always25(s11))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5306,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s10, s11)) | (~always25(s10)) | always25(s11)),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5305, 5304])).
% 1.44/1.50 tff(5307,plain,
% 1.44/1.50 ((~always25(s10)) | always25(s11)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5306, 2041, 1302])).
% 1.44/1.50 tff(5308,plain,
% 1.44/1.50 (~always25(s10)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5307, 5299])).
% 1.44/1.50 tff(5309,plain,
% 1.44/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s10) | (~node26(s10)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s10) | (~node26(s10)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5310,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s10) | (~node26(s10)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5311,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s10) | (~node26(s10))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5310, 5309])).
% 1.44/1.50 tff(5312,plain,
% 1.44/1.50 (~node26(s10)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5311, 2069, 5308])).
% 1.44/1.50 tff(5313,plain,
% 1.44/1.50 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s9, c_t2) | (~node26(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s9, c_t2) | (~node26(s9)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5314,plain,
% 1.44/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s9, c_t2) | (~node26(s9)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5315,plain,
% 1.44/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s9, c_t2) | (~node26(s9))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5314, 5313])).
% 1.44/1.50 tff(5316,plain,
% 1.44/1.50 (~node26(s9)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5315, 4976, 1192])).
% 1.44/1.50 tff(5317,plain,
% 1.44/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s8)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s8)) | (~m_main_v_state2(s8, c_c2)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5318,plain,
% 1.44/1.50 (((~m_main_v_state2(s8, c_c2)) | (~always25(s8))) <=> ((~always25(s8)) | (~m_main_v_state2(s8, c_c2)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5319,plain,
% 1.44/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s8, c_c2)) | (~always25(s8)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s8)) | (~m_main_v_state2(s8, c_c2))))),
% 1.44/1.50 inference(monotonicity,[status(thm)],[5318])).
% 1.44/1.50 tff(5320,plain,
% 1.44/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s8, c_c2)) | (~always25(s8)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s8)) | (~m_main_v_state2(s8, c_c2)))),
% 1.44/1.50 inference(transitivity,[status(thm)],[5319, 5317])).
% 1.44/1.50 tff(5321,plain,
% 1.44/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s8, c_c2)) | (~always25(s8)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5322,plain,
% 1.44/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s8)) | (~m_main_v_state2(s8, c_c2))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5321, 5320])).
% 1.44/1.50 tff(5323,plain,
% 1.44/1.50 (~always25(s8)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5322, 2024, 1121])).
% 1.44/1.50 tff(5324,plain,
% 1.44/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s7, s8)) | (~always25(s7)) | always25(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s7, s8)) | (~always25(s7)) | always25(s8))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5325,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s7, s8)) | (~always25(s7)) | always25(s8))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5326,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s7, s8)) | (~always25(s7)) | always25(s8)),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5325, 5324])).
% 1.44/1.50 tff(5327,plain,
% 1.44/1.50 ((~always25(s7)) | always25(s8)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5326, 2041, 1047])).
% 1.44/1.50 tff(5328,plain,
% 1.44/1.50 (~always25(s7)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5327, 5323])).
% 1.44/1.50 tff(5329,plain,
% 1.44/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s7) | (~node26(s7)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s7) | (~node26(s7)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5330,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s7) | (~node26(s7)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5331,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s7) | (~node26(s7))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5330, 5329])).
% 1.44/1.50 tff(5332,plain,
% 1.44/1.50 (~node26(s7)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5331, 2069, 5328])).
% 1.44/1.50 tff(5333,plain,
% 1.44/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s6, s7)) | (~always25(s6)) | always25(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s6, s7)) | (~always25(s6)) | always25(s7))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5334,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s6, s7)) | (~always25(s6)) | always25(s7))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5335,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s6, s7)) | (~always25(s6)) | always25(s7)),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5334, 5333])).
% 1.44/1.50 tff(5336,plain,
% 1.44/1.50 ((~always25(s6)) | always25(s7)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5335, 2041, 962])).
% 1.44/1.50 tff(5337,plain,
% 1.44/1.50 (~always25(s6)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5336, 5328])).
% 1.44/1.50 tff(5338,plain,
% 1.44/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s6) | (~node26(s6)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s6) | (~node26(s6)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5339,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s6) | (~node26(s6)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5340,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s6) | (~node26(s6))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5339, 5338])).
% 1.44/1.50 tff(5341,plain,
% 1.44/1.50 (~node26(s6)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5340, 2069, 5337])).
% 1.44/1.50 tff(5342,plain,
% 1.44/1.50 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s5, c_t2) | (~node26(s5)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s5, c_t2) | (~node26(s5)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5343,plain,
% 1.44/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s5, c_t2) | (~node26(s5)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5344,plain,
% 1.44/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s5, c_t2) | (~node26(s5))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5343, 5342])).
% 1.44/1.50 tff(5345,plain,
% 1.44/1.50 (~node26(s5)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5344, 4976, 867])).
% 1.44/1.50 tff(5346,plain,
% 1.44/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s4)) | (~m_main_v_state2(s4, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s4)) | (~m_main_v_state2(s4, c_c2)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5347,plain,
% 1.44/1.50 (((~m_main_v_state2(s4, c_c2)) | (~always25(s4))) <=> ((~always25(s4)) | (~m_main_v_state2(s4, c_c2)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5348,plain,
% 1.44/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s4, c_c2)) | (~always25(s4)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s4)) | (~m_main_v_state2(s4, c_c2))))),
% 1.44/1.50 inference(monotonicity,[status(thm)],[5347])).
% 1.44/1.50 tff(5349,plain,
% 1.44/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s4, c_c2)) | (~always25(s4)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s4)) | (~m_main_v_state2(s4, c_c2)))),
% 1.44/1.50 inference(transitivity,[status(thm)],[5348, 5346])).
% 1.44/1.50 tff(5350,plain,
% 1.44/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s4, c_c2)) | (~always25(s4)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5351,plain,
% 1.44/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s4)) | (~m_main_v_state2(s4, c_c2))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 1.44/1.50 tff(5352,plain,
% 1.44/1.50 (~always25(s4)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5351, 2024, 622])).
% 1.44/1.50 tff(5353,plain,
% 1.44/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s3, s4)) | (~always25(s3)) | always25(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s3, s4)) | (~always25(s3)) | always25(s4))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5354,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s3, s4)) | (~always25(s3)) | always25(s4))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5355,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s3, s4)) | (~always25(s3)) | always25(s4)),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5354, 5353])).
% 1.44/1.50 tff(5356,plain,
% 1.44/1.50 ((~always25(s3)) | always25(s4)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5355, 2041, 603])).
% 1.44/1.50 tff(5357,plain,
% 1.44/1.50 (~always25(s3)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5356, 5352])).
% 1.44/1.50 tff(5358,plain,
% 1.44/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s2, s3)) | (~always25(s2)) | always25(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s2, s3)) | (~always25(s2)) | always25(s3))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5359,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s2, s3)) | (~always25(s2)) | always25(s3))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5360,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s2, s3)) | (~always25(s2)) | always25(s3)),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 1.44/1.50 tff(5361,plain,
% 1.44/1.50 ((~always25(s2)) | always25(s3)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5360, 2041, 484])).
% 1.44/1.50 tff(5362,plain,
% 1.44/1.50 (~always25(s2)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5361, 5357])).
% 1.44/1.50 tff(5363,plain,
% 1.44/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s2) | (~node26(s2)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s2) | (~node26(s2)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5364,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s2) | (~node26(s2)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5365,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s2) | (~node26(s2))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5364, 5363])).
% 1.44/1.50 tff(5366,plain,
% 1.44/1.50 (~node26(s2)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5365, 2069, 5362])).
% 1.44/1.50 tff(5367,plain,
% 1.44/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s1, s2)) | (~always25(s1)) | always25(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s1, s2)) | (~always25(s1)) | always25(s2))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5368,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s1, s2)) | (~always25(s1)) | always25(s2))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5369,plain,
% 1.44/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s1, s2)) | (~always25(s1)) | always25(s2)),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 1.44/1.50 tff(5370,plain,
% 1.44/1.50 ((~always25(s1)) | always25(s2)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5369, 2041, 282])).
% 1.44/1.50 tff(5371,plain,
% 1.44/1.50 (~always25(s1)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5370, 5362])).
% 1.44/1.50 tff(5372,plain,
% 1.44/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s1) | (~node26(s1)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s1) | (~node26(s1)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5373,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s1) | (~node26(s1)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5374,plain,
% 1.44/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s1) | (~node26(s1))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5373, 5372])).
% 1.44/1.50 tff(5375,plain,
% 1.44/1.50 (~node26(s1)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5374, 2069, 5371])).
% 1.44/1.50 tff(5376,plain,
% 1.44/1.50 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s0, c_t2) | (~node26(s0)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s0, c_t2) | (~node26(s0)))),
% 1.44/1.50 inference(rewrite,[status(thm)],[])).
% 1.44/1.50 tff(5377,plain,
% 1.44/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s0, c_t2) | (~node26(s0)))),
% 1.44/1.50 inference(quant_inst,[status(thm)],[])).
% 1.44/1.50 tff(5378,plain,
% 1.44/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s0, c_t2) | (~node26(s0))),
% 1.44/1.50 inference(modus_ponens,[status(thm)],[5377, 5376])).
% 1.44/1.50 tff(5379,plain,
% 1.44/1.50 (~node26(s0)),
% 1.44/1.50 inference(unit_resolution,[status(thm)],[5378, 4976, 96])).
% 1.44/1.50 tff(5380,plain,
% 1.44/1.51 (until27(s0) <=> until27(s0)),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5381,axiom,(until27(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty26')).
% 1.44/1.51 tff(5382,plain,
% 1.44/1.51 (until27(s0)),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5381, 5380])).
% 1.44/1.51 tff(5383,plain,
% 1.44/1.51 (^[X: $i] : refl((node26(X) | (~until27(X)) | xuntil28(X)) <=> (node26(X) | (~until27(X)) | xuntil28(X)))),
% 1.44/1.51 inference(bind,[status(th)],[])).
% 1.44/1.51 tff(5384,plain,
% 1.44/1.51 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X)) <=> ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.44/1.51 inference(quant_intro,[status(thm)],[5383])).
% 1.44/1.51 tff(5385,plain,
% 1.44/1.51 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X)) <=> ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5386,plain,
% 1.44/1.51 (^[X: $i] : rewrite(((node26(X) | xuntil28(X)) | (~until27(X))) <=> (node26(X) | (~until27(X)) | xuntil28(X)))),
% 1.44/1.51 inference(bind,[status(th)],[])).
% 1.44/1.51 tff(5387,plain,
% 1.44/1.51 (![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X))) <=> ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.44/1.51 inference(quant_intro,[status(thm)],[5386])).
% 1.44/1.51 tff(5388,axiom,(![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty19')).
% 1.44/1.51 tff(5389,plain,
% 1.44/1.51 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5388, 5387])).
% 1.44/1.51 tff(5390,plain,
% 1.44/1.51 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5389, 5385])).
% 1.44/1.51 tff(5391,plain,(
% 1.44/1.51 ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.44/1.51 inference(skolemize,[status(sab)],[5390])).
% 1.44/1.51 tff(5392,plain,
% 1.44/1.51 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5391, 5384])).
% 1.44/1.51 tff(5393,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s0) | node26(s0) | (~until27(s0)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s0) | node26(s0) | (~until27(s0)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5394,plain,
% 1.44/1.51 ((node26(s0) | (~until27(s0)) | xuntil28(s0)) <=> (xuntil28(s0) | node26(s0) | (~until27(s0)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5395,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s0) | (~until27(s0)) | xuntil28(s0))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s0) | node26(s0) | (~until27(s0))))),
% 1.44/1.51 inference(monotonicity,[status(thm)],[5394])).
% 1.44/1.51 tff(5396,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s0) | (~until27(s0)) | xuntil28(s0))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s0) | node26(s0) | (~until27(s0)))),
% 1.44/1.51 inference(transitivity,[status(thm)],[5395, 5393])).
% 1.44/1.51 tff(5397,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s0) | (~until27(s0)) | xuntil28(s0))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5398,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s0) | node26(s0) | (~until27(s0))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5397, 5396])).
% 1.44/1.51 tff(5399,plain,
% 1.44/1.51 (xuntil28(s0) | node26(s0)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5398, 5392, 5382])).
% 1.44/1.51 tff(5400,plain,
% 1.44/1.51 (xuntil28(s0)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5399, 5379])).
% 1.44/1.51 tff(5401,plain,
% 1.44/1.51 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 1.44/1.51 inference(bind,[status(th)],[])).
% 1.44/1.51 tff(5402,plain,
% 1.44/1.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.44/1.51 inference(quant_intro,[status(thm)],[5401])).
% 1.44/1.51 tff(5403,plain,
% 1.44/1.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5404,plain,
% 1.44/1.51 (^[Y: $i, X: $i] : rewrite(((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 1.44/1.51 inference(bind,[status(th)],[])).
% 1.44/1.51 tff(5405,plain,
% 1.44/1.51 (![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.44/1.51 inference(quant_intro,[status(thm)],[5404])).
% 1.44/1.51 tff(5406,axiom,(![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty20')).
% 1.44/1.51 tff(5407,plain,
% 1.44/1.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5406, 5405])).
% 1.44/1.51 tff(5408,plain,
% 1.44/1.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5407, 5403])).
% 1.44/1.51 tff(5409,plain,(
% 1.44/1.51 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.44/1.51 inference(skolemize,[status(sab)],[5408])).
% 1.44/1.51 tff(5410,plain,
% 1.44/1.51 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5409, 5402])).
% 1.44/1.51 tff(5411,plain,
% 1.44/1.51 (((~![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))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5412,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5413,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1)),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5412, 5411])).
% 1.44/1.51 tff(5414,plain,
% 1.44/1.51 ((~xuntil28(s0)) | until27(s1)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5413, 35, 5410])).
% 1.44/1.51 tff(5415,plain,
% 1.44/1.51 (until27(s1)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5414, 5400])).
% 1.44/1.51 tff(5416,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5417,plain,
% 1.44/1.51 ((node26(s1) | (~until27(s1)) | xuntil28(s1)) <=> (xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5418,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s1) | (~until27(s1)) | xuntil28(s1))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1))))),
% 1.44/1.51 inference(monotonicity,[status(thm)],[5417])).
% 1.44/1.51 tff(5419,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s1) | (~until27(s1)) | xuntil28(s1))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 1.44/1.51 inference(transitivity,[status(thm)],[5418, 5416])).
% 1.44/1.51 tff(5420,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s1) | (~until27(s1)) | xuntil28(s1))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5421,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5420, 5419])).
% 1.44/1.51 tff(5422,plain,
% 1.44/1.51 (xuntil28(s1) | node26(s1)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5421, 5392, 5415])).
% 1.44/1.51 tff(5423,plain,
% 1.44/1.51 (xuntil28(s1)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5422, 5375])).
% 1.44/1.51 tff(5424,plain,
% 1.44/1.51 (((~![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))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5425,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5426,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2)),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5425, 5424])).
% 1.44/1.51 tff(5427,plain,
% 1.44/1.51 ((~xuntil28(s1)) | until27(s2)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5426, 278, 5410])).
% 1.44/1.51 tff(5428,plain,
% 1.44/1.51 (until27(s2)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5427, 5423])).
% 1.44/1.51 tff(5429,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5430,plain,
% 1.44/1.51 ((node26(s2) | (~until27(s2)) | xuntil28(s2)) <=> (xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5431,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s2) | (~until27(s2)) | xuntil28(s2))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2))))),
% 1.44/1.51 inference(monotonicity,[status(thm)],[5430])).
% 1.44/1.51 tff(5432,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s2) | (~until27(s2)) | xuntil28(s2))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 1.44/1.51 inference(transitivity,[status(thm)],[5431, 5429])).
% 1.44/1.51 tff(5433,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s2) | (~until27(s2)) | xuntil28(s2))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5434,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5433, 5432])).
% 1.44/1.51 tff(5435,plain,
% 1.44/1.51 (xuntil28(s2)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5434, 5392, 5428, 5366])).
% 1.44/1.51 tff(5436,plain,
% 1.44/1.51 (((~![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))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5437,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5438,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3)),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5437, 5436])).
% 1.44/1.51 tff(5439,plain,
% 1.44/1.51 ((~xuntil28(s2)) | until27(s3)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5438, 480, 5410])).
% 1.44/1.51 tff(5440,plain,
% 1.44/1.51 (until27(s3)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5439, 5435])).
% 1.44/1.51 tff(5441,plain,
% 1.44/1.51 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s3) | (~node26(s3)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s3) | (~node26(s3)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5442,plain,
% 1.44/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s3) | (~node26(s3)))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5443,plain,
% 1.44/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s3) | (~node26(s3))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5442, 5441])).
% 1.44/1.51 tff(5444,plain,
% 1.44/1.51 (~node26(s3)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5443, 2069, 5357])).
% 1.44/1.51 tff(5445,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5446,plain,
% 1.44/1.51 ((node26(s3) | (~until27(s3)) | xuntil28(s3)) <=> (xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5447,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s3) | (~until27(s3)) | xuntil28(s3))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3))))),
% 1.44/1.51 inference(monotonicity,[status(thm)],[5446])).
% 1.44/1.51 tff(5448,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s3) | (~until27(s3)) | xuntil28(s3))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.44/1.51 inference(transitivity,[status(thm)],[5447, 5445])).
% 1.44/1.51 tff(5449,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s3) | (~until27(s3)) | xuntil28(s3))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5450,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5449, 5448])).
% 1.44/1.51 tff(5451,plain,
% 1.44/1.51 (xuntil28(s3) | (~until27(s3))),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5450, 5392, 5444])).
% 1.44/1.51 tff(5452,plain,
% 1.44/1.51 (xuntil28(s3)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5451, 5440])).
% 1.44/1.51 tff(5453,plain,
% 1.44/1.51 (((~![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))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5454,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5455,plain,
% 1.44/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4)),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5454, 5453])).
% 1.44/1.51 tff(5456,plain,
% 1.44/1.51 ((~xuntil28(s3)) | until27(s4)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5455, 599, 5410])).
% 1.44/1.51 tff(5457,plain,
% 1.44/1.51 (until27(s4)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5456, 5452])).
% 1.44/1.51 tff(5458,plain,
% 1.44/1.51 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s4) | (~node26(s4)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s4) | (~node26(s4)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5459,plain,
% 1.44/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s4) | (~node26(s4)))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5460,plain,
% 1.44/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s4) | (~node26(s4))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5459, 5458])).
% 1.44/1.51 tff(5461,plain,
% 1.44/1.51 (~node26(s4)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5460, 2069, 5352])).
% 1.44/1.51 tff(5462,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5463,plain,
% 1.44/1.51 ((node26(s4) | (~until27(s4)) | xuntil28(s4)) <=> (xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.44/1.51 inference(rewrite,[status(thm)],[])).
% 1.44/1.51 tff(5464,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s4) | (~until27(s4)) | xuntil28(s4))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4))))),
% 1.44/1.51 inference(monotonicity,[status(thm)],[5463])).
% 1.44/1.51 tff(5465,plain,
% 1.44/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s4) | (~until27(s4)) | xuntil28(s4))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.44/1.51 inference(transitivity,[status(thm)],[5464, 5462])).
% 1.44/1.51 tff(5466,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s4) | (~until27(s4)) | xuntil28(s4))),
% 1.44/1.51 inference(quant_inst,[status(thm)],[])).
% 1.44/1.51 tff(5467,plain,
% 1.44/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4))),
% 1.44/1.51 inference(modus_ponens,[status(thm)],[5466, 5465])).
% 1.44/1.51 tff(5468,plain,
% 1.44/1.51 (xuntil28(s4) | (~until27(s4))),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5467, 5392, 5461])).
% 1.44/1.51 tff(5469,plain,
% 1.44/1.51 (xuntil28(s4)),
% 1.44/1.51 inference(unit_resolution,[status(thm)],[5468, 5457])).
% 1.44/1.51 tff(5470,plain,
% 1.44/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5471,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5472,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5)),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5471, 5470])).
% 1.44/1.52 tff(5473,plain,
% 1.44/1.52 ((~xuntil28(s4)) | until27(s5)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5472, 708, 5410])).
% 1.44/1.52 tff(5474,plain,
% 1.44/1.52 (until27(s5)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5473, 5469])).
% 1.44/1.52 tff(5475,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s5) | node26(s5) | (~until27(s5)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s5) | node26(s5) | (~until27(s5)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5476,plain,
% 1.44/1.52 ((node26(s5) | (~until27(s5)) | xuntil28(s5)) <=> (xuntil28(s5) | node26(s5) | (~until27(s5)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5477,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s5) | (~until27(s5)) | xuntil28(s5))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s5) | node26(s5) | (~until27(s5))))),
% 1.44/1.52 inference(monotonicity,[status(thm)],[5476])).
% 1.44/1.52 tff(5478,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s5) | (~until27(s5)) | xuntil28(s5))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s5) | node26(s5) | (~until27(s5)))),
% 1.44/1.52 inference(transitivity,[status(thm)],[5477, 5475])).
% 1.44/1.52 tff(5479,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s5) | (~until27(s5)) | xuntil28(s5))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5480,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s5) | node26(s5) | (~until27(s5))),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5479, 5478])).
% 1.44/1.52 tff(5481,plain,
% 1.44/1.52 (xuntil28(s5)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5480, 5392, 5474, 5345])).
% 1.44/1.52 tff(5482,plain,
% 1.44/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5483,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5484,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6)),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5483, 5482])).
% 1.44/1.52 tff(5485,plain,
% 1.44/1.52 ((~xuntil28(s5)) | until27(s6)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5484, 874, 5410])).
% 1.44/1.52 tff(5486,plain,
% 1.44/1.52 (until27(s6)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5485, 5481])).
% 1.44/1.52 tff(5487,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5488,plain,
% 1.44/1.52 ((node26(s6) | (~until27(s6)) | xuntil28(s6)) <=> (xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5489,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s6) | (~until27(s6)) | xuntil28(s6))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6))))),
% 1.44/1.52 inference(monotonicity,[status(thm)],[5488])).
% 1.44/1.52 tff(5490,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s6) | (~until27(s6)) | xuntil28(s6))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 1.44/1.52 inference(transitivity,[status(thm)],[5489, 5487])).
% 1.44/1.52 tff(5491,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s6) | (~until27(s6)) | xuntil28(s6))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5492,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6))),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5491, 5490])).
% 1.44/1.52 tff(5493,plain,
% 1.44/1.52 (xuntil28(s6) | node26(s6)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5492, 5392, 5486])).
% 1.44/1.52 tff(5494,plain,
% 1.44/1.52 (xuntil28(s6)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5493, 5341])).
% 1.44/1.52 tff(5495,plain,
% 1.44/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5496,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5497,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7)),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5496, 5495])).
% 1.44/1.52 tff(5498,plain,
% 1.44/1.52 ((~xuntil28(s6)) | until27(s7)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5497, 958, 5410])).
% 1.44/1.52 tff(5499,plain,
% 1.44/1.52 (until27(s7)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5498, 5494])).
% 1.44/1.52 tff(5500,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5501,plain,
% 1.44/1.52 ((node26(s7) | (~until27(s7)) | xuntil28(s7)) <=> (xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5502,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s7) | (~until27(s7)) | xuntil28(s7))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7))))),
% 1.44/1.52 inference(monotonicity,[status(thm)],[5501])).
% 1.44/1.52 tff(5503,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s7) | (~until27(s7)) | xuntil28(s7))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 1.44/1.52 inference(transitivity,[status(thm)],[5502, 5500])).
% 1.44/1.52 tff(5504,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s7) | (~until27(s7)) | xuntil28(s7))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5505,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7))),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5504, 5503])).
% 1.44/1.52 tff(5506,plain,
% 1.44/1.52 (xuntil28(s7)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5505, 5392, 5499, 5332])).
% 1.44/1.52 tff(5507,plain,
% 1.44/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5508,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5509,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8)),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5508, 5507])).
% 1.44/1.52 tff(5510,plain,
% 1.44/1.52 ((~xuntil28(s7)) | until27(s8)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5509, 1043, 5410])).
% 1.44/1.52 tff(5511,plain,
% 1.44/1.52 (until27(s8)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5510, 5506])).
% 1.44/1.52 tff(5512,plain,
% 1.44/1.52 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s8) | (~node26(s8)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s8) | (~node26(s8)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5513,plain,
% 1.44/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s8) | (~node26(s8)))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5514,plain,
% 1.44/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s8) | (~node26(s8))),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5513, 5512])).
% 1.44/1.52 tff(5515,plain,
% 1.44/1.52 (~node26(s8)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5514, 2069, 5323])).
% 1.44/1.52 tff(5516,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5517,plain,
% 1.44/1.52 ((node26(s8) | (~until27(s8)) | xuntil28(s8)) <=> (xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5518,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s8) | (~until27(s8)) | xuntil28(s8))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8))))),
% 1.44/1.52 inference(monotonicity,[status(thm)],[5517])).
% 1.44/1.52 tff(5519,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s8) | (~until27(s8)) | xuntil28(s8))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 1.44/1.52 inference(transitivity,[status(thm)],[5518, 5516])).
% 1.44/1.52 tff(5520,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s8) | (~until27(s8)) | xuntil28(s8))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5521,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8))),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5520, 5519])).
% 1.44/1.52 tff(5522,plain,
% 1.44/1.52 (xuntil28(s8) | (~until27(s8))),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5521, 5392, 5515])).
% 1.44/1.52 tff(5523,plain,
% 1.44/1.52 (xuntil28(s8)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5522, 5511])).
% 1.44/1.52 tff(5524,plain,
% 1.44/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5525,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5526,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9)),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5525, 5524])).
% 1.44/1.52 tff(5527,plain,
% 1.44/1.52 ((~xuntil28(s8)) | until27(s9)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5526, 1132, 5410])).
% 1.44/1.52 tff(5528,plain,
% 1.44/1.52 (until27(s9)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5527, 5523])).
% 1.44/1.52 tff(5529,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5530,plain,
% 1.44/1.52 ((node26(s9) | (~until27(s9)) | xuntil28(s9)) <=> (xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5531,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s9) | (~until27(s9)) | xuntil28(s9))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9))))),
% 1.44/1.52 inference(monotonicity,[status(thm)],[5530])).
% 1.44/1.52 tff(5532,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s9) | (~until27(s9)) | xuntil28(s9))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 1.44/1.52 inference(transitivity,[status(thm)],[5531, 5529])).
% 1.44/1.52 tff(5533,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s9) | (~until27(s9)) | xuntil28(s9))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5534,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9))),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5533, 5532])).
% 1.44/1.52 tff(5535,plain,
% 1.44/1.52 (xuntil28(s9)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5534, 5392, 5528, 5316])).
% 1.44/1.52 tff(5536,plain,
% 1.44/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5537,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5538,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10)),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5537, 5536])).
% 1.44/1.52 tff(5539,plain,
% 1.44/1.52 ((~xuntil28(s9)) | until27(s10)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5538, 1199, 5410])).
% 1.44/1.52 tff(5540,plain,
% 1.44/1.52 (until27(s10)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5539, 5535])).
% 1.44/1.52 tff(5541,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s10) | node26(s10) | (~until27(s10)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s10) | node26(s10) | (~until27(s10)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5542,plain,
% 1.44/1.52 ((node26(s10) | (~until27(s10)) | xuntil28(s10)) <=> (xuntil28(s10) | node26(s10) | (~until27(s10)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5543,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s10) | (~until27(s10)) | xuntil28(s10))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s10) | node26(s10) | (~until27(s10))))),
% 1.44/1.52 inference(monotonicity,[status(thm)],[5542])).
% 1.44/1.52 tff(5544,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s10) | (~until27(s10)) | xuntil28(s10))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s10) | node26(s10) | (~until27(s10)))),
% 1.44/1.52 inference(transitivity,[status(thm)],[5543, 5541])).
% 1.44/1.52 tff(5545,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s10) | (~until27(s10)) | xuntil28(s10))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5546,plain,
% 1.44/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s10) | node26(s10) | (~until27(s10))),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 1.44/1.52 tff(5547,plain,
% 1.44/1.52 (xuntil28(s10) | node26(s10)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5546, 5392, 5540])).
% 1.44/1.52 tff(5548,plain,
% 1.44/1.52 (xuntil28(s10)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5547, 5312])).
% 1.44/1.52 tff(5549,plain,
% 1.44/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5550,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))),
% 1.44/1.52 inference(quant_inst,[status(thm)],[])).
% 1.44/1.52 tff(5551,plain,
% 1.44/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11)),
% 1.44/1.52 inference(modus_ponens,[status(thm)],[5550, 5549])).
% 1.44/1.52 tff(5552,plain,
% 1.44/1.52 ((~xuntil28(s10)) | until27(s11)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5551, 1298, 5410])).
% 1.44/1.52 tff(5553,plain,
% 1.44/1.52 (until27(s11)),
% 1.44/1.52 inference(unit_resolution,[status(thm)],[5552, 5548])).
% 1.44/1.52 tff(5554,plain,
% 1.44/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s11) | node26(s11) | (~until27(s11)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s11) | node26(s11) | (~until27(s11)))),
% 1.44/1.52 inference(rewrite,[status(thm)],[])).
% 1.44/1.52 tff(5555,plain,
% 1.44/1.52 ((node26(s11) | (~until27(s11)) | xuntil28(s11)) <=> (xuntil28(s11) | node26(s11) | (~until27(s11)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5556,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s11) | (~until27(s11)) | xuntil28(s11))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s11) | node26(s11) | (~until27(s11))))),
% 1.51/1.53 inference(monotonicity,[status(thm)],[5555])).
% 1.51/1.53 tff(5557,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s11) | (~until27(s11)) | xuntil28(s11))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s11) | node26(s11) | (~until27(s11)))),
% 1.51/1.53 inference(transitivity,[status(thm)],[5556, 5554])).
% 1.51/1.53 tff(5558,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s11) | (~until27(s11)) | xuntil28(s11))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5559,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s11) | node26(s11) | (~until27(s11))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 1.51/1.53 tff(5560,plain,
% 1.51/1.53 (xuntil28(s11)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5559, 5392, 5553, 5303])).
% 1.51/1.53 tff(5561,plain,
% 1.51/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5562,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5563,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12)),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 1.51/1.53 tff(5564,plain,
% 1.51/1.53 ((~xuntil28(s11)) | until27(s12)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5563, 1376, 5410])).
% 1.51/1.53 tff(5565,plain,
% 1.51/1.53 (until27(s12)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5564, 5560])).
% 1.51/1.53 tff(5566,plain,
% 1.51/1.53 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s12) | (~node26(s12)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s12) | (~node26(s12)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5567,plain,
% 1.51/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s12) | (~node26(s12)))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5568,plain,
% 1.51/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s12) | (~node26(s12))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5567, 5566])).
% 1.51/1.53 tff(5569,plain,
% 1.51/1.53 (~node26(s12)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5568, 2069, 5294])).
% 1.51/1.53 tff(5570,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s12) | node26(s12) | (~until27(s12)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s12) | node26(s12) | (~until27(s12)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5571,plain,
% 1.51/1.53 ((node26(s12) | (~until27(s12)) | xuntil28(s12)) <=> (xuntil28(s12) | node26(s12) | (~until27(s12)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5572,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s12) | (~until27(s12)) | xuntil28(s12))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s12) | node26(s12) | (~until27(s12))))),
% 1.51/1.53 inference(monotonicity,[status(thm)],[5571])).
% 1.51/1.53 tff(5573,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s12) | (~until27(s12)) | xuntil28(s12))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s12) | node26(s12) | (~until27(s12)))),
% 1.51/1.53 inference(transitivity,[status(thm)],[5572, 5570])).
% 1.51/1.53 tff(5574,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s12) | (~until27(s12)) | xuntil28(s12))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5575,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s12) | node26(s12) | (~until27(s12))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5574, 5573])).
% 1.51/1.53 tff(5576,plain,
% 1.51/1.53 (xuntil28(s12) | (~until27(s12))),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5575, 5392, 5569])).
% 1.51/1.53 tff(5577,plain,
% 1.51/1.53 (xuntil28(s12)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5576, 5565])).
% 1.51/1.53 tff(5578,plain,
% 1.51/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5579,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5580,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13)),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5579, 5578])).
% 1.51/1.53 tff(5581,plain,
% 1.51/1.53 ((~xuntil28(s12)) | until27(s13)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5580, 1437, 5410])).
% 1.51/1.53 tff(5582,plain,
% 1.51/1.53 (until27(s13)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5581, 5577])).
% 1.51/1.53 tff(5583,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s13) | node26(s13) | (~until27(s13)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5584,plain,
% 1.51/1.53 ((node26(s13) | (~until27(s13)) | xuntil28(s13)) <=> (xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5585,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s13) | (~until27(s13)) | xuntil28(s13))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s13) | node26(s13) | (~until27(s13))))),
% 1.51/1.53 inference(monotonicity,[status(thm)],[5584])).
% 1.51/1.53 tff(5586,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s13) | (~until27(s13)) | xuntil28(s13))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 1.51/1.53 inference(transitivity,[status(thm)],[5585, 5583])).
% 1.51/1.53 tff(5587,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s13) | (~until27(s13)) | xuntil28(s13))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5588,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5587, 5586])).
% 1.51/1.53 tff(5589,plain,
% 1.51/1.53 (xuntil28(s13)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5588, 5392, 5582, 5287])).
% 1.51/1.53 tff(5590,plain,
% 1.51/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5591,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5592,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14)),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5591, 5590])).
% 1.51/1.53 tff(5593,plain,
% 1.51/1.53 ((~xuntil28(s13)) | until27(s14)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5592, 1532, 5410])).
% 1.51/1.53 tff(5594,plain,
% 1.51/1.53 (until27(s14)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5593, 5589])).
% 1.51/1.53 tff(5595,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s14) | node26(s14) | (~until27(s14)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5596,plain,
% 1.51/1.53 ((node26(s14) | (~until27(s14)) | xuntil28(s14)) <=> (xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5597,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s14) | (~until27(s14)) | xuntil28(s14))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s14) | node26(s14) | (~until27(s14))))),
% 1.51/1.53 inference(monotonicity,[status(thm)],[5596])).
% 1.51/1.53 tff(5598,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s14) | (~until27(s14)) | xuntil28(s14))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 1.51/1.53 inference(transitivity,[status(thm)],[5597, 5595])).
% 1.51/1.53 tff(5599,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s14) | (~until27(s14)) | xuntil28(s14))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5600,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5599, 5598])).
% 1.51/1.53 tff(5601,plain,
% 1.51/1.53 (xuntil28(s14) | node26(s14)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5600, 5392, 5594])).
% 1.51/1.53 tff(5602,plain,
% 1.51/1.53 (xuntil28(s14)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5601, 5283])).
% 1.51/1.53 tff(5603,plain,
% 1.51/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5604,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5605,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15)),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5604, 5603])).
% 1.51/1.53 tff(5606,plain,
% 1.51/1.53 ((~xuntil28(s14)) | until27(s15)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5605, 1596, 5410])).
% 1.51/1.53 tff(5607,plain,
% 1.51/1.53 (until27(s15)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5606, 5602])).
% 1.51/1.53 tff(5608,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s15) | node26(s15) | (~until27(s15)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s15) | node26(s15) | (~until27(s15)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5609,plain,
% 1.51/1.53 ((node26(s15) | (~until27(s15)) | xuntil28(s15)) <=> (xuntil28(s15) | node26(s15) | (~until27(s15)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5610,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s15) | (~until27(s15)) | xuntil28(s15))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s15) | node26(s15) | (~until27(s15))))),
% 1.51/1.53 inference(monotonicity,[status(thm)],[5609])).
% 1.51/1.53 tff(5611,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s15) | (~until27(s15)) | xuntil28(s15))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s15) | node26(s15) | (~until27(s15)))),
% 1.51/1.53 inference(transitivity,[status(thm)],[5610, 5608])).
% 1.51/1.53 tff(5612,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s15) | (~until27(s15)) | xuntil28(s15))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5613,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s15) | node26(s15) | (~until27(s15))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5612, 5611])).
% 1.51/1.53 tff(5614,plain,
% 1.51/1.53 (xuntil28(s15)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5613, 5392, 5607, 5274])).
% 1.51/1.53 tff(5615,plain,
% 1.51/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5616,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5617,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16)),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5616, 5615])).
% 1.51/1.53 tff(5618,plain,
% 1.51/1.53 ((~xuntil28(s15)) | until27(s16)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5617, 1671, 5410])).
% 1.51/1.53 tff(5619,plain,
% 1.51/1.53 (until27(s16)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5618, 5614])).
% 1.51/1.53 tff(5620,plain,
% 1.51/1.53 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s16) | (~node26(s16)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s16) | (~node26(s16)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5621,plain,
% 1.51/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s16) | (~node26(s16)))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5622,plain,
% 1.51/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s16) | (~node26(s16))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 1.51/1.53 tff(5623,plain,
% 1.51/1.53 (~node26(s16)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5622, 2069, 5265])).
% 1.51/1.53 tff(5624,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s16) | node26(s16) | (~until27(s16)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5625,plain,
% 1.51/1.53 ((node26(s16) | (~until27(s16)) | xuntil28(s16)) <=> (xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5626,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s16) | (~until27(s16)) | xuntil28(s16))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s16) | node26(s16) | (~until27(s16))))),
% 1.51/1.53 inference(monotonicity,[status(thm)],[5625])).
% 1.51/1.53 tff(5627,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s16) | (~until27(s16)) | xuntil28(s16))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 1.51/1.53 inference(transitivity,[status(thm)],[5626, 5624])).
% 1.51/1.53 tff(5628,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s16) | (~until27(s16)) | xuntil28(s16))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5629,plain,
% 1.51/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16))),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5628, 5627])).
% 1.51/1.53 tff(5630,plain,
% 1.51/1.53 (xuntil28(s16) | (~until27(s16))),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5629, 5392, 5623])).
% 1.51/1.53 tff(5631,plain,
% 1.51/1.53 (xuntil28(s16)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5630, 5619])).
% 1.51/1.53 tff(5632,plain,
% 1.51/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5633,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))),
% 1.51/1.53 inference(quant_inst,[status(thm)],[])).
% 1.51/1.53 tff(5634,plain,
% 1.51/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17)),
% 1.51/1.53 inference(modus_ponens,[status(thm)],[5633, 5632])).
% 1.51/1.53 tff(5635,plain,
% 1.51/1.53 ((~xuntil28(s16)) | until27(s17)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5634, 1760, 5410])).
% 1.51/1.53 tff(5636,plain,
% 1.51/1.53 (until27(s17)),
% 1.51/1.53 inference(unit_resolution,[status(thm)],[5635, 5631])).
% 1.51/1.53 tff(5637,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s17) | node26(s17) | (~until27(s17)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s17) | node26(s17) | (~until27(s17)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5638,plain,
% 1.51/1.53 ((node26(s17) | (~until27(s17)) | xuntil28(s17)) <=> (xuntil28(s17) | node26(s17) | (~until27(s17)))),
% 1.51/1.53 inference(rewrite,[status(thm)],[])).
% 1.51/1.53 tff(5639,plain,
% 1.51/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s17) | (~until27(s17)) | xuntil28(s17))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s17) | node26(s17) | (~until27(s17))))),
% 1.51/1.54 inference(monotonicity,[status(thm)],[5638])).
% 1.51/1.54 tff(5640,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s17) | (~until27(s17)) | xuntil28(s17))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s17) | node26(s17) | (~until27(s17)))),
% 1.51/1.54 inference(transitivity,[status(thm)],[5639, 5637])).
% 1.51/1.54 tff(5641,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s17) | (~until27(s17)) | xuntil28(s17))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5642,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s17) | node26(s17) | (~until27(s17))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5641, 5640])).
% 1.51/1.54 tff(5643,plain,
% 1.51/1.54 (xuntil28(s17)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5642, 5392, 5636, 5258])).
% 1.51/1.54 tff(5644,plain,
% 1.51/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5645,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5646,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18)),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5645, 5644])).
% 1.51/1.54 tff(5647,plain,
% 1.51/1.54 ((~xuntil28(s17)) | until27(s18)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5646, 1827, 5410])).
% 1.51/1.54 tff(5648,plain,
% 1.51/1.54 (until27(s18)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5647, 5643])).
% 1.51/1.54 tff(5649,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s18) | node26(s18) | (~until27(s18)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5650,plain,
% 1.51/1.54 ((node26(s18) | (~until27(s18)) | xuntil28(s18)) <=> (xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5651,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s18) | (~until27(s18)) | xuntil28(s18))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s18) | node26(s18) | (~until27(s18))))),
% 1.51/1.54 inference(monotonicity,[status(thm)],[5650])).
% 1.51/1.54 tff(5652,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s18) | (~until27(s18)) | xuntil28(s18))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 1.51/1.54 inference(transitivity,[status(thm)],[5651, 5649])).
% 1.51/1.54 tff(5653,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s18) | (~until27(s18)) | xuntil28(s18))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5654,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 1.51/1.54 tff(5655,plain,
% 1.51/1.54 (xuntil28(s18) | node26(s18)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5654, 5392, 5648])).
% 1.51/1.54 tff(5656,plain,
% 1.51/1.54 (xuntil28(s18)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5655, 5254])).
% 1.51/1.54 tff(5657,plain,
% 1.51/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5658,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5659,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19)),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5658, 5657])).
% 1.51/1.54 tff(5660,plain,
% 1.51/1.54 ((~xuntil28(s18)) | until27(s19)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5659, 1926, 5410])).
% 1.51/1.54 tff(5661,plain,
% 1.51/1.54 (until27(s19)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5660, 5656])).
% 1.51/1.54 tff(5662,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s19) | node26(s19) | (~until27(s19)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5663,plain,
% 1.51/1.54 ((node26(s19) | (~until27(s19)) | xuntil28(s19)) <=> (xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5664,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s19) | (~until27(s19)) | xuntil28(s19))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s19) | node26(s19) | (~until27(s19))))),
% 1.51/1.54 inference(monotonicity,[status(thm)],[5663])).
% 1.51/1.54 tff(5665,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s19) | (~until27(s19)) | xuntil28(s19))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 1.51/1.54 inference(transitivity,[status(thm)],[5664, 5662])).
% 1.51/1.54 tff(5666,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s19) | (~until27(s19)) | xuntil28(s19))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5667,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5666, 5665])).
% 1.51/1.54 tff(5668,plain,
% 1.51/1.54 (xuntil28(s19)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5667, 5392, 5661, 5245])).
% 1.51/1.54 tff(5669,plain,
% 1.51/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5670,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5671,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20)),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5670, 5669])).
% 1.51/1.54 tff(5672,plain,
% 1.51/1.54 ((~xuntil28(s19)) | until27(s20)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5671, 2004, 5410])).
% 1.51/1.54 tff(5673,plain,
% 1.51/1.54 (until27(s20)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5672, 5668])).
% 1.51/1.54 tff(5674,plain,
% 1.51/1.54 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s20) | (~node26(s20)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s20) | (~node26(s20)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5675,plain,
% 1.51/1.54 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s20) | (~node26(s20)))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5676,plain,
% 1.51/1.54 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s20) | (~node26(s20))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5675, 5674])).
% 1.51/1.54 tff(5677,plain,
% 1.51/1.54 (~node26(s20)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5676, 2069, 2031])).
% 1.51/1.54 tff(5678,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s20) | node26(s20) | (~until27(s20)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s20) | node26(s20) | (~until27(s20)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5679,plain,
% 1.51/1.54 ((node26(s20) | (~until27(s20)) | xuntil28(s20)) <=> (xuntil28(s20) | node26(s20) | (~until27(s20)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5680,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s20) | (~until27(s20)) | xuntil28(s20))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s20) | node26(s20) | (~until27(s20))))),
% 1.51/1.54 inference(monotonicity,[status(thm)],[5679])).
% 1.51/1.54 tff(5681,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s20) | (~until27(s20)) | xuntil28(s20))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s20) | node26(s20) | (~until27(s20)))),
% 1.51/1.54 inference(transitivity,[status(thm)],[5680, 5678])).
% 1.51/1.54 tff(5682,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s20) | (~until27(s20)) | xuntil28(s20))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5683,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s20) | node26(s20) | (~until27(s20))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5682, 5681])).
% 1.51/1.54 tff(5684,plain,
% 1.51/1.54 (xuntil28(s20) | (~until27(s20))),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5683, 5392, 5677])).
% 1.51/1.54 tff(5685,plain,
% 1.51/1.54 (xuntil28(s20)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5684, 5673])).
% 1.51/1.54 tff(5686,plain,
% 1.51/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5687,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5688,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21)),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5687, 5686])).
% 1.51/1.54 tff(5689,plain,
% 1.51/1.54 ((~xuntil28(s20)) | until27(s21)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5688, 2132, 5410])).
% 1.51/1.54 tff(5690,plain,
% 1.51/1.54 (until27(s21)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5689, 5685])).
% 1.51/1.54 tff(5691,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s21) | node26(s21) | (~until27(s21)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s21) | node26(s21) | (~until27(s21)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5692,plain,
% 1.51/1.54 ((node26(s21) | (~until27(s21)) | xuntil28(s21)) <=> (xuntil28(s21) | node26(s21) | (~until27(s21)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5693,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s21) | (~until27(s21)) | xuntil28(s21))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s21) | node26(s21) | (~until27(s21))))),
% 1.51/1.54 inference(monotonicity,[status(thm)],[5692])).
% 1.51/1.54 tff(5694,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s21) | (~until27(s21)) | xuntil28(s21))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s21) | node26(s21) | (~until27(s21)))),
% 1.51/1.54 inference(transitivity,[status(thm)],[5693, 5691])).
% 1.51/1.54 tff(5695,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s21) | (~until27(s21)) | xuntil28(s21))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5696,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s21) | node26(s21) | (~until27(s21))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5695, 5694])).
% 1.51/1.54 tff(5697,plain,
% 1.51/1.54 (xuntil28(s21)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5696, 5392, 5690, 5241])).
% 1.51/1.54 tff(5698,plain,
% 1.51/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5699,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5700,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22)),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5699, 5698])).
% 1.51/1.54 tff(5701,plain,
% 1.51/1.54 ((~xuntil28(s21)) | until27(s22)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5700, 2199, 5410])).
% 1.51/1.54 tff(5702,plain,
% 1.51/1.54 (until27(s22)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5701, 5697])).
% 1.51/1.54 tff(5703,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s22) | node26(s22) | (~until27(s22)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s22) | node26(s22) | (~until27(s22)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5704,plain,
% 1.51/1.54 ((node26(s22) | (~until27(s22)) | xuntil28(s22)) <=> (xuntil28(s22) | node26(s22) | (~until27(s22)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5705,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s22) | (~until27(s22)) | xuntil28(s22))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s22) | node26(s22) | (~until27(s22))))),
% 1.51/1.54 inference(monotonicity,[status(thm)],[5704])).
% 1.51/1.54 tff(5706,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s22) | (~until27(s22)) | xuntil28(s22))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s22) | node26(s22) | (~until27(s22)))),
% 1.51/1.54 inference(transitivity,[status(thm)],[5705, 5703])).
% 1.51/1.54 tff(5707,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s22) | (~until27(s22)) | xuntil28(s22))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5708,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s22) | node26(s22) | (~until27(s22))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5707, 5706])).
% 1.51/1.54 tff(5709,plain,
% 1.51/1.54 (xuntil28(s22) | node26(s22)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5708, 5392, 5702])).
% 1.51/1.54 tff(5710,plain,
% 1.51/1.54 (xuntil28(s22)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5709, 5237])).
% 1.51/1.54 tff(5711,plain,
% 1.51/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5712,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5713,plain,
% 1.51/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23)),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5712, 5711])).
% 1.51/1.54 tff(5714,plain,
% 1.51/1.54 ((~xuntil28(s22)) | until27(s23)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5713, 2298, 5410])).
% 1.51/1.54 tff(5715,plain,
% 1.51/1.54 (until27(s23)),
% 1.51/1.54 inference(unit_resolution,[status(thm)],[5714, 5710])).
% 1.51/1.54 tff(5716,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s23) | node26(s23) | (~until27(s23)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s23) | node26(s23) | (~until27(s23)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5717,plain,
% 1.51/1.54 ((node26(s23) | (~until27(s23)) | xuntil28(s23)) <=> (xuntil28(s23) | node26(s23) | (~until27(s23)))),
% 1.51/1.54 inference(rewrite,[status(thm)],[])).
% 1.51/1.54 tff(5718,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s23) | (~until27(s23)) | xuntil28(s23))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s23) | node26(s23) | (~until27(s23))))),
% 1.51/1.54 inference(monotonicity,[status(thm)],[5717])).
% 1.51/1.54 tff(5719,plain,
% 1.51/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s23) | (~until27(s23)) | xuntil28(s23))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s23) | node26(s23) | (~until27(s23)))),
% 1.51/1.54 inference(transitivity,[status(thm)],[5718, 5716])).
% 1.51/1.54 tff(5720,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s23) | (~until27(s23)) | xuntil28(s23))),
% 1.51/1.54 inference(quant_inst,[status(thm)],[])).
% 1.51/1.54 tff(5721,plain,
% 1.51/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s23) | node26(s23) | (~until27(s23))),
% 1.51/1.54 inference(modus_ponens,[status(thm)],[5720, 5719])).
% 1.51/1.54 tff(5722,plain,
% 1.51/1.55 (xuntil28(s23)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5721, 5392, 5715, 5228])).
% 1.51/1.55 tff(5723,plain,
% 1.51/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5724,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5725,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24)),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5724, 5723])).
% 1.51/1.55 tff(5726,plain,
% 1.51/1.55 ((~xuntil28(s23)) | until27(s24)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5725, 2376, 5410])).
% 1.51/1.55 tff(5727,plain,
% 1.51/1.55 (until27(s24)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5726, 5722])).
% 1.51/1.55 tff(5728,plain,
% 1.51/1.55 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s24) | (~node26(s24)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s24) | (~node26(s24)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5729,plain,
% 1.51/1.55 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s24) | (~node26(s24)))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5730,plain,
% 1.51/1.55 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s24) | (~node26(s24))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.51/1.55 tff(5731,plain,
% 1.51/1.55 (~node26(s24)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5730, 2069, 5219])).
% 1.51/1.55 tff(5732,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s24) | node26(s24) | (~until27(s24)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s24) | node26(s24) | (~until27(s24)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5733,plain,
% 1.51/1.55 ((node26(s24) | (~until27(s24)) | xuntil28(s24)) <=> (xuntil28(s24) | node26(s24) | (~until27(s24)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5734,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s24) | (~until27(s24)) | xuntil28(s24))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s24) | node26(s24) | (~until27(s24))))),
% 1.51/1.55 inference(monotonicity,[status(thm)],[5733])).
% 1.51/1.55 tff(5735,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s24) | (~until27(s24)) | xuntil28(s24))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s24) | node26(s24) | (~until27(s24)))),
% 1.51/1.55 inference(transitivity,[status(thm)],[5734, 5732])).
% 1.51/1.55 tff(5736,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s24) | (~until27(s24)) | xuntil28(s24))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5737,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s24) | node26(s24) | (~until27(s24))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5736, 5735])).
% 1.51/1.55 tff(5738,plain,
% 1.51/1.55 (xuntil28(s24) | (~until27(s24))),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5737, 5392, 5731])).
% 1.51/1.55 tff(5739,plain,
% 1.51/1.55 (xuntil28(s24)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5738, 5727])).
% 1.51/1.55 tff(5740,plain,
% 1.51/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5741,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5742,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25)),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5741, 5740])).
% 1.51/1.55 tff(5743,plain,
% 1.51/1.55 ((~xuntil28(s24)) | until27(s25)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5742, 2437, 5410])).
% 1.51/1.55 tff(5744,plain,
% 1.51/1.55 (until27(s25)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5743, 5739])).
% 1.51/1.55 tff(5745,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s25) | node26(s25) | (~until27(s25)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s25) | node26(s25) | (~until27(s25)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5746,plain,
% 1.51/1.55 ((node26(s25) | (~until27(s25)) | xuntil28(s25)) <=> (xuntil28(s25) | node26(s25) | (~until27(s25)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5747,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s25) | (~until27(s25)) | xuntil28(s25))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s25) | node26(s25) | (~until27(s25))))),
% 1.51/1.55 inference(monotonicity,[status(thm)],[5746])).
% 1.51/1.55 tff(5748,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s25) | (~until27(s25)) | xuntil28(s25))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s25) | node26(s25) | (~until27(s25)))),
% 1.51/1.55 inference(transitivity,[status(thm)],[5747, 5745])).
% 1.51/1.55 tff(5749,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s25) | (~until27(s25)) | xuntil28(s25))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5750,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s25) | node26(s25) | (~until27(s25))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5749, 5748])).
% 1.51/1.55 tff(5751,plain,
% 1.51/1.55 (xuntil28(s25)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5750, 5392, 5744, 5212])).
% 1.51/1.55 tff(5752,plain,
% 1.51/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s25, s26)) | (~xuntil28(s25)) | until27(s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s25, s26)) | (~xuntil28(s25)) | until27(s26))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5753,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s25, s26)) | (~xuntil28(s25)) | until27(s26))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5754,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s25, s26)) | (~xuntil28(s25)) | until27(s26)),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5753, 5752])).
% 1.51/1.55 tff(5755,plain,
% 1.51/1.55 ((~xuntil28(s25)) | until27(s26)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5754, 2532, 5410])).
% 1.51/1.55 tff(5756,plain,
% 1.51/1.55 (until27(s26)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5755, 5751])).
% 1.51/1.55 tff(5757,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s26) | node26(s26) | (~until27(s26)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s26) | node26(s26) | (~until27(s26)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5758,plain,
% 1.51/1.55 ((node26(s26) | (~until27(s26)) | xuntil28(s26)) <=> (xuntil28(s26) | node26(s26) | (~until27(s26)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5759,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s26) | (~until27(s26)) | xuntil28(s26))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s26) | node26(s26) | (~until27(s26))))),
% 1.51/1.55 inference(monotonicity,[status(thm)],[5758])).
% 1.51/1.55 tff(5760,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s26) | (~until27(s26)) | xuntil28(s26))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s26) | node26(s26) | (~until27(s26)))),
% 1.51/1.55 inference(transitivity,[status(thm)],[5759, 5757])).
% 1.51/1.55 tff(5761,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s26) | (~until27(s26)) | xuntil28(s26))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5762,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s26) | node26(s26) | (~until27(s26))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5761, 5760])).
% 1.51/1.55 tff(5763,plain,
% 1.51/1.55 (xuntil28(s26) | node26(s26)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5762, 5392, 5756])).
% 1.51/1.55 tff(5764,plain,
% 1.51/1.55 (xuntil28(s26)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5763, 5208])).
% 1.51/1.55 tff(5765,plain,
% 1.51/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s26, s27)) | (~xuntil28(s26)) | until27(s27))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s26, s27)) | (~xuntil28(s26)) | until27(s27))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5766,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s26, s27)) | (~xuntil28(s26)) | until27(s27))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5767,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s26, s27)) | (~xuntil28(s26)) | until27(s27)),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5766, 5765])).
% 1.51/1.55 tff(5768,plain,
% 1.51/1.55 ((~xuntil28(s26)) | until27(s27)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5767, 2596, 5410])).
% 1.51/1.55 tff(5769,plain,
% 1.51/1.55 (until27(s27)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5768, 5764])).
% 1.51/1.55 tff(5770,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s27) | node26(s27) | (~until27(s27)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s27) | node26(s27) | (~until27(s27)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5771,plain,
% 1.51/1.55 ((node26(s27) | (~until27(s27)) | xuntil28(s27)) <=> (xuntil28(s27) | node26(s27) | (~until27(s27)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5772,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s27) | (~until27(s27)) | xuntil28(s27))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s27) | node26(s27) | (~until27(s27))))),
% 1.51/1.55 inference(monotonicity,[status(thm)],[5771])).
% 1.51/1.55 tff(5773,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s27) | (~until27(s27)) | xuntil28(s27))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s27) | node26(s27) | (~until27(s27)))),
% 1.51/1.55 inference(transitivity,[status(thm)],[5772, 5770])).
% 1.51/1.55 tff(5774,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s27) | (~until27(s27)) | xuntil28(s27))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5775,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s27) | node26(s27) | (~until27(s27))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5774, 5773])).
% 1.51/1.55 tff(5776,plain,
% 1.51/1.55 (xuntil28(s27)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5775, 5392, 5769, 5199])).
% 1.51/1.55 tff(5777,plain,
% 1.51/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s27, s28)) | (~xuntil28(s27)) | until27(s28))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s27, s28)) | (~xuntil28(s27)) | until27(s28))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5778,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s27, s28)) | (~xuntil28(s27)) | until27(s28))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5779,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s27, s28)) | (~xuntil28(s27)) | until27(s28)),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5778, 5777])).
% 1.51/1.55 tff(5780,plain,
% 1.51/1.55 ((~xuntil28(s27)) | until27(s28)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5779, 2671, 5410])).
% 1.51/1.55 tff(5781,plain,
% 1.51/1.55 (until27(s28)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5780, 5776])).
% 1.51/1.55 tff(5782,plain,
% 1.51/1.55 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s28) | (~node26(s28)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s28) | (~node26(s28)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5783,plain,
% 1.51/1.55 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s28) | (~node26(s28)))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5784,plain,
% 1.51/1.55 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s28) | (~node26(s28))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5783, 5782])).
% 1.51/1.55 tff(5785,plain,
% 1.51/1.55 (~node26(s28)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5784, 2069, 5190])).
% 1.51/1.55 tff(5786,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s28) | node26(s28) | (~until27(s28)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s28) | node26(s28) | (~until27(s28)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5787,plain,
% 1.51/1.55 ((node26(s28) | (~until27(s28)) | xuntil28(s28)) <=> (xuntil28(s28) | node26(s28) | (~until27(s28)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5788,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s28) | (~until27(s28)) | xuntil28(s28))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s28) | node26(s28) | (~until27(s28))))),
% 1.51/1.55 inference(monotonicity,[status(thm)],[5787])).
% 1.51/1.55 tff(5789,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s28) | (~until27(s28)) | xuntil28(s28))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s28) | node26(s28) | (~until27(s28)))),
% 1.51/1.55 inference(transitivity,[status(thm)],[5788, 5786])).
% 1.51/1.55 tff(5790,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s28) | (~until27(s28)) | xuntil28(s28))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5791,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s28) | node26(s28) | (~until27(s28))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5790, 5789])).
% 1.51/1.55 tff(5792,plain,
% 1.51/1.55 (xuntil28(s28) | (~until27(s28))),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5791, 5392, 5785])).
% 1.51/1.55 tff(5793,plain,
% 1.51/1.55 (xuntil28(s28)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5792, 5781])).
% 1.51/1.55 tff(5794,plain,
% 1.51/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5795,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5796,plain,
% 1.51/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29)),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5795, 5794])).
% 1.51/1.55 tff(5797,plain,
% 1.51/1.55 ((~xuntil28(s28)) | until27(s29)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5796, 2760, 5410])).
% 1.51/1.55 tff(5798,plain,
% 1.51/1.55 (until27(s29)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5797, 5793])).
% 1.51/1.55 tff(5799,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s29) | node26(s29) | (~until27(s29)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s29) | node26(s29) | (~until27(s29)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5800,plain,
% 1.51/1.55 ((node26(s29) | (~until27(s29)) | xuntil28(s29)) <=> (xuntil28(s29) | node26(s29) | (~until27(s29)))),
% 1.51/1.55 inference(rewrite,[status(thm)],[])).
% 1.51/1.55 tff(5801,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s29) | (~until27(s29)) | xuntil28(s29))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s29) | node26(s29) | (~until27(s29))))),
% 1.51/1.55 inference(monotonicity,[status(thm)],[5800])).
% 1.51/1.55 tff(5802,plain,
% 1.51/1.55 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s29) | (~until27(s29)) | xuntil28(s29))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s29) | node26(s29) | (~until27(s29)))),
% 1.51/1.55 inference(transitivity,[status(thm)],[5801, 5799])).
% 1.51/1.55 tff(5803,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s29) | (~until27(s29)) | xuntil28(s29))),
% 1.51/1.55 inference(quant_inst,[status(thm)],[])).
% 1.51/1.55 tff(5804,plain,
% 1.51/1.55 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s29) | node26(s29) | (~until27(s29))),
% 1.51/1.55 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 1.51/1.55 tff(5805,plain,
% 1.51/1.55 (xuntil28(s29)),
% 1.51/1.55 inference(unit_resolution,[status(thm)],[5804, 5392, 5798, 5183])).
% 1.51/1.55 tff(5806,plain,
% 1.51/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5807,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5808,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30)),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5807, 5806])).
% 1.51/1.56 tff(5809,plain,
% 1.51/1.56 ((~xuntil28(s29)) | until27(s30)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5808, 2827, 5410])).
% 1.51/1.56 tff(5810,plain,
% 1.51/1.56 (until27(s30)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5809, 5805])).
% 1.51/1.56 tff(5811,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s30) | node26(s30) | (~until27(s30)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s30) | node26(s30) | (~until27(s30)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5812,plain,
% 1.51/1.56 ((node26(s30) | (~until27(s30)) | xuntil28(s30)) <=> (xuntil28(s30) | node26(s30) | (~until27(s30)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5813,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s30) | (~until27(s30)) | xuntil28(s30))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s30) | node26(s30) | (~until27(s30))))),
% 1.51/1.56 inference(monotonicity,[status(thm)],[5812])).
% 1.51/1.56 tff(5814,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s30) | (~until27(s30)) | xuntil28(s30))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s30) | node26(s30) | (~until27(s30)))),
% 1.51/1.56 inference(transitivity,[status(thm)],[5813, 5811])).
% 1.51/1.56 tff(5815,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s30) | (~until27(s30)) | xuntil28(s30))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5816,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s30) | node26(s30) | (~until27(s30))),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5815, 5814])).
% 1.51/1.56 tff(5817,plain,
% 1.51/1.56 (xuntil28(s30) | node26(s30)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5816, 5392, 5810])).
% 1.51/1.56 tff(5818,plain,
% 1.51/1.56 (xuntil28(s30)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5817, 5179])).
% 1.51/1.56 tff(5819,plain,
% 1.51/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5820,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5821,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31)),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5820, 5819])).
% 1.51/1.56 tff(5822,plain,
% 1.51/1.56 ((~xuntil28(s30)) | until27(s31)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5821, 2926, 5410])).
% 1.51/1.56 tff(5823,plain,
% 1.51/1.56 (until27(s31)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5822, 5818])).
% 1.51/1.56 tff(5824,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s31) | node26(s31) | (~until27(s31)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s31) | node26(s31) | (~until27(s31)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5825,plain,
% 1.51/1.56 ((node26(s31) | (~until27(s31)) | xuntil28(s31)) <=> (xuntil28(s31) | node26(s31) | (~until27(s31)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5826,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s31) | (~until27(s31)) | xuntil28(s31))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s31) | node26(s31) | (~until27(s31))))),
% 1.51/1.56 inference(monotonicity,[status(thm)],[5825])).
% 1.51/1.56 tff(5827,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s31) | (~until27(s31)) | xuntil28(s31))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s31) | node26(s31) | (~until27(s31)))),
% 1.51/1.56 inference(transitivity,[status(thm)],[5826, 5824])).
% 1.51/1.56 tff(5828,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s31) | (~until27(s31)) | xuntil28(s31))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5829,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s31) | node26(s31) | (~until27(s31))),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5828, 5827])).
% 1.51/1.56 tff(5830,plain,
% 1.51/1.56 (xuntil28(s31)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5829, 5392, 5823, 5170])).
% 1.51/1.56 tff(5831,plain,
% 1.51/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5832,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5833,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32)),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5832, 5831])).
% 1.51/1.56 tff(5834,plain,
% 1.51/1.56 ((~xuntil28(s31)) | until27(s32)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5833, 3004, 5410])).
% 1.51/1.56 tff(5835,plain,
% 1.51/1.56 (until27(s32)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5834, 5830])).
% 1.51/1.56 tff(5836,plain,
% 1.51/1.56 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s32) | (~node26(s32)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s32) | (~node26(s32)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5837,plain,
% 1.51/1.56 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s32) | (~node26(s32)))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5838,plain,
% 1.51/1.56 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s32) | (~node26(s32))),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5837, 5836])).
% 1.51/1.56 tff(5839,plain,
% 1.51/1.56 (~node26(s32)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5838, 2069, 5161])).
% 1.51/1.56 tff(5840,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s32) | node26(s32) | (~until27(s32)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s32) | node26(s32) | (~until27(s32)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5841,plain,
% 1.51/1.56 ((node26(s32) | (~until27(s32)) | xuntil28(s32)) <=> (xuntil28(s32) | node26(s32) | (~until27(s32)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5842,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s32) | (~until27(s32)) | xuntil28(s32))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s32) | node26(s32) | (~until27(s32))))),
% 1.51/1.56 inference(monotonicity,[status(thm)],[5841])).
% 1.51/1.56 tff(5843,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s32) | (~until27(s32)) | xuntil28(s32))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s32) | node26(s32) | (~until27(s32)))),
% 1.51/1.56 inference(transitivity,[status(thm)],[5842, 5840])).
% 1.51/1.56 tff(5844,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s32) | (~until27(s32)) | xuntil28(s32))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5845,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s32) | node26(s32) | (~until27(s32))),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 1.51/1.56 tff(5846,plain,
% 1.51/1.56 (xuntil28(s32) | (~until27(s32))),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5845, 5392, 5839])).
% 1.51/1.56 tff(5847,plain,
% 1.51/1.56 (xuntil28(s32)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5846, 5835])).
% 1.51/1.56 tff(5848,plain,
% 1.51/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5849,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5850,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33)),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5849, 5848])).
% 1.51/1.56 tff(5851,plain,
% 1.51/1.56 ((~xuntil28(s32)) | until27(s33)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5850, 3065, 5410])).
% 1.51/1.56 tff(5852,plain,
% 1.51/1.56 (until27(s33)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5851, 5847])).
% 1.51/1.56 tff(5853,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s33) | node26(s33) | (~until27(s33)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s33) | node26(s33) | (~until27(s33)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5854,plain,
% 1.51/1.56 ((node26(s33) | (~until27(s33)) | xuntil28(s33)) <=> (xuntil28(s33) | node26(s33) | (~until27(s33)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5855,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s33) | (~until27(s33)) | xuntil28(s33))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s33) | node26(s33) | (~until27(s33))))),
% 1.51/1.56 inference(monotonicity,[status(thm)],[5854])).
% 1.51/1.56 tff(5856,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s33) | (~until27(s33)) | xuntil28(s33))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s33) | node26(s33) | (~until27(s33)))),
% 1.51/1.56 inference(transitivity,[status(thm)],[5855, 5853])).
% 1.51/1.56 tff(5857,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s33) | (~until27(s33)) | xuntil28(s33))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5858,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s33) | node26(s33) | (~until27(s33))),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5857, 5856])).
% 1.51/1.56 tff(5859,plain,
% 1.51/1.56 (xuntil28(s33)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5858, 5392, 5852, 5154])).
% 1.51/1.56 tff(5860,plain,
% 1.51/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5861,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5862,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34)),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5861, 5860])).
% 1.51/1.56 tff(5863,plain,
% 1.51/1.56 ((~xuntil28(s33)) | until27(s34)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5862, 3160, 5410])).
% 1.51/1.56 tff(5864,plain,
% 1.51/1.56 (until27(s34)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5863, 5859])).
% 1.51/1.56 tff(5865,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s34) | node26(s34) | (~until27(s34)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s34) | node26(s34) | (~until27(s34)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5866,plain,
% 1.51/1.56 ((node26(s34) | (~until27(s34)) | xuntil28(s34)) <=> (xuntil28(s34) | node26(s34) | (~until27(s34)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5867,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s34) | (~until27(s34)) | xuntil28(s34))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s34) | node26(s34) | (~until27(s34))))),
% 1.51/1.56 inference(monotonicity,[status(thm)],[5866])).
% 1.51/1.56 tff(5868,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s34) | (~until27(s34)) | xuntil28(s34))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s34) | node26(s34) | (~until27(s34)))),
% 1.51/1.56 inference(transitivity,[status(thm)],[5867, 5865])).
% 1.51/1.56 tff(5869,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s34) | (~until27(s34)) | xuntil28(s34))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5870,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s34) | node26(s34) | (~until27(s34))),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5869, 5868])).
% 1.51/1.56 tff(5871,plain,
% 1.51/1.56 (xuntil28(s34) | node26(s34)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5870, 5392, 5864])).
% 1.51/1.56 tff(5872,plain,
% 1.51/1.56 (xuntil28(s34)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5871, 5150])).
% 1.51/1.56 tff(5873,plain,
% 1.51/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5874,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5875,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35)),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5874, 5873])).
% 1.51/1.56 tff(5876,plain,
% 1.51/1.56 ((~xuntil28(s34)) | until27(s35)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5875, 3224, 5410])).
% 1.51/1.56 tff(5877,plain,
% 1.51/1.56 (until27(s35)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5876, 5872])).
% 1.51/1.56 tff(5878,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s35) | node26(s35) | (~until27(s35)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s35) | node26(s35) | (~until27(s35)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5879,plain,
% 1.51/1.56 ((node26(s35) | (~until27(s35)) | xuntil28(s35)) <=> (xuntil28(s35) | node26(s35) | (~until27(s35)))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5880,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s35) | (~until27(s35)) | xuntil28(s35))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s35) | node26(s35) | (~until27(s35))))),
% 1.51/1.56 inference(monotonicity,[status(thm)],[5879])).
% 1.51/1.56 tff(5881,plain,
% 1.51/1.56 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s35) | (~until27(s35)) | xuntil28(s35))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s35) | node26(s35) | (~until27(s35)))),
% 1.51/1.56 inference(transitivity,[status(thm)],[5880, 5878])).
% 1.51/1.56 tff(5882,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s35) | (~until27(s35)) | xuntil28(s35))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5883,plain,
% 1.51/1.56 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s35) | node26(s35) | (~until27(s35))),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5882, 5881])).
% 1.51/1.56 tff(5884,plain,
% 1.51/1.56 (xuntil28(s35)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5883, 5392, 5877, 5141])).
% 1.51/1.56 tff(5885,plain,
% 1.51/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36))),
% 1.51/1.56 inference(rewrite,[status(thm)],[])).
% 1.51/1.56 tff(5886,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36))),
% 1.51/1.56 inference(quant_inst,[status(thm)],[])).
% 1.51/1.56 tff(5887,plain,
% 1.51/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36)),
% 1.51/1.56 inference(modus_ponens,[status(thm)],[5886, 5885])).
% 1.51/1.56 tff(5888,plain,
% 1.51/1.56 ((~xuntil28(s35)) | until27(s36)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5887, 3299, 5410])).
% 1.51/1.56 tff(5889,plain,
% 1.51/1.56 (until27(s36)),
% 1.51/1.56 inference(unit_resolution,[status(thm)],[5888, 5884])).
% 1.51/1.56 tff(5890,plain,
% 1.55/1.57 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s36) | (~node26(s36)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s36) | (~node26(s36)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5891,plain,
% 1.55/1.57 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s36) | (~node26(s36)))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5892,plain,
% 1.55/1.57 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s36) | (~node26(s36))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5891, 5890])).
% 1.55/1.57 tff(5893,plain,
% 1.55/1.57 (~node26(s36)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5892, 2069, 5132])).
% 1.55/1.57 tff(5894,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s36) | node26(s36) | (~until27(s36)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s36) | node26(s36) | (~until27(s36)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5895,plain,
% 1.55/1.57 ((node26(s36) | (~until27(s36)) | xuntil28(s36)) <=> (xuntil28(s36) | node26(s36) | (~until27(s36)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5896,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s36) | (~until27(s36)) | xuntil28(s36))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s36) | node26(s36) | (~until27(s36))))),
% 1.55/1.57 inference(monotonicity,[status(thm)],[5895])).
% 1.55/1.57 tff(5897,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s36) | (~until27(s36)) | xuntil28(s36))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s36) | node26(s36) | (~until27(s36)))),
% 1.55/1.57 inference(transitivity,[status(thm)],[5896, 5894])).
% 1.55/1.57 tff(5898,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s36) | (~until27(s36)) | xuntil28(s36))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5899,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s36) | node26(s36) | (~until27(s36))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5898, 5897])).
% 1.55/1.57 tff(5900,plain,
% 1.55/1.57 (xuntil28(s36) | (~until27(s36))),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5899, 5392, 5893])).
% 1.55/1.57 tff(5901,plain,
% 1.55/1.57 (xuntil28(s36)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5900, 5889])).
% 1.55/1.57 tff(5902,plain,
% 1.55/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5903,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5904,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37)),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5903, 5902])).
% 1.55/1.57 tff(5905,plain,
% 1.55/1.57 ((~xuntil28(s36)) | until27(s37)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5904, 3388, 5410])).
% 1.55/1.57 tff(5906,plain,
% 1.55/1.57 (until27(s37)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5905, 5901])).
% 1.55/1.57 tff(5907,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s37) | node26(s37) | (~until27(s37)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s37) | node26(s37) | (~until27(s37)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5908,plain,
% 1.55/1.57 ((node26(s37) | (~until27(s37)) | xuntil28(s37)) <=> (xuntil28(s37) | node26(s37) | (~until27(s37)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5909,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s37) | (~until27(s37)) | xuntil28(s37))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s37) | node26(s37) | (~until27(s37))))),
% 1.55/1.57 inference(monotonicity,[status(thm)],[5908])).
% 1.55/1.57 tff(5910,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s37) | (~until27(s37)) | xuntil28(s37))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s37) | node26(s37) | (~until27(s37)))),
% 1.55/1.57 inference(transitivity,[status(thm)],[5909, 5907])).
% 1.55/1.57 tff(5911,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s37) | (~until27(s37)) | xuntil28(s37))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5912,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s37) | node26(s37) | (~until27(s37))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 1.55/1.57 tff(5913,plain,
% 1.55/1.57 (xuntil28(s37)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5912, 5392, 5906, 5125])).
% 1.55/1.57 tff(5914,plain,
% 1.55/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5915,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5916,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38)),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5915, 5914])).
% 1.55/1.57 tff(5917,plain,
% 1.55/1.57 ((~xuntil28(s37)) | until27(s38)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5916, 3455, 5410])).
% 1.55/1.57 tff(5918,plain,
% 1.55/1.57 (until27(s38)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5917, 5913])).
% 1.55/1.57 tff(5919,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s38) | node26(s38) | (~until27(s38)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s38) | node26(s38) | (~until27(s38)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5920,plain,
% 1.55/1.57 ((node26(s38) | (~until27(s38)) | xuntil28(s38)) <=> (xuntil28(s38) | node26(s38) | (~until27(s38)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5921,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s38) | (~until27(s38)) | xuntil28(s38))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s38) | node26(s38) | (~until27(s38))))),
% 1.55/1.57 inference(monotonicity,[status(thm)],[5920])).
% 1.55/1.57 tff(5922,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s38) | (~until27(s38)) | xuntil28(s38))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s38) | node26(s38) | (~until27(s38)))),
% 1.55/1.57 inference(transitivity,[status(thm)],[5921, 5919])).
% 1.55/1.57 tff(5923,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s38) | (~until27(s38)) | xuntil28(s38))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5924,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s38) | node26(s38) | (~until27(s38))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5923, 5922])).
% 1.55/1.57 tff(5925,plain,
% 1.55/1.57 (xuntil28(s38) | node26(s38)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5924, 5392, 5918])).
% 1.55/1.57 tff(5926,plain,
% 1.55/1.57 (xuntil28(s38)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5925, 5121])).
% 1.55/1.57 tff(5927,plain,
% 1.55/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5928,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5929,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39)),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5928, 5927])).
% 1.55/1.57 tff(5930,plain,
% 1.55/1.57 ((~xuntil28(s38)) | until27(s39)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5929, 3554, 5410])).
% 1.55/1.57 tff(5931,plain,
% 1.55/1.57 (until27(s39)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5930, 5926])).
% 1.55/1.57 tff(5932,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s39) | node26(s39) | (~until27(s39)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s39) | node26(s39) | (~until27(s39)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5933,plain,
% 1.55/1.57 ((node26(s39) | (~until27(s39)) | xuntil28(s39)) <=> (xuntil28(s39) | node26(s39) | (~until27(s39)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5934,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s39) | (~until27(s39)) | xuntil28(s39))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s39) | node26(s39) | (~until27(s39))))),
% 1.55/1.57 inference(monotonicity,[status(thm)],[5933])).
% 1.55/1.57 tff(5935,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s39) | (~until27(s39)) | xuntil28(s39))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s39) | node26(s39) | (~until27(s39)))),
% 1.55/1.57 inference(transitivity,[status(thm)],[5934, 5932])).
% 1.55/1.57 tff(5936,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s39) | (~until27(s39)) | xuntil28(s39))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5937,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s39) | node26(s39) | (~until27(s39))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5936, 5935])).
% 1.55/1.57 tff(5938,plain,
% 1.55/1.57 (xuntil28(s39)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5937, 5392, 5931, 5112])).
% 1.55/1.57 tff(5939,plain,
% 1.55/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5940,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5941,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40)),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5940, 5939])).
% 1.55/1.57 tff(5942,plain,
% 1.55/1.57 ((~xuntil28(s39)) | until27(s40)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5941, 3632, 5410])).
% 1.55/1.57 tff(5943,plain,
% 1.55/1.57 (until27(s40)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5942, 5938])).
% 1.55/1.57 tff(5944,plain,
% 1.55/1.57 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s40) | (~node26(s40)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s40) | (~node26(s40)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5945,plain,
% 1.55/1.57 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s40) | (~node26(s40)))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5946,plain,
% 1.55/1.57 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s40) | (~node26(s40))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5945, 5944])).
% 1.55/1.57 tff(5947,plain,
% 1.55/1.57 (~node26(s40)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5946, 2069, 5103])).
% 1.55/1.57 tff(5948,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s40) | node26(s40) | (~until27(s40)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s40) | node26(s40) | (~until27(s40)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5949,plain,
% 1.55/1.57 ((node26(s40) | (~until27(s40)) | xuntil28(s40)) <=> (xuntil28(s40) | node26(s40) | (~until27(s40)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5950,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s40) | (~until27(s40)) | xuntil28(s40))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s40) | node26(s40) | (~until27(s40))))),
% 1.55/1.57 inference(monotonicity,[status(thm)],[5949])).
% 1.55/1.57 tff(5951,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s40) | (~until27(s40)) | xuntil28(s40))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s40) | node26(s40) | (~until27(s40)))),
% 1.55/1.57 inference(transitivity,[status(thm)],[5950, 5948])).
% 1.55/1.57 tff(5952,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s40) | (~until27(s40)) | xuntil28(s40))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5953,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s40) | node26(s40) | (~until27(s40))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5952, 5951])).
% 1.55/1.57 tff(5954,plain,
% 1.55/1.57 (xuntil28(s40) | (~until27(s40))),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5953, 5392, 5947])).
% 1.55/1.57 tff(5955,plain,
% 1.55/1.57 (xuntil28(s40)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5954, 5943])).
% 1.55/1.57 tff(5956,plain,
% 1.55/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5957,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5958,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41)),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5957, 5956])).
% 1.55/1.57 tff(5959,plain,
% 1.55/1.57 ((~xuntil28(s40)) | until27(s41)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5958, 3693, 5410])).
% 1.55/1.57 tff(5960,plain,
% 1.55/1.57 (until27(s41)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5959, 5955])).
% 1.55/1.57 tff(5961,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s41) | node26(s41) | (~until27(s41)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s41) | node26(s41) | (~until27(s41)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5962,plain,
% 1.55/1.57 ((node26(s41) | (~until27(s41)) | xuntil28(s41)) <=> (xuntil28(s41) | node26(s41) | (~until27(s41)))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5963,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s41) | (~until27(s41)) | xuntil28(s41))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s41) | node26(s41) | (~until27(s41))))),
% 1.55/1.57 inference(monotonicity,[status(thm)],[5962])).
% 1.55/1.57 tff(5964,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s41) | (~until27(s41)) | xuntil28(s41))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s41) | node26(s41) | (~until27(s41)))),
% 1.55/1.57 inference(transitivity,[status(thm)],[5963, 5961])).
% 1.55/1.57 tff(5965,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s41) | (~until27(s41)) | xuntil28(s41))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5966,plain,
% 1.55/1.57 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s41) | node26(s41) | (~until27(s41))),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 1.55/1.57 tff(5967,plain,
% 1.55/1.57 (xuntil28(s41)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5966, 5392, 5960, 5096])).
% 1.55/1.57 tff(5968,plain,
% 1.55/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42))),
% 1.55/1.57 inference(rewrite,[status(thm)],[])).
% 1.55/1.57 tff(5969,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42))),
% 1.55/1.57 inference(quant_inst,[status(thm)],[])).
% 1.55/1.57 tff(5970,plain,
% 1.55/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42)),
% 1.55/1.57 inference(modus_ponens,[status(thm)],[5969, 5968])).
% 1.55/1.57 tff(5971,plain,
% 1.55/1.57 ((~xuntil28(s41)) | until27(s42)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5970, 3788, 5410])).
% 1.55/1.57 tff(5972,plain,
% 1.55/1.57 (until27(s42)),
% 1.55/1.57 inference(unit_resolution,[status(thm)],[5971, 5967])).
% 1.55/1.57 tff(5973,plain,
% 1.55/1.57 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s42) | node26(s42) | (~until27(s42)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s42) | node26(s42) | (~until27(s42)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(5974,plain,
% 1.55/1.58 ((node26(s42) | (~until27(s42)) | xuntil28(s42)) <=> (xuntil28(s42) | node26(s42) | (~until27(s42)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(5975,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s42) | (~until27(s42)) | xuntil28(s42))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s42) | node26(s42) | (~until27(s42))))),
% 1.55/1.58 inference(monotonicity,[status(thm)],[5974])).
% 1.55/1.58 tff(5976,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s42) | (~until27(s42)) | xuntil28(s42))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s42) | node26(s42) | (~until27(s42)))),
% 1.55/1.58 inference(transitivity,[status(thm)],[5975, 5973])).
% 1.55/1.58 tff(5977,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s42) | (~until27(s42)) | xuntil28(s42))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(5978,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s42) | node26(s42) | (~until27(s42))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[5977, 5976])).
% 1.55/1.58 tff(5979,plain,
% 1.55/1.58 (xuntil28(s42) | node26(s42)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[5978, 5392, 5972])).
% 1.55/1.58 tff(5980,plain,
% 1.55/1.58 (xuntil28(s42)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[5979, 5092])).
% 1.55/1.58 tff(5981,plain,
% 1.55/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(5982,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(5983,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43)),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[5982, 5981])).
% 1.55/1.58 tff(5984,plain,
% 1.55/1.58 ((~xuntil28(s42)) | until27(s43)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[5983, 3852, 5410])).
% 1.55/1.58 tff(5985,plain,
% 1.55/1.58 (until27(s43)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[5984, 5980])).
% 1.55/1.58 tff(5986,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s43) | node26(s43) | (~until27(s43)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s43) | node26(s43) | (~until27(s43)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(5987,plain,
% 1.55/1.58 ((node26(s43) | (~until27(s43)) | xuntil28(s43)) <=> (xuntil28(s43) | node26(s43) | (~until27(s43)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(5988,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s43) | (~until27(s43)) | xuntil28(s43))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s43) | node26(s43) | (~until27(s43))))),
% 1.55/1.58 inference(monotonicity,[status(thm)],[5987])).
% 1.55/1.58 tff(5989,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s43) | (~until27(s43)) | xuntil28(s43))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s43) | node26(s43) | (~until27(s43)))),
% 1.55/1.58 inference(transitivity,[status(thm)],[5988, 5986])).
% 1.55/1.58 tff(5990,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s43) | (~until27(s43)) | xuntil28(s43))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(5991,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s43) | node26(s43) | (~until27(s43))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 1.55/1.58 tff(5992,plain,
% 1.55/1.58 (xuntil28(s43)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[5991, 5392, 5985, 5083])).
% 1.55/1.58 tff(5993,plain,
% 1.55/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(5994,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(5995,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44)),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[5994, 5993])).
% 1.55/1.58 tff(5996,plain,
% 1.55/1.58 ((~xuntil28(s43)) | until27(s44)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[5995, 3927, 5410])).
% 1.55/1.58 tff(5997,plain,
% 1.55/1.58 (until27(s44)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[5996, 5992])).
% 1.55/1.58 tff(5998,plain,
% 1.55/1.58 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s44) | (~node26(s44)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s44) | (~node26(s44)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(5999,plain,
% 1.55/1.58 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s44) | (~node26(s44)))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6000,plain,
% 1.55/1.58 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s44) | (~node26(s44))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[5999, 5998])).
% 1.55/1.58 tff(6001,plain,
% 1.55/1.58 (~node26(s44)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6000, 2069, 5074])).
% 1.55/1.58 tff(6002,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s44) | node26(s44) | (~until27(s44)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s44) | node26(s44) | (~until27(s44)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6003,plain,
% 1.55/1.58 ((node26(s44) | (~until27(s44)) | xuntil28(s44)) <=> (xuntil28(s44) | node26(s44) | (~until27(s44)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6004,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s44) | (~until27(s44)) | xuntil28(s44))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s44) | node26(s44) | (~until27(s44))))),
% 1.55/1.58 inference(monotonicity,[status(thm)],[6003])).
% 1.55/1.58 tff(6005,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s44) | (~until27(s44)) | xuntil28(s44))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s44) | node26(s44) | (~until27(s44)))),
% 1.55/1.58 inference(transitivity,[status(thm)],[6004, 6002])).
% 1.55/1.58 tff(6006,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s44) | (~until27(s44)) | xuntil28(s44))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6007,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s44) | node26(s44) | (~until27(s44))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6006, 6005])).
% 1.55/1.58 tff(6008,plain,
% 1.55/1.58 (xuntil28(s44) | (~until27(s44))),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6007, 5392, 6001])).
% 1.55/1.58 tff(6009,plain,
% 1.55/1.58 (xuntil28(s44)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6008, 5997])).
% 1.55/1.58 tff(6010,plain,
% 1.55/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6011,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6012,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45)),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6011, 6010])).
% 1.55/1.58 tff(6013,plain,
% 1.55/1.58 ((~xuntil28(s44)) | until27(s45)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6012, 4016, 5410])).
% 1.55/1.58 tff(6014,plain,
% 1.55/1.58 (until27(s45)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6013, 6009])).
% 1.55/1.58 tff(6015,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s45) | node26(s45) | (~until27(s45)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s45) | node26(s45) | (~until27(s45)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6016,plain,
% 1.55/1.58 ((node26(s45) | (~until27(s45)) | xuntil28(s45)) <=> (xuntil28(s45) | node26(s45) | (~until27(s45)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6017,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s45) | (~until27(s45)) | xuntil28(s45))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s45) | node26(s45) | (~until27(s45))))),
% 1.55/1.58 inference(monotonicity,[status(thm)],[6016])).
% 1.55/1.58 tff(6018,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s45) | (~until27(s45)) | xuntil28(s45))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s45) | node26(s45) | (~until27(s45)))),
% 1.55/1.58 inference(transitivity,[status(thm)],[6017, 6015])).
% 1.55/1.58 tff(6019,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s45) | (~until27(s45)) | xuntil28(s45))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6020,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s45) | node26(s45) | (~until27(s45))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6019, 6018])).
% 1.55/1.58 tff(6021,plain,
% 1.55/1.58 (xuntil28(s45)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6020, 5392, 6014, 5067])).
% 1.55/1.58 tff(6022,plain,
% 1.55/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6023,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6024,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46)),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6023, 6022])).
% 1.55/1.58 tff(6025,plain,
% 1.55/1.58 ((~xuntil28(s45)) | until27(s46)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6024, 4083, 5410])).
% 1.55/1.58 tff(6026,plain,
% 1.55/1.58 (until27(s46)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6025, 6021])).
% 1.55/1.58 tff(6027,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s46) | node26(s46) | (~until27(s46)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s46) | node26(s46) | (~until27(s46)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6028,plain,
% 1.55/1.58 ((node26(s46) | (~until27(s46)) | xuntil28(s46)) <=> (xuntil28(s46) | node26(s46) | (~until27(s46)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6029,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s46) | (~until27(s46)) | xuntil28(s46))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s46) | node26(s46) | (~until27(s46))))),
% 1.55/1.58 inference(monotonicity,[status(thm)],[6028])).
% 1.55/1.58 tff(6030,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s46) | (~until27(s46)) | xuntil28(s46))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s46) | node26(s46) | (~until27(s46)))),
% 1.55/1.58 inference(transitivity,[status(thm)],[6029, 6027])).
% 1.55/1.58 tff(6031,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s46) | (~until27(s46)) | xuntil28(s46))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6032,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s46) | node26(s46) | (~until27(s46))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6031, 6030])).
% 1.55/1.58 tff(6033,plain,
% 1.55/1.58 (xuntil28(s46) | node26(s46)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6032, 5392, 6026])).
% 1.55/1.58 tff(6034,plain,
% 1.55/1.58 (xuntil28(s46)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6033, 5063])).
% 1.55/1.58 tff(6035,plain,
% 1.55/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6036,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6037,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47)),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6036, 6035])).
% 1.55/1.58 tff(6038,plain,
% 1.55/1.58 ((~xuntil28(s46)) | until27(s47)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6037, 4182, 5410])).
% 1.55/1.58 tff(6039,plain,
% 1.55/1.58 (until27(s47)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6038, 6034])).
% 1.55/1.58 tff(6040,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s47) | node26(s47) | (~until27(s47)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s47) | node26(s47) | (~until27(s47)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6041,plain,
% 1.55/1.58 ((node26(s47) | (~until27(s47)) | xuntil28(s47)) <=> (xuntil28(s47) | node26(s47) | (~until27(s47)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6042,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s47) | (~until27(s47)) | xuntil28(s47))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s47) | node26(s47) | (~until27(s47))))),
% 1.55/1.58 inference(monotonicity,[status(thm)],[6041])).
% 1.55/1.58 tff(6043,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s47) | (~until27(s47)) | xuntil28(s47))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s47) | node26(s47) | (~until27(s47)))),
% 1.55/1.58 inference(transitivity,[status(thm)],[6042, 6040])).
% 1.55/1.58 tff(6044,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s47) | (~until27(s47)) | xuntil28(s47))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6045,plain,
% 1.55/1.58 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s47) | node26(s47) | (~until27(s47))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6044, 6043])).
% 1.55/1.58 tff(6046,plain,
% 1.55/1.58 (xuntil28(s47)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6045, 5392, 6039, 5054])).
% 1.55/1.58 tff(6047,plain,
% 1.55/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6048,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6049,plain,
% 1.55/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48)),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6048, 6047])).
% 1.55/1.58 tff(6050,plain,
% 1.55/1.58 ((~xuntil28(s47)) | until27(s48)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6049, 4260, 5410])).
% 1.55/1.58 tff(6051,plain,
% 1.55/1.58 (until27(s48)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6050, 6046])).
% 1.55/1.58 tff(6052,plain,
% 1.55/1.58 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s48) | (~node26(s48)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s48) | (~node26(s48)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6053,plain,
% 1.55/1.58 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s48) | (~node26(s48)))),
% 1.55/1.58 inference(quant_inst,[status(thm)],[])).
% 1.55/1.58 tff(6054,plain,
% 1.55/1.58 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s48) | (~node26(s48))),
% 1.55/1.58 inference(modus_ponens,[status(thm)],[6053, 6052])).
% 1.55/1.58 tff(6055,plain,
% 1.55/1.58 (~node26(s48)),
% 1.55/1.58 inference(unit_resolution,[status(thm)],[6054, 2069, 5045])).
% 1.55/1.58 tff(6056,plain,
% 1.55/1.58 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s48) | node26(s48) | (~until27(s48)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s48) | node26(s48) | (~until27(s48)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.58 tff(6057,plain,
% 1.55/1.58 ((node26(s48) | (~until27(s48)) | xuntil28(s48)) <=> (xuntil28(s48) | node26(s48) | (~until27(s48)))),
% 1.55/1.58 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6058,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s48) | (~until27(s48)) | xuntil28(s48))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s48) | node26(s48) | (~until27(s48))))),
% 1.55/1.59 inference(monotonicity,[status(thm)],[6057])).
% 1.55/1.59 tff(6059,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s48) | (~until27(s48)) | xuntil28(s48))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s48) | node26(s48) | (~until27(s48)))),
% 1.55/1.59 inference(transitivity,[status(thm)],[6058, 6056])).
% 1.55/1.59 tff(6060,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s48) | (~until27(s48)) | xuntil28(s48))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6061,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s48) | node26(s48) | (~until27(s48))),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6060, 6059])).
% 1.55/1.59 tff(6062,plain,
% 1.55/1.59 (xuntil28(s48) | (~until27(s48))),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6061, 5392, 6055])).
% 1.55/1.59 tff(6063,plain,
% 1.55/1.59 (xuntil28(s48)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6062, 6051])).
% 1.55/1.59 tff(6064,plain,
% 1.55/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6065,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6066,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49)),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6065, 6064])).
% 1.55/1.59 tff(6067,plain,
% 1.55/1.59 ((~xuntil28(s48)) | until27(s49)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6066, 4321, 5410])).
% 1.55/1.59 tff(6068,plain,
% 1.55/1.59 (until27(s49)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6067, 6063])).
% 1.55/1.59 tff(6069,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s49) | node26(s49) | (~until27(s49)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s49) | node26(s49) | (~until27(s49)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6070,plain,
% 1.55/1.59 ((node26(s49) | (~until27(s49)) | xuntil28(s49)) <=> (xuntil28(s49) | node26(s49) | (~until27(s49)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6071,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s49) | (~until27(s49)) | xuntil28(s49))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s49) | node26(s49) | (~until27(s49))))),
% 1.55/1.59 inference(monotonicity,[status(thm)],[6070])).
% 1.55/1.59 tff(6072,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s49) | (~until27(s49)) | xuntil28(s49))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s49) | node26(s49) | (~until27(s49)))),
% 1.55/1.59 inference(transitivity,[status(thm)],[6071, 6069])).
% 1.55/1.59 tff(6073,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s49) | (~until27(s49)) | xuntil28(s49))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6074,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s49) | node26(s49) | (~until27(s49))),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6073, 6072])).
% 1.55/1.59 tff(6075,plain,
% 1.55/1.59 (xuntil28(s49)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6074, 5392, 6068, 5038])).
% 1.55/1.59 tff(6076,plain,
% 1.55/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6077,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6078,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50)),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6077, 6076])).
% 1.55/1.59 tff(6079,plain,
% 1.55/1.59 ((~xuntil28(s49)) | until27(s50)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6078, 4416, 5410])).
% 1.55/1.59 tff(6080,plain,
% 1.55/1.59 (until27(s50)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6079, 6075])).
% 1.55/1.59 tff(6081,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s50) | node26(s50) | (~until27(s50)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s50) | node26(s50) | (~until27(s50)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6082,plain,
% 1.55/1.59 ((node26(s50) | (~until27(s50)) | xuntil28(s50)) <=> (xuntil28(s50) | node26(s50) | (~until27(s50)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6083,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s50) | (~until27(s50)) | xuntil28(s50))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s50) | node26(s50) | (~until27(s50))))),
% 1.55/1.59 inference(monotonicity,[status(thm)],[6082])).
% 1.55/1.59 tff(6084,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s50) | (~until27(s50)) | xuntil28(s50))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s50) | node26(s50) | (~until27(s50)))),
% 1.55/1.59 inference(transitivity,[status(thm)],[6083, 6081])).
% 1.55/1.59 tff(6085,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s50) | (~until27(s50)) | xuntil28(s50))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6086,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s50) | node26(s50) | (~until27(s50))),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6085, 6084])).
% 1.55/1.59 tff(6087,plain,
% 1.55/1.59 (xuntil28(s50) | node26(s50)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6086, 5392, 6080])).
% 1.55/1.59 tff(6088,plain,
% 1.55/1.59 (xuntil28(s50)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6087, 5034])).
% 1.55/1.59 tff(6089,plain,
% 1.55/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6090,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6091,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51)),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6090, 6089])).
% 1.55/1.59 tff(6092,plain,
% 1.55/1.59 ((~xuntil28(s50)) | until27(s51)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6091, 4480, 5410])).
% 1.55/1.59 tff(6093,plain,
% 1.55/1.59 (until27(s51)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6092, 6088])).
% 1.55/1.59 tff(6094,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s51) | node26(s51) | (~until27(s51)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s51) | node26(s51) | (~until27(s51)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6095,plain,
% 1.55/1.59 ((node26(s51) | (~until27(s51)) | xuntil28(s51)) <=> (xuntil28(s51) | node26(s51) | (~until27(s51)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6096,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s51) | (~until27(s51)) | xuntil28(s51))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s51) | node26(s51) | (~until27(s51))))),
% 1.55/1.59 inference(monotonicity,[status(thm)],[6095])).
% 1.55/1.59 tff(6097,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s51) | (~until27(s51)) | xuntil28(s51))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s51) | node26(s51) | (~until27(s51)))),
% 1.55/1.59 inference(transitivity,[status(thm)],[6096, 6094])).
% 1.55/1.59 tff(6098,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s51) | (~until27(s51)) | xuntil28(s51))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6099,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s51) | node26(s51) | (~until27(s51))),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6098, 6097])).
% 1.55/1.59 tff(6100,plain,
% 1.55/1.59 (xuntil28(s51)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6099, 5392, 6093, 5025])).
% 1.55/1.59 tff(6101,plain,
% 1.55/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6102,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6103,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52)),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6102, 6101])).
% 1.55/1.59 tff(6104,plain,
% 1.55/1.59 ((~xuntil28(s51)) | until27(s52)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6103, 4555, 5410])).
% 1.55/1.59 tff(6105,plain,
% 1.55/1.59 (until27(s52)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6104, 6100])).
% 1.55/1.59 tff(6106,plain,
% 1.55/1.59 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s52) | (~node26(s52)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s52) | (~node26(s52)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6107,plain,
% 1.55/1.59 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s52) | (~node26(s52)))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6108,plain,
% 1.55/1.59 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s52) | (~node26(s52))),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6107, 6106])).
% 1.55/1.59 tff(6109,plain,
% 1.55/1.59 (~node26(s52)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6108, 2069, 5016])).
% 1.55/1.59 tff(6110,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s52) | node26(s52) | (~until27(s52)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s52) | node26(s52) | (~until27(s52)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6111,plain,
% 1.55/1.59 ((node26(s52) | (~until27(s52)) | xuntil28(s52)) <=> (xuntil28(s52) | node26(s52) | (~until27(s52)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6112,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s52) | (~until27(s52)) | xuntil28(s52))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s52) | node26(s52) | (~until27(s52))))),
% 1.55/1.59 inference(monotonicity,[status(thm)],[6111])).
% 1.55/1.59 tff(6113,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s52) | (~until27(s52)) | xuntil28(s52))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s52) | node26(s52) | (~until27(s52)))),
% 1.55/1.59 inference(transitivity,[status(thm)],[6112, 6110])).
% 1.55/1.59 tff(6114,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s52) | (~until27(s52)) | xuntil28(s52))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6115,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s52) | node26(s52) | (~until27(s52))),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 1.55/1.59 tff(6116,plain,
% 1.55/1.59 (xuntil28(s52) | (~until27(s52))),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6115, 5392, 6109])).
% 1.55/1.59 tff(6117,plain,
% 1.55/1.59 (xuntil28(s52)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6116, 6105])).
% 1.55/1.59 tff(6118,plain,
% 1.55/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6119,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6120,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53)),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6119, 6118])).
% 1.55/1.59 tff(6121,plain,
% 1.55/1.59 ((~xuntil28(s52)) | until27(s53)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6120, 4644, 5410])).
% 1.55/1.59 tff(6122,plain,
% 1.55/1.59 (until27(s53)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6121, 6117])).
% 1.55/1.59 tff(6123,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s53) | node26(s53) | (~until27(s53)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s53) | node26(s53) | (~until27(s53)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6124,plain,
% 1.55/1.59 ((node26(s53) | (~until27(s53)) | xuntil28(s53)) <=> (xuntil28(s53) | node26(s53) | (~until27(s53)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6125,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s53) | (~until27(s53)) | xuntil28(s53))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s53) | node26(s53) | (~until27(s53))))),
% 1.55/1.59 inference(monotonicity,[status(thm)],[6124])).
% 1.55/1.59 tff(6126,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s53) | (~until27(s53)) | xuntil28(s53))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s53) | node26(s53) | (~until27(s53)))),
% 1.55/1.59 inference(transitivity,[status(thm)],[6125, 6123])).
% 1.55/1.59 tff(6127,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s53) | (~until27(s53)) | xuntil28(s53))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6128,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s53) | node26(s53) | (~until27(s53))),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6127, 6126])).
% 1.55/1.59 tff(6129,plain,
% 1.55/1.59 (xuntil28(s53)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6128, 5392, 6122, 5009])).
% 1.55/1.59 tff(6130,plain,
% 1.55/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6131,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6132,plain,
% 1.55/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54)),
% 1.55/1.59 inference(modus_ponens,[status(thm)],[6131, 6130])).
% 1.55/1.59 tff(6133,plain,
% 1.55/1.59 ((~xuntil28(s53)) | until27(s54)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6132, 4711, 5410])).
% 1.55/1.59 tff(6134,plain,
% 1.55/1.59 (until27(s54)),
% 1.55/1.59 inference(unit_resolution,[status(thm)],[6133, 6129])).
% 1.55/1.59 tff(6135,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s54) | node26(s54) | (~until27(s54)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s54) | node26(s54) | (~until27(s54)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6136,plain,
% 1.55/1.59 ((node26(s54) | (~until27(s54)) | xuntil28(s54)) <=> (xuntil28(s54) | node26(s54) | (~until27(s54)))),
% 1.55/1.59 inference(rewrite,[status(thm)],[])).
% 1.55/1.59 tff(6137,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s54) | (~until27(s54)) | xuntil28(s54))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s54) | node26(s54) | (~until27(s54))))),
% 1.55/1.59 inference(monotonicity,[status(thm)],[6136])).
% 1.55/1.59 tff(6138,plain,
% 1.55/1.59 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s54) | (~until27(s54)) | xuntil28(s54))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s54) | node26(s54) | (~until27(s54)))),
% 1.55/1.59 inference(transitivity,[status(thm)],[6137, 6135])).
% 1.55/1.59 tff(6139,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s54) | (~until27(s54)) | xuntil28(s54))),
% 1.55/1.59 inference(quant_inst,[status(thm)],[])).
% 1.55/1.59 tff(6140,plain,
% 1.55/1.59 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s54) | node26(s54) | (~until27(s54))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6139, 6138])).
% 1.55/1.60 tff(6141,plain,
% 1.55/1.60 (xuntil28(s54) | node26(s54)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6140, 5392, 6134])).
% 1.55/1.60 tff(6142,plain,
% 1.55/1.60 (xuntil28(s54)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6141, 5005])).
% 1.55/1.60 tff(6143,plain,
% 1.55/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6144,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6145,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55)),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6144, 6143])).
% 1.55/1.60 tff(6146,plain,
% 1.55/1.60 ((~xuntil28(s54)) | until27(s55)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6145, 4810, 5410])).
% 1.55/1.60 tff(6147,plain,
% 1.55/1.60 (until27(s55)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6146, 6142])).
% 1.55/1.60 tff(6148,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s55) | node26(s55) | (~until27(s55)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s55) | node26(s55) | (~until27(s55)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6149,plain,
% 1.55/1.60 ((node26(s55) | (~until27(s55)) | xuntil28(s55)) <=> (xuntil28(s55) | node26(s55) | (~until27(s55)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6150,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s55) | (~until27(s55)) | xuntil28(s55))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s55) | node26(s55) | (~until27(s55))))),
% 1.55/1.60 inference(monotonicity,[status(thm)],[6149])).
% 1.55/1.60 tff(6151,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s55) | (~until27(s55)) | xuntil28(s55))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s55) | node26(s55) | (~until27(s55)))),
% 1.55/1.60 inference(transitivity,[status(thm)],[6150, 6148])).
% 1.55/1.60 tff(6152,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s55) | (~until27(s55)) | xuntil28(s55))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6153,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s55) | node26(s55) | (~until27(s55))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6152, 6151])).
% 1.55/1.60 tff(6154,plain,
% 1.55/1.60 (xuntil28(s55)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6153, 5392, 6147, 4996])).
% 1.55/1.60 tff(6155,plain,
% 1.55/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6156,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6157,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56)),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6156, 6155])).
% 1.55/1.60 tff(6158,plain,
% 1.55/1.60 ((~xuntil28(s55)) | until27(s56)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6157, 4888, 5410])).
% 1.55/1.60 tff(6159,plain,
% 1.55/1.60 (until27(s56)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6158, 6154])).
% 1.55/1.60 tff(6160,plain,
% 1.55/1.60 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s56) | (~node26(s56)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s56) | (~node26(s56)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6161,plain,
% 1.55/1.60 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s56) | (~node26(s56)))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6162,plain,
% 1.55/1.60 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s56) | (~node26(s56))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6161, 6160])).
% 1.55/1.60 tff(6163,plain,
% 1.55/1.60 (~node26(s56)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6162, 2069, 4987])).
% 1.55/1.60 tff(6164,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s56) | node26(s56) | (~until27(s56)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s56) | node26(s56) | (~until27(s56)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6165,plain,
% 1.55/1.60 ((node26(s56) | (~until27(s56)) | xuntil28(s56)) <=> (xuntil28(s56) | node26(s56) | (~until27(s56)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6166,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s56) | (~until27(s56)) | xuntil28(s56))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s56) | node26(s56) | (~until27(s56))))),
% 1.55/1.60 inference(monotonicity,[status(thm)],[6165])).
% 1.55/1.60 tff(6167,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s56) | (~until27(s56)) | xuntil28(s56))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s56) | node26(s56) | (~until27(s56)))),
% 1.55/1.60 inference(transitivity,[status(thm)],[6166, 6164])).
% 1.55/1.60 tff(6168,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s56) | (~until27(s56)) | xuntil28(s56))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6169,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s56) | node26(s56) | (~until27(s56))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6168, 6167])).
% 1.55/1.60 tff(6170,plain,
% 1.55/1.60 (xuntil28(s56) | (~until27(s56))),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6169, 5392, 6163])).
% 1.55/1.60 tff(6171,plain,
% 1.55/1.60 (xuntil28(s56)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6170, 6159])).
% 1.55/1.60 tff(6172,plain,
% 1.55/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6173,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6174,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57)),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6173, 6172])).
% 1.55/1.60 tff(6175,plain,
% 1.55/1.60 ((~xuntil28(s56)) | until27(s57)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6174, 4949, 5410])).
% 1.55/1.60 tff(6176,plain,
% 1.55/1.60 (until27(s57)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6175, 6171])).
% 1.55/1.60 tff(6177,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s57) | node26(s57) | (~until27(s57)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s57) | node26(s57) | (~until27(s57)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6178,plain,
% 1.55/1.60 ((node26(s57) | (~until27(s57)) | xuntil28(s57)) <=> (xuntil28(s57) | node26(s57) | (~until27(s57)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6179,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s57) | (~until27(s57)) | xuntil28(s57))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s57) | node26(s57) | (~until27(s57))))),
% 1.55/1.60 inference(monotonicity,[status(thm)],[6178])).
% 1.55/1.60 tff(6180,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s57) | (~until27(s57)) | xuntil28(s57))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s57) | node26(s57) | (~until27(s57)))),
% 1.55/1.60 inference(transitivity,[status(thm)],[6179, 6177])).
% 1.55/1.60 tff(6181,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s57) | (~until27(s57)) | xuntil28(s57))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6182,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s57) | node26(s57) | (~until27(s57))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 1.55/1.60 tff(6183,plain,
% 1.55/1.60 (xuntil28(s57)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6182, 5392, 6176, 4980])).
% 1.55/1.60 tff(6184,plain,
% 1.55/1.60 (succ(s57, s58) <=> succ(s57, s58)),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6185,axiom,(succ(s57, s58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound58')).
% 1.55/1.60 tff(6186,plain,
% 1.55/1.60 (succ(s57, s58)),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6185, 6184])).
% 1.55/1.60 tff(6187,plain,
% 1.55/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6188,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6189,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58)),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6188, 6187])).
% 1.55/1.60 tff(6190,plain,
% 1.55/1.60 ((~xuntil28(s57)) | until27(s58)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6189, 6186, 5410])).
% 1.55/1.60 tff(6191,plain,
% 1.55/1.60 (until27(s58)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6190, 6183])).
% 1.55/1.60 tff(6192,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s58) | node26(s58) | (~until27(s58)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s58) | node26(s58) | (~until27(s58)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6193,plain,
% 1.55/1.60 ((node26(s58) | (~until27(s58)) | xuntil28(s58)) <=> (xuntil28(s58) | node26(s58) | (~until27(s58)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6194,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s58) | (~until27(s58)) | xuntil28(s58))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s58) | node26(s58) | (~until27(s58))))),
% 1.55/1.60 inference(monotonicity,[status(thm)],[6193])).
% 1.55/1.60 tff(6195,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s58) | (~until27(s58)) | xuntil28(s58))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s58) | node26(s58) | (~until27(s58)))),
% 1.55/1.60 inference(transitivity,[status(thm)],[6194, 6192])).
% 1.55/1.60 tff(6196,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s58) | (~until27(s58)) | xuntil28(s58))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6197,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s58) | node26(s58) | (~until27(s58))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6196, 6195])).
% 1.55/1.60 tff(6198,plain,
% 1.55/1.60 (xuntil28(s58) | node26(s58)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6197, 5392, 6191])).
% 1.55/1.60 tff(6199,plain,
% 1.55/1.60 (xuntil28(s58)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6198, 2075])).
% 1.55/1.60 tff(6200,plain,
% 1.55/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6201,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6202,plain,
% 1.55/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59)),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6201, 6200])).
% 1.55/1.60 tff(6203,plain,
% 1.55/1.60 ((~xuntil28(s58)) | until27(s59)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6202, 2050, 5410])).
% 1.55/1.60 tff(6204,plain,
% 1.55/1.60 (until27(s59)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6203, 6199])).
% 1.55/1.60 tff(6205,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s59) | node26(s59) | (~until27(s59)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s59) | node26(s59) | (~until27(s59)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6206,plain,
% 1.55/1.60 ((node26(s59) | (~until27(s59)) | xuntil28(s59)) <=> (xuntil28(s59) | node26(s59) | (~until27(s59)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6207,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s59) | (~until27(s59)) | xuntil28(s59))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s59) | node26(s59) | (~until27(s59))))),
% 1.55/1.60 inference(monotonicity,[status(thm)],[6206])).
% 1.55/1.60 tff(6208,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s59) | (~until27(s59)) | xuntil28(s59))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s59) | node26(s59) | (~until27(s59)))),
% 1.55/1.60 inference(transitivity,[status(thm)],[6207, 6205])).
% 1.55/1.60 tff(6209,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s59) | (~until27(s59)) | xuntil28(s59))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6210,plain,
% 1.55/1.60 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s59) | node26(s59) | (~until27(s59))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6209, 6208])).
% 1.55/1.60 tff(6211,plain,
% 1.55/1.60 (xuntil28(s59) | node26(s59)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6210, 5392, 6204])).
% 1.55/1.60 tff(6212,plain,
% 1.55/1.60 (xuntil28(s59)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6211, 2074])).
% 1.55/1.60 tff(6213,plain,
% 1.55/1.60 (^[X: $i] : refl(((~last(X)) | (~xuntil2p30(X))) <=> ((~last(X)) | (~xuntil2p30(X))))),
% 1.55/1.60 inference(bind,[status(th)],[])).
% 1.55/1.60 tff(6214,plain,
% 1.55/1.60 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.55/1.60 inference(quant_intro,[status(thm)],[6213])).
% 1.55/1.60 tff(6215,plain,
% 1.55/1.60 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6216,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty25')).
% 1.55/1.60 tff(6217,plain,
% 1.55/1.60 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6216, 6215])).
% 1.55/1.60 tff(6218,plain,(
% 1.55/1.60 ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.55/1.60 inference(skolemize,[status(sab)],[6217])).
% 1.55/1.60 tff(6219,plain,
% 1.55/1.60 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6218, 6214])).
% 1.55/1.60 tff(6220,plain,
% 1.55/1.60 (last(s59) <=> last(s59)),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6221,axiom,(last(s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound60')).
% 1.55/1.60 tff(6222,plain,
% 1.55/1.60 (last(s59)),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6221, 6220])).
% 1.55/1.60 tff(6223,plain,
% 1.55/1.60 (((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s59)) | (~xuntil2p30(s59)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s59)) | (~xuntil2p30(s59)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6224,plain,
% 1.55/1.60 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s59)) | (~xuntil2p30(s59)))),
% 1.55/1.60 inference(quant_inst,[status(thm)],[])).
% 1.55/1.60 tff(6225,plain,
% 1.55/1.60 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s59)) | (~xuntil2p30(s59))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6224, 6223])).
% 1.55/1.60 tff(6226,plain,
% 1.55/1.60 (~xuntil2p30(s59)),
% 1.55/1.60 inference(unit_resolution,[status(thm)],[6225, 6222, 6219])).
% 1.55/1.60 tff(6227,plain,
% 1.55/1.60 (^[X: $i] : refl((node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 1.55/1.60 inference(bind,[status(th)],[])).
% 1.55/1.60 tff(6228,plain,
% 1.55/1.60 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.55/1.60 inference(quant_intro,[status(thm)],[6227])).
% 1.55/1.60 tff(6229,plain,
% 1.55/1.60 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.55/1.60 inference(rewrite,[status(thm)],[])).
% 1.55/1.60 tff(6230,plain,
% 1.55/1.60 (^[X: $i] : rewrite(((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 1.55/1.60 inference(bind,[status(th)],[])).
% 1.55/1.60 tff(6231,plain,
% 1.55/1.60 (![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.55/1.60 inference(quant_intro,[status(thm)],[6230])).
% 1.55/1.60 tff(6232,axiom,(![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty23')).
% 1.55/1.60 tff(6233,plain,
% 1.55/1.60 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6232, 6231])).
% 1.55/1.60 tff(6234,plain,
% 1.55/1.60 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6233, 6229])).
% 1.55/1.60 tff(6235,plain,(
% 1.55/1.60 ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.55/1.60 inference(skolemize,[status(sab)],[6234])).
% 1.55/1.60 tff(6236,plain,
% 1.55/1.60 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.55/1.60 inference(modus_ponens,[status(thm)],[6235, 6228])).
% 1.55/1.60 tff(6237,plain,
% 1.55/1.60 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s59) | xuntil2p30(s59) | (~until2p29(s59)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s59) | xuntil2p30(s59) | (~until2p29(s59)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6238,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s59) | xuntil2p30(s59) | (~until2p29(s59)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6239,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s59) | xuntil2p30(s59) | (~until2p29(s59))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6238, 6237])).
% 1.55/1.61 tff(6240,plain,
% 1.55/1.61 (node26(s59) | (~until2p29(s59))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6239, 6236, 6226])).
% 1.55/1.61 tff(6241,plain,
% 1.55/1.61 (~until2p29(s59)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6240, 2074])).
% 1.55/1.61 tff(6242,plain,
% 1.55/1.61 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 1.55/1.61 inference(bind,[status(th)],[])).
% 1.55/1.61 tff(6243,plain,
% 1.55/1.61 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.55/1.61 inference(quant_intro,[status(thm)],[6242])).
% 1.55/1.61 tff(6244,plain,
% 1.55/1.61 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6245,plain,
% 1.55/1.61 (^[Y: $i, X: $i] : rewrite(((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 1.55/1.61 inference(bind,[status(th)],[])).
% 1.55/1.61 tff(6246,plain,
% 1.55/1.61 (![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.55/1.61 inference(quant_intro,[status(thm)],[6245])).
% 1.55/1.61 tff(6247,axiom,(![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty24')).
% 1.55/1.61 tff(6248,plain,
% 1.55/1.61 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6247, 6246])).
% 1.55/1.61 tff(6249,plain,
% 1.55/1.61 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6248, 6244])).
% 1.55/1.61 tff(6250,plain,(
% 1.55/1.61 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.55/1.61 inference(skolemize,[status(sab)],[6249])).
% 1.55/1.61 tff(6251,plain,
% 1.55/1.61 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6250, 6243])).
% 1.55/1.61 tff(6252,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6253,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6254,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6253, 6252])).
% 1.55/1.61 tff(6255,plain,
% 1.55/1.61 (until2p29(s59) | (~xuntil2p30(s58))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6254, 2050, 6251])).
% 1.55/1.61 tff(6256,plain,
% 1.55/1.61 (~xuntil2p30(s58)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6255, 6241])).
% 1.55/1.61 tff(6257,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s58) | xuntil2p30(s58) | (~until2p29(s58)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s58) | xuntil2p30(s58) | (~until2p29(s58)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6258,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s58) | xuntil2p30(s58) | (~until2p29(s58)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6259,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s58) | xuntil2p30(s58) | (~until2p29(s58))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 1.55/1.61 tff(6260,plain,
% 1.55/1.61 (xuntil2p30(s58) | (~until2p29(s58))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6259, 6236, 2075])).
% 1.55/1.61 tff(6261,plain,
% 1.55/1.61 (~until2p29(s58)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6260, 6256])).
% 1.55/1.61 tff(6262,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6263,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6264,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6263, 6262])).
% 1.55/1.61 tff(6265,plain,
% 1.55/1.61 (until2p29(s58) | (~xuntil2p30(s57))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6264, 6186, 6251])).
% 1.55/1.61 tff(6266,plain,
% 1.55/1.61 (~xuntil2p30(s57)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6265, 6261])).
% 1.55/1.61 tff(6267,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s57) | xuntil2p30(s57) | (~until2p29(s57)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s57) | xuntil2p30(s57) | (~until2p29(s57)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6268,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s57) | xuntil2p30(s57) | (~until2p29(s57)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6269,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s57) | xuntil2p30(s57) | (~until2p29(s57))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6268, 6267])).
% 1.55/1.61 tff(6270,plain,
% 1.55/1.61 (xuntil2p30(s57) | (~until2p29(s57))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6269, 6236, 4980])).
% 1.55/1.61 tff(6271,plain,
% 1.55/1.61 (~until2p29(s57)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6270, 6266])).
% 1.55/1.61 tff(6272,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6273,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6274,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6273, 6272])).
% 1.55/1.61 tff(6275,plain,
% 1.55/1.61 (until2p29(s57) | (~xuntil2p30(s56))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6274, 4949, 6251])).
% 1.55/1.61 tff(6276,plain,
% 1.55/1.61 (~xuntil2p30(s56)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6275, 6271])).
% 1.55/1.61 tff(6277,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s56) | xuntil2p30(s56) | (~until2p29(s56)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s56) | xuntil2p30(s56) | (~until2p29(s56)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6278,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s56) | xuntil2p30(s56) | (~until2p29(s56)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6279,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s56) | xuntil2p30(s56) | (~until2p29(s56))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6278, 6277])).
% 1.55/1.61 tff(6280,plain,
% 1.55/1.61 (xuntil2p30(s56) | (~until2p29(s56))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6279, 6236, 6163])).
% 1.55/1.61 tff(6281,plain,
% 1.55/1.61 (~until2p29(s56)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6280, 6276])).
% 1.55/1.61 tff(6282,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6283,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6284,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6283, 6282])).
% 1.55/1.61 tff(6285,plain,
% 1.55/1.61 (until2p29(s56) | (~xuntil2p30(s55))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6284, 4888, 6251])).
% 1.55/1.61 tff(6286,plain,
% 1.55/1.61 (~xuntil2p30(s55)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6285, 6281])).
% 1.55/1.61 tff(6287,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s55) | xuntil2p30(s55) | (~until2p29(s55)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s55) | xuntil2p30(s55) | (~until2p29(s55)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6288,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s55) | xuntil2p30(s55) | (~until2p29(s55)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6289,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s55) | xuntil2p30(s55) | (~until2p29(s55))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6288, 6287])).
% 1.55/1.61 tff(6290,plain,
% 1.55/1.61 (xuntil2p30(s55) | (~until2p29(s55))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6289, 6236, 4996])).
% 1.55/1.61 tff(6291,plain,
% 1.55/1.61 (~until2p29(s55)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6290, 6286])).
% 1.55/1.61 tff(6292,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6293,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6294,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6293, 6292])).
% 1.55/1.61 tff(6295,plain,
% 1.55/1.61 (until2p29(s55) | (~xuntil2p30(s54))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6294, 4810, 6251])).
% 1.55/1.61 tff(6296,plain,
% 1.55/1.61 (~xuntil2p30(s54)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6295, 6291])).
% 1.55/1.61 tff(6297,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s54) | xuntil2p30(s54) | (~until2p29(s54)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s54) | xuntil2p30(s54) | (~until2p29(s54)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6298,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s54) | xuntil2p30(s54) | (~until2p29(s54)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6299,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s54) | xuntil2p30(s54) | (~until2p29(s54))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6298, 6297])).
% 1.55/1.61 tff(6300,plain,
% 1.55/1.61 (xuntil2p30(s54) | (~until2p29(s54))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6299, 6236, 5005])).
% 1.55/1.61 tff(6301,plain,
% 1.55/1.61 (~until2p29(s54)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6300, 6296])).
% 1.55/1.61 tff(6302,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6303,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6304,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6303, 6302])).
% 1.55/1.61 tff(6305,plain,
% 1.55/1.61 (until2p29(s54) | (~xuntil2p30(s53))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6304, 4711, 6251])).
% 1.55/1.61 tff(6306,plain,
% 1.55/1.61 (~xuntil2p30(s53)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6305, 6301])).
% 1.55/1.61 tff(6307,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s53) | xuntil2p30(s53) | (~until2p29(s53)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s53) | xuntil2p30(s53) | (~until2p29(s53)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6308,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s53) | xuntil2p30(s53) | (~until2p29(s53)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6309,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s53) | xuntil2p30(s53) | (~until2p29(s53))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6308, 6307])).
% 1.55/1.61 tff(6310,plain,
% 1.55/1.61 (xuntil2p30(s53) | (~until2p29(s53))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6309, 6236, 5009])).
% 1.55/1.61 tff(6311,plain,
% 1.55/1.61 (~until2p29(s53)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6310, 6306])).
% 1.55/1.61 tff(6312,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6313,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6314,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6313, 6312])).
% 1.55/1.61 tff(6315,plain,
% 1.55/1.61 (until2p29(s53) | (~xuntil2p30(s52))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6314, 4644, 6251])).
% 1.55/1.61 tff(6316,plain,
% 1.55/1.61 (~xuntil2p30(s52)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6315, 6311])).
% 1.55/1.61 tff(6317,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s52) | xuntil2p30(s52) | (~until2p29(s52)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s52) | xuntil2p30(s52) | (~until2p29(s52)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6318,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s52) | xuntil2p30(s52) | (~until2p29(s52)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6319,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s52) | xuntil2p30(s52) | (~until2p29(s52))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6318, 6317])).
% 1.55/1.61 tff(6320,plain,
% 1.55/1.61 (xuntil2p30(s52) | (~until2p29(s52))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6319, 6236, 6109])).
% 1.55/1.61 tff(6321,plain,
% 1.55/1.61 (~until2p29(s52)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6320, 6316])).
% 1.55/1.61 tff(6322,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6323,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6324,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6323, 6322])).
% 1.55/1.61 tff(6325,plain,
% 1.55/1.61 (until2p29(s52) | (~xuntil2p30(s51))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6324, 4555, 6251])).
% 1.55/1.61 tff(6326,plain,
% 1.55/1.61 (~xuntil2p30(s51)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6325, 6321])).
% 1.55/1.61 tff(6327,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s51) | xuntil2p30(s51) | (~until2p29(s51)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s51) | xuntil2p30(s51) | (~until2p29(s51)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6328,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s51) | xuntil2p30(s51) | (~until2p29(s51)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6329,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s51) | xuntil2p30(s51) | (~until2p29(s51))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6328, 6327])).
% 1.55/1.61 tff(6330,plain,
% 1.55/1.61 (xuntil2p30(s51) | (~until2p29(s51))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6329, 6236, 5025])).
% 1.55/1.61 tff(6331,plain,
% 1.55/1.61 (~until2p29(s51)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6330, 6326])).
% 1.55/1.61 tff(6332,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6333,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6334,plain,
% 1.55/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 1.55/1.61 tff(6335,plain,
% 1.55/1.61 (until2p29(s51) | (~xuntil2p30(s50))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6334, 4480, 6251])).
% 1.55/1.61 tff(6336,plain,
% 1.55/1.61 (~xuntil2p30(s50)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6335, 6331])).
% 1.55/1.61 tff(6337,plain,
% 1.55/1.61 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s50) | xuntil2p30(s50) | (~until2p29(s50)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s50) | xuntil2p30(s50) | (~until2p29(s50)))),
% 1.55/1.61 inference(rewrite,[status(thm)],[])).
% 1.55/1.61 tff(6338,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s50) | xuntil2p30(s50) | (~until2p29(s50)))),
% 1.55/1.61 inference(quant_inst,[status(thm)],[])).
% 1.55/1.61 tff(6339,plain,
% 1.55/1.61 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s50) | xuntil2p30(s50) | (~until2p29(s50))),
% 1.55/1.61 inference(modus_ponens,[status(thm)],[6338, 6337])).
% 1.55/1.61 tff(6340,plain,
% 1.55/1.61 (xuntil2p30(s50) | (~until2p29(s50))),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6339, 6236, 5034])).
% 1.55/1.61 tff(6341,plain,
% 1.55/1.61 (~until2p29(s50)),
% 1.55/1.61 inference(unit_resolution,[status(thm)],[6340, 6336])).
% 1.55/1.61 tff(6342,plain,
% 1.55/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6343,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6344,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6343, 6342])).
% 1.55/1.62 tff(6345,plain,
% 1.55/1.62 (until2p29(s50) | (~xuntil2p30(s49))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6344, 4416, 6251])).
% 1.55/1.62 tff(6346,plain,
% 1.55/1.62 (~xuntil2p30(s49)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6345, 6341])).
% 1.55/1.62 tff(6347,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s49) | xuntil2p30(s49) | (~until2p29(s49)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s49) | xuntil2p30(s49) | (~until2p29(s49)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6348,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s49) | xuntil2p30(s49) | (~until2p29(s49)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6349,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s49) | xuntil2p30(s49) | (~until2p29(s49))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6348, 6347])).
% 1.55/1.62 tff(6350,plain,
% 1.55/1.62 (xuntil2p30(s49) | (~until2p29(s49))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6349, 6236, 5038])).
% 1.55/1.62 tff(6351,plain,
% 1.55/1.62 (~until2p29(s49)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6350, 6346])).
% 1.55/1.62 tff(6352,plain,
% 1.55/1.62 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)))),
% 1.55/1.62 inference(bind,[status(th)],[])).
% 1.55/1.62 tff(6353,plain,
% 1.55/1.62 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.55/1.62 inference(quant_intro,[status(thm)],[6352])).
% 1.55/1.62 tff(6354,plain,
% 1.55/1.62 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6355,plain,
% 1.55/1.62 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((until2p29(Y) | (~trans(X, Y))) | (~last(X))) <=> ((~trans(X, Y)) | (~last(X)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> (((~trans(X, Y)) | (~last(X)) | until2p29(Y)) | (~xuntil28(X))))), rewrite((((~trans(X, Y)) | (~last(X)) | until2p29(Y)) | (~xuntil28(X))) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))))),
% 1.55/1.62 inference(bind,[status(th)],[])).
% 1.55/1.62 tff(6356,plain,
% 1.55/1.62 (![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.55/1.62 inference(quant_intro,[status(thm)],[6355])).
% 1.55/1.62 tff(6357,axiom,(![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty22')).
% 1.55/1.62 tff(6358,plain,
% 1.55/1.62 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6357, 6356])).
% 1.55/1.62 tff(6359,plain,
% 1.55/1.62 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6358, 6354])).
% 1.55/1.62 tff(6360,plain,(
% 1.55/1.62 ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.55/1.62 inference(skolemize,[status(sab)],[6359])).
% 1.55/1.62 tff(6361,plain,
% 1.55/1.62 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6360, 6353])).
% 1.55/1.62 tff(6362,plain,
% 1.55/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6363,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6364,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6363, 6362])).
% 1.55/1.62 tff(6365,plain,
% 1.55/1.62 (until2p29(s49) | (~xuntil2p30(s48))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6364, 4321, 6251])).
% 1.55/1.62 tff(6366,plain,
% 1.55/1.62 (~xuntil2p30(s48)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6365, 6351])).
% 1.55/1.62 tff(6367,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s48) | xuntil2p30(s48) | (~until2p29(s48)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s48) | xuntil2p30(s48) | (~until2p29(s48)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6368,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s48) | xuntil2p30(s48) | (~until2p29(s48)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6369,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s48) | xuntil2p30(s48) | (~until2p29(s48))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6368, 6367])).
% 1.55/1.62 tff(6370,plain,
% 1.55/1.62 (xuntil2p30(s48) | (~until2p29(s48))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6369, 6236, 6055])).
% 1.55/1.62 tff(6371,plain,
% 1.55/1.62 (~until2p29(s48)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6370, 6366])).
% 1.55/1.62 tff(6372,plain,
% 1.55/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6373,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6374,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6373, 6372])).
% 1.55/1.62 tff(6375,plain,
% 1.55/1.62 (until2p29(s48) | (~xuntil2p30(s47))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6374, 4260, 6251])).
% 1.55/1.62 tff(6376,plain,
% 1.55/1.62 (~xuntil2p30(s47)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6375, 6371])).
% 1.55/1.62 tff(6377,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s47) | xuntil2p30(s47) | (~until2p29(s47)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s47) | xuntil2p30(s47) | (~until2p29(s47)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6378,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s47) | xuntil2p30(s47) | (~until2p29(s47)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6379,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s47) | xuntil2p30(s47) | (~until2p29(s47))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6378, 6377])).
% 1.55/1.62 tff(6380,plain,
% 1.55/1.62 (xuntil2p30(s47) | (~until2p29(s47))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6379, 6236, 5054])).
% 1.55/1.62 tff(6381,plain,
% 1.55/1.62 (~until2p29(s47)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6380, 6376])).
% 1.55/1.62 tff(6382,plain,
% 1.55/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6383,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6384,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6383, 6382])).
% 1.55/1.62 tff(6385,plain,
% 1.55/1.62 (until2p29(s47) | (~xuntil2p30(s46))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6384, 4182, 6251])).
% 1.55/1.62 tff(6386,plain,
% 1.55/1.62 (~xuntil2p30(s46)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6385, 6381])).
% 1.55/1.62 tff(6387,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s46) | xuntil2p30(s46) | (~until2p29(s46)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s46) | xuntil2p30(s46) | (~until2p29(s46)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6388,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s46) | xuntil2p30(s46) | (~until2p29(s46)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6389,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s46) | xuntil2p30(s46) | (~until2p29(s46))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6388, 6387])).
% 1.55/1.62 tff(6390,plain,
% 1.55/1.62 (xuntil2p30(s46) | (~until2p29(s46))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6389, 6236, 5063])).
% 1.55/1.62 tff(6391,plain,
% 1.55/1.62 (~until2p29(s46)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6390, 6386])).
% 1.55/1.62 tff(6392,plain,
% 1.55/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6393,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6394,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6393, 6392])).
% 1.55/1.62 tff(6395,plain,
% 1.55/1.62 (until2p29(s46) | (~xuntil2p30(s45))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6394, 4083, 6251])).
% 1.55/1.62 tff(6396,plain,
% 1.55/1.62 (~xuntil2p30(s45)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6395, 6391])).
% 1.55/1.62 tff(6397,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s45) | xuntil2p30(s45) | (~until2p29(s45)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s45) | xuntil2p30(s45) | (~until2p29(s45)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6398,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s45) | xuntil2p30(s45) | (~until2p29(s45)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6399,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s45) | xuntil2p30(s45) | (~until2p29(s45))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6398, 6397])).
% 1.55/1.62 tff(6400,plain,
% 1.55/1.62 (xuntil2p30(s45) | (~until2p29(s45))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6399, 6236, 5067])).
% 1.55/1.62 tff(6401,plain,
% 1.55/1.62 (~until2p29(s45)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6400, 6396])).
% 1.55/1.62 tff(6402,plain,
% 1.55/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6403,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6404,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6403, 6402])).
% 1.55/1.62 tff(6405,plain,
% 1.55/1.62 (until2p29(s45) | (~xuntil2p30(s44))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6404, 4016, 6251])).
% 1.55/1.62 tff(6406,plain,
% 1.55/1.62 (~xuntil2p30(s44)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6405, 6401])).
% 1.55/1.62 tff(6407,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s44) | xuntil2p30(s44) | (~until2p29(s44)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s44) | xuntil2p30(s44) | (~until2p29(s44)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6408,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s44) | xuntil2p30(s44) | (~until2p29(s44)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6409,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s44) | xuntil2p30(s44) | (~until2p29(s44))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6408, 6407])).
% 1.55/1.62 tff(6410,plain,
% 1.55/1.62 (xuntil2p30(s44) | (~until2p29(s44))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6409, 6236, 6001])).
% 1.55/1.62 tff(6411,plain,
% 1.55/1.62 (~until2p29(s44)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6410, 6406])).
% 1.55/1.62 tff(6412,plain,
% 1.55/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6413,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6414,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6413, 6412])).
% 1.55/1.62 tff(6415,plain,
% 1.55/1.62 (until2p29(s44) | (~xuntil2p30(s43))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6414, 3927, 6251])).
% 1.55/1.62 tff(6416,plain,
% 1.55/1.62 (~xuntil2p30(s43)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6415, 6411])).
% 1.55/1.62 tff(6417,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s43) | xuntil2p30(s43) | (~until2p29(s43)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s43) | xuntil2p30(s43) | (~until2p29(s43)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6418,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s43) | xuntil2p30(s43) | (~until2p29(s43)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6419,plain,
% 1.55/1.62 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s43) | xuntil2p30(s43) | (~until2p29(s43))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6418, 6417])).
% 1.55/1.62 tff(6420,plain,
% 1.55/1.62 (xuntil2p30(s43) | (~until2p29(s43))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6419, 6236, 5083])).
% 1.55/1.62 tff(6421,plain,
% 1.55/1.62 (~until2p29(s43)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6420, 6416])).
% 1.55/1.62 tff(6422,plain,
% 1.55/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42)))),
% 1.55/1.62 inference(rewrite,[status(thm)],[])).
% 1.55/1.62 tff(6423,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42)))),
% 1.55/1.62 inference(quant_inst,[status(thm)],[])).
% 1.55/1.62 tff(6424,plain,
% 1.55/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42))),
% 1.55/1.62 inference(modus_ponens,[status(thm)],[6423, 6422])).
% 1.55/1.62 tff(6425,plain,
% 1.55/1.62 (until2p29(s43) | (~xuntil2p30(s42))),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6424, 3852, 6251])).
% 1.55/1.62 tff(6426,plain,
% 1.55/1.62 (~xuntil2p30(s42)),
% 1.55/1.62 inference(unit_resolution,[status(thm)],[6425, 6421])).
% 1.55/1.62 tff(6427,plain,
% 1.55/1.62 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s42) | xuntil2p30(s42) | (~until2p29(s42)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s42) | xuntil2p30(s42) | (~until2p29(s42)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6428,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s42) | xuntil2p30(s42) | (~until2p29(s42)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6429,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s42) | xuntil2p30(s42) | (~until2p29(s42))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6428, 6427])).
% 1.55/1.63 tff(6430,plain,
% 1.55/1.63 (xuntil2p30(s42) | (~until2p29(s42))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6429, 6236, 5092])).
% 1.55/1.63 tff(6431,plain,
% 1.55/1.63 (~until2p29(s42)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6430, 6426])).
% 1.55/1.63 tff(6432,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6433,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6434,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6433, 6432])).
% 1.55/1.63 tff(6435,plain,
% 1.55/1.63 (until2p29(s42) | (~xuntil2p30(s41))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6434, 3788, 6251])).
% 1.55/1.63 tff(6436,plain,
% 1.55/1.63 (~xuntil2p30(s41)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6435, 6431])).
% 1.55/1.63 tff(6437,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s41) | xuntil2p30(s41) | (~until2p29(s41)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s41) | xuntil2p30(s41) | (~until2p29(s41)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6438,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s41) | xuntil2p30(s41) | (~until2p29(s41)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6439,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s41) | xuntil2p30(s41) | (~until2p29(s41))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6438, 6437])).
% 1.55/1.63 tff(6440,plain,
% 1.55/1.63 (xuntil2p30(s41) | (~until2p29(s41))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6439, 6236, 5096])).
% 1.55/1.63 tff(6441,plain,
% 1.55/1.63 (~until2p29(s41)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6440, 6436])).
% 1.55/1.63 tff(6442,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6443,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6444,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6443, 6442])).
% 1.55/1.63 tff(6445,plain,
% 1.55/1.63 (until2p29(s41) | (~xuntil2p30(s40))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6444, 3693, 6251])).
% 1.55/1.63 tff(6446,plain,
% 1.55/1.63 (~xuntil2p30(s40)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6445, 6441])).
% 1.55/1.63 tff(6447,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s40) | xuntil2p30(s40) | (~until2p29(s40)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s40) | xuntil2p30(s40) | (~until2p29(s40)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6448,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s40) | xuntil2p30(s40) | (~until2p29(s40)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6449,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s40) | xuntil2p30(s40) | (~until2p29(s40))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6448, 6447])).
% 1.55/1.63 tff(6450,plain,
% 1.55/1.63 (xuntil2p30(s40) | (~until2p29(s40))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6449, 6236, 5947])).
% 1.55/1.63 tff(6451,plain,
% 1.55/1.63 (~until2p29(s40)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6450, 6446])).
% 1.55/1.63 tff(6452,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6453,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6454,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6453, 6452])).
% 1.55/1.63 tff(6455,plain,
% 1.55/1.63 (until2p29(s40) | (~xuntil2p30(s39))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6454, 3632, 6251])).
% 1.55/1.63 tff(6456,plain,
% 1.55/1.63 (~xuntil2p30(s39)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6455, 6451])).
% 1.55/1.63 tff(6457,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s39) | xuntil2p30(s39) | (~until2p29(s39)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s39) | xuntil2p30(s39) | (~until2p29(s39)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6458,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s39) | xuntil2p30(s39) | (~until2p29(s39)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6459,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s39) | xuntil2p30(s39) | (~until2p29(s39))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6458, 6457])).
% 1.55/1.63 tff(6460,plain,
% 1.55/1.63 (xuntil2p30(s39) | (~until2p29(s39))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6459, 6236, 5112])).
% 1.55/1.63 tff(6461,plain,
% 1.55/1.63 (~until2p29(s39)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6460, 6456])).
% 1.55/1.63 tff(6462,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6463,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6464,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6463, 6462])).
% 1.55/1.63 tff(6465,plain,
% 1.55/1.63 (until2p29(s39) | (~xuntil2p30(s38))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6464, 3554, 6251])).
% 1.55/1.63 tff(6466,plain,
% 1.55/1.63 (~xuntil2p30(s38)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6465, 6461])).
% 1.55/1.63 tff(6467,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s38) | xuntil2p30(s38) | (~until2p29(s38)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s38) | xuntil2p30(s38) | (~until2p29(s38)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6468,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s38) | xuntil2p30(s38) | (~until2p29(s38)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6469,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s38) | xuntil2p30(s38) | (~until2p29(s38))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6468, 6467])).
% 1.55/1.63 tff(6470,plain,
% 1.55/1.63 (xuntil2p30(s38) | (~until2p29(s38))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6469, 6236, 5121])).
% 1.55/1.63 tff(6471,plain,
% 1.55/1.63 (~until2p29(s38)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6470, 6466])).
% 1.55/1.63 tff(6472,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6473,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6474,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6473, 6472])).
% 1.55/1.63 tff(6475,plain,
% 1.55/1.63 (until2p29(s38) | (~xuntil2p30(s37))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6474, 3455, 6251])).
% 1.55/1.63 tff(6476,plain,
% 1.55/1.63 (~xuntil2p30(s37)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6475, 6471])).
% 1.55/1.63 tff(6477,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s37) | xuntil2p30(s37) | (~until2p29(s37)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s37) | xuntil2p30(s37) | (~until2p29(s37)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6478,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s37) | xuntil2p30(s37) | (~until2p29(s37)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6479,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s37) | xuntil2p30(s37) | (~until2p29(s37))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6478, 6477])).
% 1.55/1.63 tff(6480,plain,
% 1.55/1.63 (xuntil2p30(s37) | (~until2p29(s37))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6479, 6236, 5125])).
% 1.55/1.63 tff(6481,plain,
% 1.55/1.63 (~until2p29(s37)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6480, 6476])).
% 1.55/1.63 tff(6482,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6483,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6484,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6483, 6482])).
% 1.55/1.63 tff(6485,plain,
% 1.55/1.63 (until2p29(s37) | (~xuntil2p30(s36))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6484, 3388, 6251])).
% 1.55/1.63 tff(6486,plain,
% 1.55/1.63 (~xuntil2p30(s36)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6485, 6481])).
% 1.55/1.63 tff(6487,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s36) | xuntil2p30(s36) | (~until2p29(s36)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s36) | xuntil2p30(s36) | (~until2p29(s36)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6488,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s36) | xuntil2p30(s36) | (~until2p29(s36)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6489,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s36) | xuntil2p30(s36) | (~until2p29(s36))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6488, 6487])).
% 1.55/1.63 tff(6490,plain,
% 1.55/1.63 (xuntil2p30(s36) | (~until2p29(s36))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6489, 6236, 5893])).
% 1.55/1.63 tff(6491,plain,
% 1.55/1.63 (~until2p29(s36)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6490, 6486])).
% 1.55/1.63 tff(6492,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6493,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6494,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6493, 6492])).
% 1.55/1.63 tff(6495,plain,
% 1.55/1.63 (until2p29(s36) | (~xuntil2p30(s35))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6494, 3299, 6251])).
% 1.55/1.63 tff(6496,plain,
% 1.55/1.63 (~xuntil2p30(s35)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6495, 6491])).
% 1.55/1.63 tff(6497,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s35) | xuntil2p30(s35) | (~until2p29(s35)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s35) | xuntil2p30(s35) | (~until2p29(s35)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6498,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s35) | xuntil2p30(s35) | (~until2p29(s35)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6499,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s35) | xuntil2p30(s35) | (~until2p29(s35))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6498, 6497])).
% 1.55/1.63 tff(6500,plain,
% 1.55/1.63 (xuntil2p30(s35) | (~until2p29(s35))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6499, 6236, 5141])).
% 1.55/1.63 tff(6501,plain,
% 1.55/1.63 (~until2p29(s35)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6500, 6496])).
% 1.55/1.63 tff(6502,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6503,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6504,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6503, 6502])).
% 1.55/1.63 tff(6505,plain,
% 1.55/1.63 (until2p29(s35) | (~xuntil2p30(s34))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6504, 3224, 6251])).
% 1.55/1.63 tff(6506,plain,
% 1.55/1.63 (~xuntil2p30(s34)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6505, 6501])).
% 1.55/1.63 tff(6507,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s34) | xuntil2p30(s34) | (~until2p29(s34)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s34) | xuntil2p30(s34) | (~until2p29(s34)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6508,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s34) | xuntil2p30(s34) | (~until2p29(s34)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6509,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s34) | xuntil2p30(s34) | (~until2p29(s34))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6508, 6507])).
% 1.55/1.63 tff(6510,plain,
% 1.55/1.63 (xuntil2p30(s34) | (~until2p29(s34))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6509, 6236, 5150])).
% 1.55/1.63 tff(6511,plain,
% 1.55/1.63 (~until2p29(s34)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6510, 6506])).
% 1.55/1.63 tff(6512,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6513,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6514,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6513, 6512])).
% 1.55/1.63 tff(6515,plain,
% 1.55/1.63 (until2p29(s34) | (~xuntil2p30(s33))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6514, 3160, 6251])).
% 1.55/1.63 tff(6516,plain,
% 1.55/1.63 (~xuntil2p30(s33)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6515, 6511])).
% 1.55/1.63 tff(6517,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s33) | xuntil2p30(s33) | (~until2p29(s33)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s33) | xuntil2p30(s33) | (~until2p29(s33)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6518,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s33) | xuntil2p30(s33) | (~until2p29(s33)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6519,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s33) | xuntil2p30(s33) | (~until2p29(s33))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6518, 6517])).
% 1.55/1.63 tff(6520,plain,
% 1.55/1.63 (xuntil2p30(s33) | (~until2p29(s33))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6519, 6236, 5154])).
% 1.55/1.63 tff(6521,plain,
% 1.55/1.63 (~until2p29(s33)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6520, 6516])).
% 1.55/1.63 tff(6522,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6523,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6524,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6523, 6522])).
% 1.55/1.63 tff(6525,plain,
% 1.55/1.63 (until2p29(s33) | (~xuntil2p30(s32))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6524, 3065, 6251])).
% 1.55/1.63 tff(6526,plain,
% 1.55/1.63 (~xuntil2p30(s32)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6525, 6521])).
% 1.55/1.63 tff(6527,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s32) | xuntil2p30(s32) | (~until2p29(s32)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s32) | xuntil2p30(s32) | (~until2p29(s32)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6528,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s32) | xuntil2p30(s32) | (~until2p29(s32)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6529,plain,
% 1.55/1.63 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s32) | xuntil2p30(s32) | (~until2p29(s32))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6528, 6527])).
% 1.55/1.63 tff(6530,plain,
% 1.55/1.63 (xuntil2p30(s32) | (~until2p29(s32))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6529, 6236, 5839])).
% 1.55/1.63 tff(6531,plain,
% 1.55/1.63 (~until2p29(s32)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6530, 6526])).
% 1.55/1.63 tff(6532,plain,
% 1.55/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31)))),
% 1.55/1.63 inference(rewrite,[status(thm)],[])).
% 1.55/1.63 tff(6533,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31)))),
% 1.55/1.63 inference(quant_inst,[status(thm)],[])).
% 1.55/1.63 tff(6534,plain,
% 1.55/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31))),
% 1.55/1.63 inference(modus_ponens,[status(thm)],[6533, 6532])).
% 1.55/1.63 tff(6535,plain,
% 1.55/1.63 (until2p29(s32) | (~xuntil2p30(s31))),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6534, 3004, 6251])).
% 1.55/1.63 tff(6536,plain,
% 1.55/1.63 (~xuntil2p30(s31)),
% 1.55/1.63 inference(unit_resolution,[status(thm)],[6535, 6531])).
% 1.55/1.63 tff(6537,plain,
% 1.55/1.63 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s31) | xuntil2p30(s31) | (~until2p29(s31)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s31) | xuntil2p30(s31) | (~until2p29(s31)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6538,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s31) | xuntil2p30(s31) | (~until2p29(s31)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6539,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s31) | xuntil2p30(s31) | (~until2p29(s31))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6538, 6537])).
% 1.55/1.64 tff(6540,plain,
% 1.55/1.64 (xuntil2p30(s31) | (~until2p29(s31))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6539, 6236, 5170])).
% 1.55/1.64 tff(6541,plain,
% 1.55/1.64 (~until2p29(s31)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6540, 6536])).
% 1.55/1.64 tff(6542,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6543,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6544,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6543, 6542])).
% 1.55/1.64 tff(6545,plain,
% 1.55/1.64 (until2p29(s31) | (~xuntil2p30(s30))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6544, 2926, 6251])).
% 1.55/1.64 tff(6546,plain,
% 1.55/1.64 (~xuntil2p30(s30)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6545, 6541])).
% 1.55/1.64 tff(6547,plain,
% 1.55/1.64 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s30) | xuntil2p30(s30) | (~until2p29(s30)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s30) | xuntil2p30(s30) | (~until2p29(s30)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6548,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s30) | xuntil2p30(s30) | (~until2p29(s30)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6549,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s30) | xuntil2p30(s30) | (~until2p29(s30))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6548, 6547])).
% 1.55/1.64 tff(6550,plain,
% 1.55/1.64 (xuntil2p30(s30) | (~until2p29(s30))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6549, 6236, 5179])).
% 1.55/1.64 tff(6551,plain,
% 1.55/1.64 (~until2p29(s30)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6550, 6546])).
% 1.55/1.64 tff(6552,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6553,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6554,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6553, 6552])).
% 1.55/1.64 tff(6555,plain,
% 1.55/1.64 (until2p29(s30) | (~xuntil2p30(s29))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6554, 2827, 6251])).
% 1.55/1.64 tff(6556,plain,
% 1.55/1.64 (~xuntil2p30(s29)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6555, 6551])).
% 1.55/1.64 tff(6557,plain,
% 1.55/1.64 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s29) | xuntil2p30(s29) | (~until2p29(s29)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s29) | xuntil2p30(s29) | (~until2p29(s29)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6558,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s29) | xuntil2p30(s29) | (~until2p29(s29)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6559,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s29) | xuntil2p30(s29) | (~until2p29(s29))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6558, 6557])).
% 1.55/1.64 tff(6560,plain,
% 1.55/1.64 (xuntil2p30(s29) | (~until2p29(s29))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6559, 6236, 5183])).
% 1.55/1.64 tff(6561,plain,
% 1.55/1.64 (~until2p29(s29)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6560, 6556])).
% 1.55/1.64 tff(6562,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6563,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6564,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6563, 6562])).
% 1.55/1.64 tff(6565,plain,
% 1.55/1.64 (until2p29(s29) | (~xuntil2p30(s28))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6564, 2760, 6251])).
% 1.55/1.64 tff(6566,plain,
% 1.55/1.64 (~xuntil2p30(s28)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6565, 6561])).
% 1.55/1.64 tff(6567,plain,
% 1.55/1.64 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s28) | xuntil2p30(s28) | (~until2p29(s28)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s28) | xuntil2p30(s28) | (~until2p29(s28)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6568,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s28) | xuntil2p30(s28) | (~until2p29(s28)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6569,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s28) | xuntil2p30(s28) | (~until2p29(s28))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6568, 6567])).
% 1.55/1.64 tff(6570,plain,
% 1.55/1.64 (xuntil2p30(s28) | (~until2p29(s28))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6569, 6236, 5785])).
% 1.55/1.64 tff(6571,plain,
% 1.55/1.64 (~until2p29(s28)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6570, 6566])).
% 1.55/1.64 tff(6572,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6573,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6574,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6573, 6572])).
% 1.55/1.64 tff(6575,plain,
% 1.55/1.64 (until2p29(s28) | (~xuntil2p30(s27))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6574, 2671, 6251])).
% 1.55/1.64 tff(6576,plain,
% 1.55/1.64 (~xuntil2p30(s27)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6575, 6571])).
% 1.55/1.64 tff(6577,plain,
% 1.55/1.64 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s27) | xuntil2p30(s27) | (~until2p29(s27)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s27) | xuntil2p30(s27) | (~until2p29(s27)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6578,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s27) | xuntil2p30(s27) | (~until2p29(s27)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6579,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s27) | xuntil2p30(s27) | (~until2p29(s27))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6578, 6577])).
% 1.55/1.64 tff(6580,plain,
% 1.55/1.64 (xuntil2p30(s27) | (~until2p29(s27))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6579, 6236, 5199])).
% 1.55/1.64 tff(6581,plain,
% 1.55/1.64 (~until2p29(s27)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6580, 6576])).
% 1.55/1.64 tff(6582,assumption,(xuntil28(s59)), introduced(assumption)).
% 1.55/1.64 tff(6583,assumption,(~until2p29(s27)), introduced(assumption)).
% 1.55/1.64 tff(6584,assumption,(trans(s59, s27)), introduced(assumption)).
% 1.55/1.64 tff(6585,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s27) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s27)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s27) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s27)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6586,plain,
% 1.55/1.64 (((~trans(s59, s27)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s27)) <=> (until2p29(s27) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s27)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6587,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s27)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s27) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s27))))),
% 1.55/1.64 inference(monotonicity,[status(thm)],[6586])).
% 1.55/1.64 tff(6588,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s27)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s27) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s27)))),
% 1.55/1.64 inference(transitivity,[status(thm)],[6587, 6585])).
% 1.55/1.64 tff(6589,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s27)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s27))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6590,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s27) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s27))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6589, 6588])).
% 1.55/1.64 tff(6591,plain,
% 1.55/1.64 ($false),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6590, 6222, 6584, 6361, 6583, 6582])).
% 1.55/1.64 tff(6592,plain,((~trans(s59, s27)) | until2p29(s27) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.64 tff(6593,plain,
% 1.55/1.64 (~trans(s59, s27)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6592, 6581, 6212])).
% 1.55/1.64 tff(6594,assumption,(~until2p29(s54)), introduced(assumption)).
% 1.55/1.64 tff(6595,assumption,(trans(s59, s54)), introduced(assumption)).
% 1.55/1.64 tff(6596,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s54) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s54)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s54) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s54)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6597,plain,
% 1.55/1.64 (((~trans(s59, s54)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s54)) <=> (until2p29(s54) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s54)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6598,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s54)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s54) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s54))))),
% 1.55/1.64 inference(monotonicity,[status(thm)],[6597])).
% 1.55/1.64 tff(6599,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s54)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s54) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s54)))),
% 1.55/1.64 inference(transitivity,[status(thm)],[6598, 6596])).
% 1.55/1.64 tff(6600,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s54)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s54))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6601,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s54) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s54))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6600, 6599])).
% 1.55/1.64 tff(6602,plain,
% 1.55/1.64 ($false),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6601, 6222, 6595, 6361, 6594, 6582])).
% 1.55/1.64 tff(6603,plain,((~trans(s59, s54)) | until2p29(s54) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.64 tff(6604,plain,
% 1.55/1.64 (~trans(s59, s54)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6603, 6301, 6212])).
% 1.55/1.64 tff(6605,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6606,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6607,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6606, 6605])).
% 1.55/1.64 tff(6608,plain,
% 1.55/1.64 (until2p29(s27) | (~xuntil2p30(s26))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6607, 2596, 6251])).
% 1.55/1.64 tff(6609,plain,
% 1.55/1.64 (~xuntil2p30(s26)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6608, 6581])).
% 1.55/1.64 tff(6610,plain,
% 1.55/1.64 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s26) | xuntil2p30(s26) | (~until2p29(s26)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s26) | xuntil2p30(s26) | (~until2p29(s26)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6611,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s26) | xuntil2p30(s26) | (~until2p29(s26)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6612,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s26) | xuntil2p30(s26) | (~until2p29(s26))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6611, 6610])).
% 1.55/1.64 tff(6613,plain,
% 1.55/1.64 (xuntil2p30(s26) | (~until2p29(s26))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6612, 6236, 5208])).
% 1.55/1.64 tff(6614,plain,
% 1.55/1.64 (~until2p29(s26)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6613, 6609])).
% 1.55/1.64 tff(6615,plain,
% 1.55/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6616,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6617,plain,
% 1.55/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6616, 6615])).
% 1.55/1.64 tff(6618,plain,
% 1.55/1.64 (until2p29(s26) | (~xuntil2p30(s25))),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6617, 2532, 6251])).
% 1.55/1.64 tff(6619,plain,
% 1.55/1.64 (~xuntil2p30(s25)),
% 1.55/1.64 inference(unit_resolution,[status(thm)],[6618, 6614])).
% 1.55/1.64 tff(6620,plain,
% 1.55/1.64 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s25) | xuntil2p30(s25) | (~until2p29(s25)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s25) | xuntil2p30(s25) | (~until2p29(s25)))),
% 1.55/1.64 inference(rewrite,[status(thm)],[])).
% 1.55/1.64 tff(6621,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s25) | xuntil2p30(s25) | (~until2p29(s25)))),
% 1.55/1.64 inference(quant_inst,[status(thm)],[])).
% 1.55/1.64 tff(6622,plain,
% 1.55/1.64 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s25) | xuntil2p30(s25) | (~until2p29(s25))),
% 1.55/1.64 inference(modus_ponens,[status(thm)],[6621, 6620])).
% 1.55/1.64 tff(6623,plain,
% 1.55/1.64 (xuntil2p30(s25) | (~until2p29(s25))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6622, 6236, 5212])).
% 1.55/1.65 tff(6624,plain,
% 1.55/1.65 (~until2p29(s25)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6623, 6619])).
% 1.55/1.65 tff(6625,plain,
% 1.55/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6626,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6627,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6626, 6625])).
% 1.55/1.65 tff(6628,plain,
% 1.55/1.65 (until2p29(s25) | (~xuntil2p30(s24))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6627, 2437, 6251])).
% 1.55/1.65 tff(6629,plain,
% 1.55/1.65 (~xuntil2p30(s24)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6628, 6624])).
% 1.55/1.65 tff(6630,plain,
% 1.55/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s24) | xuntil2p30(s24) | (~until2p29(s24)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s24) | xuntil2p30(s24) | (~until2p29(s24)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6631,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s24) | xuntil2p30(s24) | (~until2p29(s24)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6632,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s24) | xuntil2p30(s24) | (~until2p29(s24))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6631, 6630])).
% 1.55/1.65 tff(6633,plain,
% 1.55/1.65 (xuntil2p30(s24) | (~until2p29(s24))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6632, 6236, 5731])).
% 1.55/1.65 tff(6634,plain,
% 1.55/1.65 (~until2p29(s24)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6633, 6629])).
% 1.55/1.65 tff(6635,plain,
% 1.55/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6636,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6637,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6636, 6635])).
% 1.55/1.65 tff(6638,plain,
% 1.55/1.65 (until2p29(s24) | (~xuntil2p30(s23))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6637, 2376, 6251])).
% 1.55/1.65 tff(6639,plain,
% 1.55/1.65 (~xuntil2p30(s23)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6638, 6634])).
% 1.55/1.65 tff(6640,plain,
% 1.55/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s23) | xuntil2p30(s23) | (~until2p29(s23)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s23) | xuntil2p30(s23) | (~until2p29(s23)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6641,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s23) | xuntil2p30(s23) | (~until2p29(s23)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6642,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s23) | xuntil2p30(s23) | (~until2p29(s23))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6641, 6640])).
% 1.55/1.65 tff(6643,plain,
% 1.55/1.65 (xuntil2p30(s23) | (~until2p29(s23))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6642, 6236, 5228])).
% 1.55/1.65 tff(6644,plain,
% 1.55/1.65 (~until2p29(s23)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6643, 6639])).
% 1.55/1.65 tff(6645,plain,
% 1.55/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6646,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6647,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6646, 6645])).
% 1.55/1.65 tff(6648,plain,
% 1.55/1.65 (until2p29(s23) | (~xuntil2p30(s22))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6647, 2298, 6251])).
% 1.55/1.65 tff(6649,plain,
% 1.55/1.65 (~xuntil2p30(s22)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6648, 6644])).
% 1.55/1.65 tff(6650,plain,
% 1.55/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s22) | xuntil2p30(s22) | (~until2p29(s22)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s22) | xuntil2p30(s22) | (~until2p29(s22)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6651,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s22) | xuntil2p30(s22) | (~until2p29(s22)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6652,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s22) | xuntil2p30(s22) | (~until2p29(s22))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6651, 6650])).
% 1.55/1.65 tff(6653,plain,
% 1.55/1.65 (xuntil2p30(s22) | (~until2p29(s22))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6652, 6236, 5237])).
% 1.55/1.65 tff(6654,plain,
% 1.55/1.65 (~until2p29(s22)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6653, 6649])).
% 1.55/1.65 tff(6655,plain,
% 1.55/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6656,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6657,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6656, 6655])).
% 1.55/1.65 tff(6658,plain,
% 1.55/1.65 (until2p29(s22) | (~xuntil2p30(s21))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6657, 2199, 6251])).
% 1.55/1.65 tff(6659,plain,
% 1.55/1.65 (~xuntil2p30(s21)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6658, 6654])).
% 1.55/1.65 tff(6660,plain,
% 1.55/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s21) | xuntil2p30(s21) | (~until2p29(s21)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s21) | xuntil2p30(s21) | (~until2p29(s21)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6661,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s21) | xuntil2p30(s21) | (~until2p29(s21)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6662,plain,
% 1.55/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s21) | xuntil2p30(s21) | (~until2p29(s21))),
% 1.55/1.65 inference(modus_ponens,[status(thm)],[6661, 6660])).
% 1.55/1.65 tff(6663,plain,
% 1.55/1.65 (xuntil2p30(s21) | (~until2p29(s21))),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6662, 6236, 5241])).
% 1.55/1.65 tff(6664,plain,
% 1.55/1.65 (~until2p29(s21)),
% 1.55/1.65 inference(unit_resolution,[status(thm)],[6663, 6659])).
% 1.55/1.65 tff(6665,plain,
% 1.55/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20)))),
% 1.55/1.65 inference(rewrite,[status(thm)],[])).
% 1.55/1.65 tff(6666,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20)))),
% 1.55/1.65 inference(quant_inst,[status(thm)],[])).
% 1.55/1.65 tff(6667,plain,
% 1.55/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6666, 6665])).
% 1.63/1.65 tff(6668,plain,
% 1.63/1.65 (until2p29(s21) | (~xuntil2p30(s20))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6667, 2132, 6251])).
% 1.63/1.65 tff(6669,plain,
% 1.63/1.65 (~xuntil2p30(s20)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6668, 6664])).
% 1.63/1.65 tff(6670,plain,
% 1.63/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s20) | xuntil2p30(s20) | (~until2p29(s20)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s20) | xuntil2p30(s20) | (~until2p29(s20)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6671,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s20) | xuntil2p30(s20) | (~until2p29(s20)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6672,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s20) | xuntil2p30(s20) | (~until2p29(s20))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6671, 6670])).
% 1.63/1.65 tff(6673,plain,
% 1.63/1.65 (xuntil2p30(s20) | (~until2p29(s20))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6672, 6236, 5677])).
% 1.63/1.65 tff(6674,plain,
% 1.63/1.65 (~until2p29(s20)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6673, 6669])).
% 1.63/1.65 tff(6675,plain,
% 1.63/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6676,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6677,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6676, 6675])).
% 1.63/1.65 tff(6678,plain,
% 1.63/1.65 (until2p29(s20) | (~xuntil2p30(s19))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6677, 2004, 6251])).
% 1.63/1.65 tff(6679,plain,
% 1.63/1.65 (~xuntil2p30(s19)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6678, 6674])).
% 1.63/1.65 tff(6680,plain,
% 1.63/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6681,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6682,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s19) | xuntil2p30(s19) | (~until2p29(s19))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6681, 6680])).
% 1.63/1.65 tff(6683,plain,
% 1.63/1.65 (xuntil2p30(s19) | (~until2p29(s19))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6682, 6236, 5245])).
% 1.63/1.65 tff(6684,plain,
% 1.63/1.65 (~until2p29(s19)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6683, 6679])).
% 1.63/1.65 tff(6685,plain,
% 1.63/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6686,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6687,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6686, 6685])).
% 1.63/1.65 tff(6688,plain,
% 1.63/1.65 (until2p29(s19) | (~xuntil2p30(s18))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6687, 1926, 6251])).
% 1.63/1.65 tff(6689,plain,
% 1.63/1.65 (~xuntil2p30(s18)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6688, 6684])).
% 1.63/1.65 tff(6690,plain,
% 1.63/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6691,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6692,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s18) | xuntil2p30(s18) | (~until2p29(s18))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6691, 6690])).
% 1.63/1.65 tff(6693,plain,
% 1.63/1.65 (xuntil2p30(s18) | (~until2p29(s18))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6692, 6236, 5254])).
% 1.63/1.65 tff(6694,plain,
% 1.63/1.65 (~until2p29(s18)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6693, 6689])).
% 1.63/1.65 tff(6695,plain,
% 1.63/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6696,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6697,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6696, 6695])).
% 1.63/1.65 tff(6698,plain,
% 1.63/1.65 (until2p29(s18) | (~xuntil2p30(s17))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6697, 1827, 6251])).
% 1.63/1.65 tff(6699,plain,
% 1.63/1.65 (~xuntil2p30(s17)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6698, 6694])).
% 1.63/1.65 tff(6700,plain,
% 1.63/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6701,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6702,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s17) | xuntil2p30(s17) | (~until2p29(s17))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6701, 6700])).
% 1.63/1.65 tff(6703,plain,
% 1.63/1.65 (xuntil2p30(s17) | (~until2p29(s17))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6702, 6236, 5258])).
% 1.63/1.65 tff(6704,plain,
% 1.63/1.65 (~until2p29(s17)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6703, 6699])).
% 1.63/1.65 tff(6705,plain,
% 1.63/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6706,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))),
% 1.63/1.65 inference(quant_inst,[status(thm)],[])).
% 1.63/1.65 tff(6707,plain,
% 1.63/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16))),
% 1.63/1.65 inference(modus_ponens,[status(thm)],[6706, 6705])).
% 1.63/1.65 tff(6708,plain,
% 1.63/1.65 (until2p29(s17) | (~xuntil2p30(s16))),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6707, 1760, 6251])).
% 1.63/1.65 tff(6709,plain,
% 1.63/1.65 (~xuntil2p30(s16)),
% 1.63/1.65 inference(unit_resolution,[status(thm)],[6708, 6704])).
% 1.63/1.65 tff(6710,plain,
% 1.63/1.65 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))),
% 1.63/1.65 inference(rewrite,[status(thm)],[])).
% 1.63/1.65 tff(6711,plain,
% 1.63/1.65 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6712,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s16) | xuntil2p30(s16) | (~until2p29(s16))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6711, 6710])).
% 1.63/1.66 tff(6713,plain,
% 1.63/1.66 (xuntil2p30(s16) | (~until2p29(s16))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6712, 6236, 5623])).
% 1.63/1.66 tff(6714,plain,
% 1.63/1.66 (~until2p29(s16)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6713, 6709])).
% 1.63/1.66 tff(6715,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6716,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6717,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6716, 6715])).
% 1.63/1.66 tff(6718,plain,
% 1.63/1.66 (until2p29(s16) | (~xuntil2p30(s15))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6717, 1671, 6251])).
% 1.63/1.66 tff(6719,plain,
% 1.63/1.66 (~xuntil2p30(s15)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6718, 6714])).
% 1.63/1.66 tff(6720,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6721,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6722,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s15) | xuntil2p30(s15) | (~until2p29(s15))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6721, 6720])).
% 1.63/1.66 tff(6723,plain,
% 1.63/1.66 (xuntil2p30(s15) | (~until2p29(s15))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6722, 6236, 5274])).
% 1.63/1.66 tff(6724,plain,
% 1.63/1.66 (~until2p29(s15)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6723, 6719])).
% 1.63/1.66 tff(6725,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6726,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6727,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6726, 6725])).
% 1.63/1.66 tff(6728,plain,
% 1.63/1.66 (until2p29(s15) | (~xuntil2p30(s14))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6727, 1596, 6251])).
% 1.63/1.66 tff(6729,plain,
% 1.63/1.66 (~xuntil2p30(s14)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6728, 6724])).
% 1.63/1.66 tff(6730,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6731,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6732,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s14) | xuntil2p30(s14) | (~until2p29(s14))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6731, 6730])).
% 1.63/1.66 tff(6733,plain,
% 1.63/1.66 (xuntil2p30(s14) | (~until2p29(s14))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6732, 6236, 5283])).
% 1.63/1.66 tff(6734,plain,
% 1.63/1.66 (~until2p29(s14)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6733, 6729])).
% 1.63/1.66 tff(6735,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6736,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6737,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6736, 6735])).
% 1.63/1.66 tff(6738,plain,
% 1.63/1.66 (until2p29(s14) | (~xuntil2p30(s13))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6737, 1532, 6251])).
% 1.63/1.66 tff(6739,plain,
% 1.63/1.66 (~xuntil2p30(s13)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6738, 6734])).
% 1.63/1.66 tff(6740,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6741,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6742,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s13) | xuntil2p30(s13) | (~until2p29(s13))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6741, 6740])).
% 1.63/1.66 tff(6743,plain,
% 1.63/1.66 (xuntil2p30(s13) | (~until2p29(s13))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6742, 6236, 5287])).
% 1.63/1.66 tff(6744,plain,
% 1.63/1.66 (~until2p29(s13)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6743, 6739])).
% 1.63/1.66 tff(6745,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6746,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6747,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 1.63/1.66 tff(6748,plain,
% 1.63/1.66 (until2p29(s13) | (~xuntil2p30(s12))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6747, 1437, 6251])).
% 1.63/1.66 tff(6749,plain,
% 1.63/1.66 (~xuntil2p30(s12)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6748, 6744])).
% 1.63/1.66 tff(6750,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6751,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6752,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s12) | xuntil2p30(s12) | (~until2p29(s12))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6751, 6750])).
% 1.63/1.66 tff(6753,plain,
% 1.63/1.66 (xuntil2p30(s12) | (~until2p29(s12))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6752, 6236, 5569])).
% 1.63/1.66 tff(6754,plain,
% 1.63/1.66 (~until2p29(s12)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6753, 6749])).
% 1.63/1.66 tff(6755,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6756,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6757,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6756, 6755])).
% 1.63/1.66 tff(6758,plain,
% 1.63/1.66 (until2p29(s12) | (~xuntil2p30(s11))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6757, 1376, 6251])).
% 1.63/1.66 tff(6759,plain,
% 1.63/1.66 (~xuntil2p30(s11)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6758, 6754])).
% 1.63/1.66 tff(6760,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6761,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6762,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s11) | xuntil2p30(s11) | (~until2p29(s11))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6761, 6760])).
% 1.63/1.66 tff(6763,plain,
% 1.63/1.66 (xuntil2p30(s11) | (~until2p29(s11))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6762, 6236, 5303])).
% 1.63/1.66 tff(6764,plain,
% 1.63/1.66 (~until2p29(s11)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6763, 6759])).
% 1.63/1.66 tff(6765,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6766,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6767,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6766, 6765])).
% 1.63/1.66 tff(6768,plain,
% 1.63/1.66 (until2p29(s11) | (~xuntil2p30(s10))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6767, 1298, 6251])).
% 1.63/1.66 tff(6769,plain,
% 1.63/1.66 (~xuntil2p30(s10)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6768, 6764])).
% 1.63/1.66 tff(6770,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6771,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6772,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s10) | xuntil2p30(s10) | (~until2p29(s10))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6771, 6770])).
% 1.63/1.66 tff(6773,plain,
% 1.63/1.66 (xuntil2p30(s10) | (~until2p29(s10))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6772, 6236, 5312])).
% 1.63/1.66 tff(6774,plain,
% 1.63/1.66 (~until2p29(s10)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6773, 6769])).
% 1.63/1.66 tff(6775,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6776,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6777,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6776, 6775])).
% 1.63/1.66 tff(6778,plain,
% 1.63/1.66 (until2p29(s10) | (~xuntil2p30(s9))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6777, 1199, 6251])).
% 1.63/1.66 tff(6779,plain,
% 1.63/1.66 (~xuntil2p30(s9)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6778, 6774])).
% 1.63/1.66 tff(6780,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6781,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6782,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6781, 6780])).
% 1.63/1.66 tff(6783,plain,
% 1.63/1.66 (xuntil2p30(s9) | (~until2p29(s9))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6782, 6236, 5316])).
% 1.63/1.66 tff(6784,plain,
% 1.63/1.66 (~until2p29(s9)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6783, 6779])).
% 1.63/1.66 tff(6785,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6786,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6787,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6786, 6785])).
% 1.63/1.66 tff(6788,plain,
% 1.63/1.66 (until2p29(s9) | (~xuntil2p30(s8))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6787, 1132, 6251])).
% 1.63/1.66 tff(6789,plain,
% 1.63/1.66 (~xuntil2p30(s8)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6788, 6784])).
% 1.63/1.66 tff(6790,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6791,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6792,plain,
% 1.63/1.66 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6791, 6790])).
% 1.63/1.66 tff(6793,plain,
% 1.63/1.66 (xuntil2p30(s8) | (~until2p29(s8))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6792, 6236, 5515])).
% 1.63/1.66 tff(6794,plain,
% 1.63/1.66 (~until2p29(s8)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6793, 6789])).
% 1.63/1.66 tff(6795,plain,
% 1.63/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 1.63/1.66 inference(rewrite,[status(thm)],[])).
% 1.63/1.66 tff(6796,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 1.63/1.66 inference(quant_inst,[status(thm)],[])).
% 1.63/1.66 tff(6797,plain,
% 1.63/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7))),
% 1.63/1.66 inference(modus_ponens,[status(thm)],[6796, 6795])).
% 1.63/1.66 tff(6798,plain,
% 1.63/1.66 (until2p29(s8) | (~xuntil2p30(s7))),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6797, 1043, 6251])).
% 1.63/1.66 tff(6799,plain,
% 1.63/1.66 (~xuntil2p30(s7)),
% 1.63/1.66 inference(unit_resolution,[status(thm)],[6798, 6794])).
% 1.63/1.66 tff(6800,plain,
% 1.63/1.66 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6801,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6802,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6801, 6800])).
% 1.63/1.67 tff(6803,plain,
% 1.63/1.67 (xuntil2p30(s7) | (~until2p29(s7))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6802, 6236, 5332])).
% 1.63/1.67 tff(6804,plain,
% 1.63/1.67 (~until2p29(s7)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6803, 6799])).
% 1.63/1.67 tff(6805,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6806,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6807,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6806, 6805])).
% 1.63/1.67 tff(6808,plain,
% 1.63/1.67 (until2p29(s7) | (~xuntil2p30(s6))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6807, 958, 6251])).
% 1.63/1.67 tff(6809,plain,
% 1.63/1.67 (~xuntil2p30(s6)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6808, 6804])).
% 1.63/1.67 tff(6810,plain,
% 1.63/1.67 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6811,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6812,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6811, 6810])).
% 1.63/1.67 tff(6813,plain,
% 1.63/1.67 (xuntil2p30(s6) | (~until2p29(s6))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6812, 6236, 5341])).
% 1.63/1.67 tff(6814,plain,
% 1.63/1.67 (~until2p29(s6)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6813, 6809])).
% 1.63/1.67 tff(6815,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6816,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6817,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6816, 6815])).
% 1.63/1.67 tff(6818,plain,
% 1.63/1.67 (until2p29(s6) | (~xuntil2p30(s5))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6817, 874, 6251])).
% 1.63/1.67 tff(6819,plain,
% 1.63/1.67 (~xuntil2p30(s5)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6818, 6814])).
% 1.63/1.67 tff(6820,plain,
% 1.63/1.67 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6821,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6822,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6821, 6820])).
% 1.63/1.67 tff(6823,plain,
% 1.63/1.67 (xuntil2p30(s5) | (~until2p29(s5))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6822, 6236, 5345])).
% 1.63/1.67 tff(6824,plain,
% 1.63/1.67 (~until2p29(s5)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6823, 6819])).
% 1.63/1.67 tff(6825,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6826,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6827,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6826, 6825])).
% 1.63/1.67 tff(6828,plain,
% 1.63/1.67 (until2p29(s5) | (~xuntil2p30(s4))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6827, 708, 6251])).
% 1.63/1.67 tff(6829,plain,
% 1.63/1.67 (~xuntil2p30(s4)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6828, 6824])).
% 1.63/1.67 tff(6830,plain,
% 1.63/1.67 (((~![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)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6831,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6832,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6831, 6830])).
% 1.63/1.67 tff(6833,plain,
% 1.63/1.67 (xuntil2p30(s4) | (~until2p29(s4))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6832, 6236, 5461])).
% 1.63/1.67 tff(6834,plain,
% 1.63/1.67 (~until2p29(s4)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6833, 6829])).
% 1.63/1.67 tff(6835,plain,
% 1.63/1.67 (((~![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)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6836,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6837,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6836, 6835])).
% 1.63/1.67 tff(6838,plain,
% 1.63/1.67 (until2p29(s4) | (~xuntil2p30(s3))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6837, 599, 6251])).
% 1.63/1.67 tff(6839,plain,
% 1.63/1.67 (~xuntil2p30(s3)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6838, 6834])).
% 1.63/1.67 tff(6840,plain,
% 1.63/1.67 (((~![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)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6841,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6842,plain,
% 1.63/1.67 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6841, 6840])).
% 1.63/1.67 tff(6843,plain,
% 1.63/1.67 (xuntil2p30(s3) | (~until2p29(s3))),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6842, 6236, 5444])).
% 1.63/1.67 tff(6844,plain,
% 1.63/1.67 (~until2p29(s3)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6843, 6839])).
% 1.63/1.67 tff(6845,assumption,(~until2p29(s3)), introduced(assumption)).
% 1.63/1.67 tff(6846,assumption,(trans(s59, s3)), introduced(assumption)).
% 1.63/1.67 tff(6847,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s3) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s3)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s3) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s3)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6848,plain,
% 1.63/1.67 (((~trans(s59, s3)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s3)) <=> (until2p29(s3) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s3)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6849,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s3)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s3) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s3))))),
% 1.63/1.67 inference(monotonicity,[status(thm)],[6848])).
% 1.63/1.67 tff(6850,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s3)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s3) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s3)))),
% 1.63/1.67 inference(transitivity,[status(thm)],[6849, 6847])).
% 1.63/1.67 tff(6851,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s3)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s3))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6852,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s3) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s3))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6851, 6850])).
% 1.63/1.67 tff(6853,plain,
% 1.63/1.67 ($false),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6852, 6222, 6846, 6361, 6845, 6582])).
% 1.63/1.67 tff(6854,plain,((~trans(s59, s3)) | until2p29(s3) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.67 tff(6855,plain,
% 1.63/1.67 (~trans(s59, s3)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6854, 6844, 6212])).
% 1.63/1.67 tff(6856,assumption,(~until2p29(s43)), introduced(assumption)).
% 1.63/1.67 tff(6857,assumption,(trans(s59, s43)), introduced(assumption)).
% 1.63/1.67 tff(6858,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s43) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s43)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s43) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s43)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6859,plain,
% 1.63/1.67 (((~trans(s59, s43)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s43)) <=> (until2p29(s43) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s43)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6860,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s43)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s43) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s43))))),
% 1.63/1.67 inference(monotonicity,[status(thm)],[6859])).
% 1.63/1.67 tff(6861,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s43)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s43) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s43)))),
% 1.63/1.67 inference(transitivity,[status(thm)],[6860, 6858])).
% 1.63/1.67 tff(6862,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s43)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s43))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6863,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s43) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s43))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6862, 6861])).
% 1.63/1.67 tff(6864,plain,
% 1.63/1.67 ($false),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6863, 6222, 6857, 6361, 6856, 6582])).
% 1.63/1.67 tff(6865,plain,((~trans(s59, s43)) | until2p29(s43) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.67 tff(6866,plain,
% 1.63/1.67 (~trans(s59, s43)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6865, 6421, 6212])).
% 1.63/1.67 tff(6867,assumption,(~until2p29(s4)), introduced(assumption)).
% 1.63/1.67 tff(6868,assumption,(trans(s59, s4)), introduced(assumption)).
% 1.63/1.67 tff(6869,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s4) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s4)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s4) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s4)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6870,plain,
% 1.63/1.67 (((~trans(s59, s4)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s4)) <=> (until2p29(s4) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s4)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6871,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s4)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s4) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s4))))),
% 1.63/1.67 inference(monotonicity,[status(thm)],[6870])).
% 1.63/1.67 tff(6872,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s4)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s4) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s4)))),
% 1.63/1.67 inference(transitivity,[status(thm)],[6871, 6869])).
% 1.63/1.67 tff(6873,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s4)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s4))),
% 1.63/1.67 inference(quant_inst,[status(thm)],[])).
% 1.63/1.67 tff(6874,plain,
% 1.63/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s4) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s4))),
% 1.63/1.67 inference(modus_ponens,[status(thm)],[6873, 6872])).
% 1.63/1.67 tff(6875,plain,
% 1.63/1.67 ($false),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6874, 6222, 6868, 6361, 6867, 6582])).
% 1.63/1.67 tff(6876,plain,((~trans(s59, s4)) | until2p29(s4) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.67 tff(6877,plain,
% 1.63/1.67 (~trans(s59, s4)),
% 1.63/1.67 inference(unit_resolution,[status(thm)],[6876, 6834, 6212])).
% 1.63/1.67 tff(6878,assumption,(~until2p29(s17)), introduced(assumption)).
% 1.63/1.67 tff(6879,assumption,(trans(s59, s17)), introduced(assumption)).
% 1.63/1.67 tff(6880,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s17) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s17)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s17) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s17)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6881,plain,
% 1.63/1.67 (((~trans(s59, s17)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s17)) <=> (until2p29(s17) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s17)))),
% 1.63/1.67 inference(rewrite,[status(thm)],[])).
% 1.63/1.67 tff(6882,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s17)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s17) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s17))))),
% 1.63/1.67 inference(monotonicity,[status(thm)],[6881])).
% 1.63/1.67 tff(6883,plain,
% 1.63/1.67 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s17)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s17) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s17)))),
% 1.63/1.68 inference(transitivity,[status(thm)],[6882, 6880])).
% 1.63/1.68 tff(6884,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s17)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s17))),
% 1.63/1.68 inference(quant_inst,[status(thm)],[])).
% 1.63/1.68 tff(6885,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s17) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s17))),
% 1.63/1.68 inference(modus_ponens,[status(thm)],[6884, 6883])).
% 1.63/1.68 tff(6886,plain,
% 1.63/1.68 ($false),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6885, 6222, 6879, 6361, 6878, 6582])).
% 1.63/1.68 tff(6887,plain,((~trans(s59, s17)) | until2p29(s17) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.68 tff(6888,plain,
% 1.63/1.68 (~trans(s59, s17)),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6887, 6704, 6212])).
% 1.63/1.68 tff(6889,plain,
% 1.63/1.68 (((~![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)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6890,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 1.63/1.68 inference(quant_inst,[status(thm)],[])).
% 1.63/1.68 tff(6891,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2))),
% 1.63/1.68 inference(modus_ponens,[status(thm)],[6890, 6889])).
% 1.63/1.68 tff(6892,plain,
% 1.63/1.68 (until2p29(s3) | (~xuntil2p30(s2))),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6891, 480, 6251])).
% 1.63/1.68 tff(6893,plain,
% 1.63/1.68 (~xuntil2p30(s2)),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6892, 6844])).
% 1.63/1.68 tff(6894,plain,
% 1.63/1.68 (((~![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)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6895,plain,
% 1.63/1.68 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 1.63/1.68 inference(quant_inst,[status(thm)],[])).
% 1.63/1.68 tff(6896,plain,
% 1.63/1.68 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2))),
% 1.63/1.68 inference(modus_ponens,[status(thm)],[6895, 6894])).
% 1.63/1.68 tff(6897,plain,
% 1.63/1.68 (xuntil2p30(s2) | (~until2p29(s2))),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6896, 6236, 5366])).
% 1.63/1.68 tff(6898,plain,
% 1.63/1.68 (~until2p29(s2)),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6897, 6893])).
% 1.63/1.68 tff(6899,assumption,(~until2p29(s2)), introduced(assumption)).
% 1.63/1.68 tff(6900,assumption,(trans(s59, s2)), introduced(assumption)).
% 1.63/1.68 tff(6901,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s2) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s2)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s2) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s2)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6902,plain,
% 1.63/1.68 (((~trans(s59, s2)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s2)) <=> (until2p29(s2) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s2)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6903,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s2)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s2) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s2))))),
% 1.63/1.68 inference(monotonicity,[status(thm)],[6902])).
% 1.63/1.68 tff(6904,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s2)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s2) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s2)))),
% 1.63/1.68 inference(transitivity,[status(thm)],[6903, 6901])).
% 1.63/1.68 tff(6905,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s2)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s2))),
% 1.63/1.68 inference(quant_inst,[status(thm)],[])).
% 1.63/1.68 tff(6906,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s2) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s2))),
% 1.63/1.68 inference(modus_ponens,[status(thm)],[6905, 6904])).
% 1.63/1.68 tff(6907,plain,
% 1.63/1.68 ($false),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6906, 6222, 6900, 6361, 6899, 6582])).
% 1.63/1.68 tff(6908,plain,((~trans(s59, s2)) | until2p29(s2) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.68 tff(6909,plain,
% 1.63/1.68 (~trans(s59, s2)),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6908, 6898, 6212])).
% 1.63/1.68 tff(6910,assumption,(~until2p29(s8)), introduced(assumption)).
% 1.63/1.68 tff(6911,assumption,(trans(s59, s8)), introduced(assumption)).
% 1.63/1.68 tff(6912,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s8) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s8)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s8) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s8)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6913,plain,
% 1.63/1.68 (((~trans(s59, s8)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s8)) <=> (until2p29(s8) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s8)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6914,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s8)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s8) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s8))))),
% 1.63/1.68 inference(monotonicity,[status(thm)],[6913])).
% 1.63/1.68 tff(6915,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s8)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s8) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s8)))),
% 1.63/1.68 inference(transitivity,[status(thm)],[6914, 6912])).
% 1.63/1.68 tff(6916,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s8)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s8))),
% 1.63/1.68 inference(quant_inst,[status(thm)],[])).
% 1.63/1.68 tff(6917,plain,
% 1.63/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s8) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s8))),
% 1.63/1.68 inference(modus_ponens,[status(thm)],[6916, 6915])).
% 1.63/1.68 tff(6918,plain,
% 1.63/1.68 ($false),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6917, 6222, 6911, 6361, 6910, 6582])).
% 1.63/1.68 tff(6919,plain,((~trans(s59, s8)) | until2p29(s8) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.68 tff(6920,plain,
% 1.63/1.68 (~trans(s59, s8)),
% 1.63/1.68 inference(unit_resolution,[status(thm)],[6919, 6794, 6212])).
% 1.63/1.68 tff(6921,assumption,(~until2p29(s25)), introduced(assumption)).
% 1.63/1.68 tff(6922,assumption,(trans(s59, s25)), introduced(assumption)).
% 1.63/1.68 tff(6923,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s25) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s25)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s25) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s25)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6924,plain,
% 1.63/1.68 (((~trans(s59, s25)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s25)) <=> (until2p29(s25) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s25)))),
% 1.63/1.68 inference(rewrite,[status(thm)],[])).
% 1.63/1.68 tff(6925,plain,
% 1.63/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s25)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s25) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s25))))),
% 1.66/1.68 inference(monotonicity,[status(thm)],[6924])).
% 1.66/1.68 tff(6926,plain,
% 1.66/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s25)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s25) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s25)))),
% 1.66/1.68 inference(transitivity,[status(thm)],[6925, 6923])).
% 1.66/1.68 tff(6927,plain,
% 1.66/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s25)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s25))),
% 1.66/1.68 inference(quant_inst,[status(thm)],[])).
% 1.66/1.68 tff(6928,plain,
% 1.66/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s25) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s25))),
% 1.66/1.68 inference(modus_ponens,[status(thm)],[6927, 6926])).
% 1.66/1.68 tff(6929,plain,
% 1.66/1.68 ($false),
% 1.66/1.68 inference(unit_resolution,[status(thm)],[6928, 6222, 6922, 6361, 6921, 6582])).
% 1.66/1.68 tff(6930,plain,((~trans(s59, s25)) | until2p29(s25) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.68 tff(6931,plain,
% 1.66/1.68 (~trans(s59, s25)),
% 1.66/1.68 inference(unit_resolution,[status(thm)],[6930, 6624, 6212])).
% 1.66/1.68 tff(6932,assumption,(~until2p29(s35)), introduced(assumption)).
% 1.66/1.68 tff(6933,assumption,(trans(s59, s35)), introduced(assumption)).
% 1.66/1.68 tff(6934,plain,
% 1.66/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s35) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s35)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s35) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s35)))),
% 1.66/1.68 inference(rewrite,[status(thm)],[])).
% 1.66/1.68 tff(6935,plain,
% 1.66/1.68 (((~trans(s59, s35)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s35)) <=> (until2p29(s35) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s35)))),
% 1.66/1.68 inference(rewrite,[status(thm)],[])).
% 1.66/1.68 tff(6936,plain,
% 1.66/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s35)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s35) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s35))))),
% 1.66/1.68 inference(monotonicity,[status(thm)],[6935])).
% 1.66/1.68 tff(6937,plain,
% 1.66/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s35)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s35) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s35)))),
% 1.66/1.68 inference(transitivity,[status(thm)],[6936, 6934])).
% 1.66/1.68 tff(6938,plain,
% 1.66/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s35)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s35))),
% 1.66/1.68 inference(quant_inst,[status(thm)],[])).
% 1.66/1.68 tff(6939,plain,
% 1.66/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s35) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s35))),
% 1.66/1.68 inference(modus_ponens,[status(thm)],[6938, 6937])).
% 1.66/1.68 tff(6940,plain,
% 1.66/1.68 ($false),
% 1.66/1.68 inference(unit_resolution,[status(thm)],[6939, 6222, 6933, 6361, 6932, 6582])).
% 1.66/1.68 tff(6941,plain,((~trans(s59, s35)) | until2p29(s35) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.68 tff(6942,plain,
% 1.66/1.68 (~trans(s59, s35)),
% 1.66/1.68 inference(unit_resolution,[status(thm)],[6941, 6501, 6212])).
% 1.66/1.68 tff(6943,assumption,(~until2p29(s36)), introduced(assumption)).
% 1.66/1.68 tff(6944,assumption,(trans(s59, s36)), introduced(assumption)).
% 1.66/1.68 tff(6945,plain,
% 1.66/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s36) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s36)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s36) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s36)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6946,plain,
% 1.66/1.69 (((~trans(s59, s36)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s36)) <=> (until2p29(s36) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s36)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6947,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s36)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s36) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s36))))),
% 1.66/1.69 inference(monotonicity,[status(thm)],[6946])).
% 1.66/1.69 tff(6948,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s36)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s36) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s36)))),
% 1.66/1.69 inference(transitivity,[status(thm)],[6947, 6945])).
% 1.66/1.69 tff(6949,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s36)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s36))),
% 1.66/1.69 inference(quant_inst,[status(thm)],[])).
% 1.66/1.69 tff(6950,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s36) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s36))),
% 1.66/1.69 inference(modus_ponens,[status(thm)],[6949, 6948])).
% 1.66/1.69 tff(6951,plain,
% 1.66/1.69 ($false),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6950, 6222, 6944, 6361, 6943, 6582])).
% 1.66/1.69 tff(6952,plain,((~trans(s59, s36)) | until2p29(s36) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.69 tff(6953,plain,
% 1.66/1.69 (~trans(s59, s36)),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6952, 6491, 6212])).
% 1.66/1.69 tff(6954,assumption,(~until2p29(s38)), introduced(assumption)).
% 1.66/1.69 tff(6955,assumption,(trans(s59, s38)), introduced(assumption)).
% 1.66/1.69 tff(6956,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s38) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s38)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s38) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s38)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6957,plain,
% 1.66/1.69 (((~trans(s59, s38)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s38)) <=> (until2p29(s38) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s38)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6958,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s38)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s38) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s38))))),
% 1.66/1.69 inference(monotonicity,[status(thm)],[6957])).
% 1.66/1.69 tff(6959,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s38)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s38) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s38)))),
% 1.66/1.69 inference(transitivity,[status(thm)],[6958, 6956])).
% 1.66/1.69 tff(6960,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s38)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s38))),
% 1.66/1.69 inference(quant_inst,[status(thm)],[])).
% 1.66/1.69 tff(6961,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s38) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s38))),
% 1.66/1.69 inference(modus_ponens,[status(thm)],[6960, 6959])).
% 1.66/1.69 tff(6962,plain,
% 1.66/1.69 ($false),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6961, 6222, 6955, 6361, 6954, 6582])).
% 1.66/1.69 tff(6963,plain,((~trans(s59, s38)) | until2p29(s38) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.69 tff(6964,plain,
% 1.66/1.69 (~trans(s59, s38)),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6963, 6471, 6212])).
% 1.66/1.69 tff(6965,assumption,(~until2p29(s26)), introduced(assumption)).
% 1.66/1.69 tff(6966,assumption,(trans(s59, s26)), introduced(assumption)).
% 1.66/1.69 tff(6967,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s26) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s26)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s26) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s26)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6968,plain,
% 1.66/1.69 (((~trans(s59, s26)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s26)) <=> (until2p29(s26) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s26)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6969,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s26)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s26) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s26))))),
% 1.66/1.69 inference(monotonicity,[status(thm)],[6968])).
% 1.66/1.69 tff(6970,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s26)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s26) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s26)))),
% 1.66/1.69 inference(transitivity,[status(thm)],[6969, 6967])).
% 1.66/1.69 tff(6971,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s26)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s26))),
% 1.66/1.69 inference(quant_inst,[status(thm)],[])).
% 1.66/1.69 tff(6972,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s26) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s26))),
% 1.66/1.69 inference(modus_ponens,[status(thm)],[6971, 6970])).
% 1.66/1.69 tff(6973,plain,
% 1.66/1.69 ($false),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6972, 6222, 6966, 6361, 6965, 6582])).
% 1.66/1.69 tff(6974,plain,((~trans(s59, s26)) | until2p29(s26) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.69 tff(6975,plain,
% 1.66/1.69 (~trans(s59, s26)),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6974, 6614, 6212])).
% 1.66/1.69 tff(6976,assumption,(~until2p29(s18)), introduced(assumption)).
% 1.66/1.69 tff(6977,assumption,(trans(s59, s18)), introduced(assumption)).
% 1.66/1.69 tff(6978,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s18) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s18)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s18) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s18)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6979,plain,
% 1.66/1.69 (((~trans(s59, s18)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s18)) <=> (until2p29(s18) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s18)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6980,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s18)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s18) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s18))))),
% 1.66/1.69 inference(monotonicity,[status(thm)],[6979])).
% 1.66/1.69 tff(6981,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s18)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s18) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s18)))),
% 1.66/1.69 inference(transitivity,[status(thm)],[6980, 6978])).
% 1.66/1.69 tff(6982,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s18)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s18))),
% 1.66/1.69 inference(quant_inst,[status(thm)],[])).
% 1.66/1.69 tff(6983,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s18) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s18))),
% 1.66/1.69 inference(modus_ponens,[status(thm)],[6982, 6981])).
% 1.66/1.69 tff(6984,plain,
% 1.66/1.69 ($false),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6983, 6222, 6977, 6361, 6976, 6582])).
% 1.66/1.69 tff(6985,plain,((~trans(s59, s18)) | until2p29(s18) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.69 tff(6986,plain,
% 1.66/1.69 (~trans(s59, s18)),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6985, 6694, 6212])).
% 1.66/1.69 tff(6987,assumption,(~until2p29(s52)), introduced(assumption)).
% 1.66/1.69 tff(6988,assumption,(trans(s59, s52)), introduced(assumption)).
% 1.66/1.69 tff(6989,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s52) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s52)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s52) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s52)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6990,plain,
% 1.66/1.69 (((~trans(s59, s52)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s52)) <=> (until2p29(s52) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s52)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(6991,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s52)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s52) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s52))))),
% 1.66/1.69 inference(monotonicity,[status(thm)],[6990])).
% 1.66/1.69 tff(6992,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s52)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s52) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s52)))),
% 1.66/1.69 inference(transitivity,[status(thm)],[6991, 6989])).
% 1.66/1.69 tff(6993,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s52)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s52))),
% 1.66/1.69 inference(quant_inst,[status(thm)],[])).
% 1.66/1.69 tff(6994,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s52) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s52))),
% 1.66/1.69 inference(modus_ponens,[status(thm)],[6993, 6992])).
% 1.66/1.69 tff(6995,plain,
% 1.66/1.69 ($false),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6994, 6222, 6988, 6361, 6987, 6582])).
% 1.66/1.69 tff(6996,plain,((~trans(s59, s52)) | until2p29(s52) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.69 tff(6997,plain,
% 1.66/1.69 (~trans(s59, s52)),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[6996, 6321, 6212])).
% 1.66/1.69 tff(6998,assumption,(~until2p29(s21)), introduced(assumption)).
% 1.66/1.69 tff(6999,assumption,(trans(s59, s21)), introduced(assumption)).
% 1.66/1.69 tff(7000,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s21) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s21)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s21) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s21)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(7001,plain,
% 1.66/1.69 (((~trans(s59, s21)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s21)) <=> (until2p29(s21) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s21)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(7002,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s21)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s21) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s21))))),
% 1.66/1.69 inference(monotonicity,[status(thm)],[7001])).
% 1.66/1.69 tff(7003,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s21)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s21) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s21)))),
% 1.66/1.69 inference(transitivity,[status(thm)],[7002, 7000])).
% 1.66/1.69 tff(7004,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s21)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s21))),
% 1.66/1.69 inference(quant_inst,[status(thm)],[])).
% 1.66/1.69 tff(7005,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s21) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s21))),
% 1.66/1.69 inference(modus_ponens,[status(thm)],[7004, 7003])).
% 1.66/1.69 tff(7006,plain,
% 1.66/1.69 ($false),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[7005, 6222, 6999, 6361, 6998, 6582])).
% 1.66/1.69 tff(7007,plain,((~trans(s59, s21)) | until2p29(s21) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.69 tff(7008,plain,
% 1.66/1.69 (~trans(s59, s21)),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[7007, 6664, 6212])).
% 1.66/1.69 tff(7009,assumption,(~until2p29(s50)), introduced(assumption)).
% 1.66/1.69 tff(7010,assumption,(trans(s59, s50)), introduced(assumption)).
% 1.66/1.69 tff(7011,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s50) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s50)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s50) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s50)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(7012,plain,
% 1.66/1.69 (((~trans(s59, s50)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s50)) <=> (until2p29(s50) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s50)))),
% 1.66/1.69 inference(rewrite,[status(thm)],[])).
% 1.66/1.69 tff(7013,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s50)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s50) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s50))))),
% 1.66/1.69 inference(monotonicity,[status(thm)],[7012])).
% 1.66/1.69 tff(7014,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s50)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s50) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s50)))),
% 1.66/1.69 inference(transitivity,[status(thm)],[7013, 7011])).
% 1.66/1.69 tff(7015,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s50)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s50))),
% 1.66/1.69 inference(quant_inst,[status(thm)],[])).
% 1.66/1.69 tff(7016,plain,
% 1.66/1.69 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s50) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s50))),
% 1.66/1.69 inference(modus_ponens,[status(thm)],[7015, 7014])).
% 1.66/1.69 tff(7017,plain,
% 1.66/1.69 ($false),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[7016, 6222, 7010, 6361, 7009, 6582])).
% 1.66/1.69 tff(7018,plain,((~trans(s59, s50)) | until2p29(s50) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.69 tff(7019,plain,
% 1.66/1.69 (~trans(s59, s50)),
% 1.66/1.69 inference(unit_resolution,[status(thm)],[7018, 6341, 6212])).
% 1.66/1.69 tff(7020,assumption,(~until2p29(s31)), introduced(assumption)).
% 1.66/1.69 tff(7021,assumption,(trans(s59, s31)), introduced(assumption)).
% 1.66/1.69 tff(7022,plain,
% 1.66/1.69 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s31) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s31)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s31) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s31)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7023,plain,
% 1.66/1.70 (((~trans(s59, s31)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s31)) <=> (until2p29(s31) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s31)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7024,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s31)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s31) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s31))))),
% 1.66/1.70 inference(monotonicity,[status(thm)],[7023])).
% 1.66/1.70 tff(7025,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s31)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s31) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s31)))),
% 1.66/1.70 inference(transitivity,[status(thm)],[7024, 7022])).
% 1.66/1.70 tff(7026,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s31)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s31))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7027,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s31) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s31))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7026, 7025])).
% 1.66/1.70 tff(7028,plain,
% 1.66/1.70 ($false),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7027, 6222, 7021, 6361, 7020, 6582])).
% 1.66/1.70 tff(7029,plain,((~trans(s59, s31)) | until2p29(s31) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.70 tff(7030,plain,
% 1.66/1.70 (~trans(s59, s31)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7029, 6541, 6212])).
% 1.66/1.70 tff(7031,assumption,(~until2p29(s32)), introduced(assumption)).
% 1.66/1.70 tff(7032,assumption,(trans(s59, s32)), introduced(assumption)).
% 1.66/1.70 tff(7033,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s32) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s32)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s32) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s32)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7034,plain,
% 1.66/1.70 (((~trans(s59, s32)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s32)) <=> (until2p29(s32) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s32)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7035,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s32)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s32) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s32))))),
% 1.66/1.70 inference(monotonicity,[status(thm)],[7034])).
% 1.66/1.70 tff(7036,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s32)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s32) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s32)))),
% 1.66/1.70 inference(transitivity,[status(thm)],[7035, 7033])).
% 1.66/1.70 tff(7037,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s32)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s32))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7038,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s32) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s32))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7037, 7036])).
% 1.66/1.70 tff(7039,plain,
% 1.66/1.70 ($false),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7038, 6222, 7032, 6361, 7031, 6582])).
% 1.66/1.70 tff(7040,plain,((~trans(s59, s32)) | until2p29(s32) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.70 tff(7041,plain,
% 1.66/1.70 (~trans(s59, s32)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7040, 6531, 6212])).
% 1.66/1.70 tff(7042,assumption,(~until2p29(s34)), introduced(assumption)).
% 1.66/1.70 tff(7043,assumption,(trans(s59, s34)), introduced(assumption)).
% 1.66/1.70 tff(7044,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s34) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s34)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s34) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s34)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7045,plain,
% 1.66/1.70 (((~trans(s59, s34)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s34)) <=> (until2p29(s34) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s34)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7046,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s34)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s34) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s34))))),
% 1.66/1.70 inference(monotonicity,[status(thm)],[7045])).
% 1.66/1.70 tff(7047,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s34)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s34) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s34)))),
% 1.66/1.70 inference(transitivity,[status(thm)],[7046, 7044])).
% 1.66/1.70 tff(7048,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s34)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s34))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7049,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s34) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s34))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7048, 7047])).
% 1.66/1.70 tff(7050,plain,
% 1.66/1.70 ($false),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7049, 6222, 7043, 6361, 7042, 6582])).
% 1.66/1.70 tff(7051,plain,((~trans(s59, s34)) | until2p29(s34) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.70 tff(7052,plain,
% 1.66/1.70 (~trans(s59, s34)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7051, 6511, 6212])).
% 1.66/1.70 tff(7053,assumption,(~until2p29(s55)), introduced(assumption)).
% 1.66/1.70 tff(7054,assumption,(trans(s59, s55)), introduced(assumption)).
% 1.66/1.70 tff(7055,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s55) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s55)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s55) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s55)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7056,plain,
% 1.66/1.70 (((~trans(s59, s55)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s55)) <=> (until2p29(s55) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s55)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7057,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s55)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s55) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s55))))),
% 1.66/1.70 inference(monotonicity,[status(thm)],[7056])).
% 1.66/1.70 tff(7058,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s55)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s55) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s55)))),
% 1.66/1.70 inference(transitivity,[status(thm)],[7057, 7055])).
% 1.66/1.70 tff(7059,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s55)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s55))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7060,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s55) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s55))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7059, 7058])).
% 1.66/1.70 tff(7061,plain,
% 1.66/1.70 ($false),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7060, 6222, 7054, 6361, 7053, 6582])).
% 1.66/1.70 tff(7062,plain,((~trans(s59, s55)) | until2p29(s55) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.70 tff(7063,plain,
% 1.66/1.70 (~trans(s59, s55)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7062, 6291, 6212])).
% 1.66/1.70 tff(7064,assumption,(~until2p29(s16)), introduced(assumption)).
% 1.66/1.70 tff(7065,assumption,(trans(s59, s16)), introduced(assumption)).
% 1.66/1.70 tff(7066,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s16) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s16)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s16) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s16)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7067,plain,
% 1.66/1.70 (((~trans(s59, s16)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s16)) <=> (until2p29(s16) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s16)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7068,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s16)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s16) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s16))))),
% 1.66/1.70 inference(monotonicity,[status(thm)],[7067])).
% 1.66/1.70 tff(7069,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s16)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s16) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s16)))),
% 1.66/1.70 inference(transitivity,[status(thm)],[7068, 7066])).
% 1.66/1.70 tff(7070,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s16)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s16))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7071,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s16) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s16))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7070, 7069])).
% 1.66/1.70 tff(7072,plain,
% 1.66/1.70 ($false),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7071, 6222, 7065, 6361, 7064, 6582])).
% 1.66/1.70 tff(7073,plain,((~trans(s59, s16)) | until2p29(s16) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.70 tff(7074,plain,
% 1.66/1.70 (~trans(s59, s16)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7073, 6714, 6212])).
% 1.66/1.70 tff(7075,assumption,(~until2p29(s12)), introduced(assumption)).
% 1.66/1.70 tff(7076,assumption,(trans(s59, s12)), introduced(assumption)).
% 1.66/1.70 tff(7077,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s12) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s12)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s12) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s12)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7078,plain,
% 1.66/1.70 (((~trans(s59, s12)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s12)) <=> (until2p29(s12) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s12)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7079,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s12)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s12) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s12))))),
% 1.66/1.70 inference(monotonicity,[status(thm)],[7078])).
% 1.66/1.70 tff(7080,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s12)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s12) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s12)))),
% 1.66/1.70 inference(transitivity,[status(thm)],[7079, 7077])).
% 1.66/1.70 tff(7081,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s12)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s12))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7082,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s12) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s12))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7081, 7080])).
% 1.66/1.70 tff(7083,plain,
% 1.66/1.70 ($false),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7082, 6222, 7076, 6361, 7075, 6582])).
% 1.66/1.70 tff(7084,plain,((~trans(s59, s12)) | until2p29(s12) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.70 tff(7085,plain,
% 1.66/1.70 (~trans(s59, s12)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7084, 6754, 6212])).
% 1.66/1.70 tff(7086,plain,
% 1.66/1.70 (((~![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)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7087,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7088,plain,
% 1.66/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7087, 7086])).
% 1.66/1.70 tff(7089,plain,
% 1.66/1.70 (until2p29(s2) | (~xuntil2p30(s1))),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7088, 278, 6251])).
% 1.66/1.70 tff(7090,plain,
% 1.66/1.70 (~xuntil2p30(s1)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7089, 6898])).
% 1.66/1.70 tff(7091,plain,
% 1.66/1.70 (((~![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)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7092,plain,
% 1.66/1.70 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 1.66/1.70 inference(quant_inst,[status(thm)],[])).
% 1.66/1.70 tff(7093,plain,
% 1.66/1.70 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1))),
% 1.66/1.70 inference(modus_ponens,[status(thm)],[7092, 7091])).
% 1.66/1.70 tff(7094,plain,
% 1.66/1.70 (xuntil2p30(s1) | (~until2p29(s1))),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7093, 6236, 5375])).
% 1.66/1.70 tff(7095,plain,
% 1.66/1.70 (~until2p29(s1)),
% 1.66/1.70 inference(unit_resolution,[status(thm)],[7094, 7090])).
% 1.66/1.70 tff(7096,assumption,(~until2p29(s1)), introduced(assumption)).
% 1.66/1.70 tff(7097,assumption,(trans(s59, s1)), introduced(assumption)).
% 1.66/1.70 tff(7098,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s1) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s1)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s1) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s1)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7099,plain,
% 1.66/1.70 (((~trans(s59, s1)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s1)) <=> (until2p29(s1) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s1)))),
% 1.66/1.70 inference(rewrite,[status(thm)],[])).
% 1.66/1.70 tff(7100,plain,
% 1.66/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s1)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s1) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s1))))),
% 1.66/1.70 inference(monotonicity,[status(thm)],[7099])).
% 1.66/1.70 tff(7101,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s1)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s1) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s1)))),
% 1.66/1.71 inference(transitivity,[status(thm)],[7100, 7098])).
% 1.66/1.71 tff(7102,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s1)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s1))),
% 1.66/1.71 inference(quant_inst,[status(thm)],[])).
% 1.66/1.71 tff(7103,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s1) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s1))),
% 1.66/1.71 inference(modus_ponens,[status(thm)],[7102, 7101])).
% 1.66/1.71 tff(7104,plain,
% 1.66/1.71 ($false),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7103, 6222, 7097, 6361, 7096, 6582])).
% 1.66/1.71 tff(7105,plain,((~trans(s59, s1)) | until2p29(s1) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.71 tff(7106,plain,
% 1.66/1.71 (~trans(s59, s1)),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7105, 7095, 6212])).
% 1.66/1.71 tff(7107,assumption,(~until2p29(s51)), introduced(assumption)).
% 1.66/1.71 tff(7108,assumption,(trans(s59, s51)), introduced(assumption)).
% 1.66/1.71 tff(7109,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s51) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s51)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s51) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s51)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7110,plain,
% 1.66/1.71 (((~trans(s59, s51)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s51)) <=> (until2p29(s51) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s51)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7111,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s51)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s51) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s51))))),
% 1.66/1.71 inference(monotonicity,[status(thm)],[7110])).
% 1.66/1.71 tff(7112,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s51)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s51) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s51)))),
% 1.66/1.71 inference(transitivity,[status(thm)],[7111, 7109])).
% 1.66/1.71 tff(7113,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s51)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s51))),
% 1.66/1.71 inference(quant_inst,[status(thm)],[])).
% 1.66/1.71 tff(7114,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s51) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s51))),
% 1.66/1.71 inference(modus_ponens,[status(thm)],[7113, 7112])).
% 1.66/1.71 tff(7115,plain,
% 1.66/1.71 ($false),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7114, 6222, 7108, 6361, 7107, 6582])).
% 1.66/1.71 tff(7116,plain,((~trans(s59, s51)) | until2p29(s51) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.71 tff(7117,plain,
% 1.66/1.71 (~trans(s59, s51)),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7116, 6331, 6212])).
% 1.66/1.71 tff(7118,assumption,(~until2p29(s33)), introduced(assumption)).
% 1.66/1.71 tff(7119,assumption,(trans(s59, s33)), introduced(assumption)).
% 1.66/1.71 tff(7120,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s33) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s33)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s33) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s33)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7121,plain,
% 1.66/1.71 (((~trans(s59, s33)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s33)) <=> (until2p29(s33) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s33)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7122,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s33)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s33) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s33))))),
% 1.66/1.71 inference(monotonicity,[status(thm)],[7121])).
% 1.66/1.71 tff(7123,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s33)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s33) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s33)))),
% 1.66/1.71 inference(transitivity,[status(thm)],[7122, 7120])).
% 1.66/1.71 tff(7124,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s33)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s33))),
% 1.66/1.71 inference(quant_inst,[status(thm)],[])).
% 1.66/1.71 tff(7125,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s33) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s33))),
% 1.66/1.71 inference(modus_ponens,[status(thm)],[7124, 7123])).
% 1.66/1.71 tff(7126,plain,
% 1.66/1.71 ($false),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7125, 6222, 7119, 6361, 7118, 6582])).
% 1.66/1.71 tff(7127,plain,((~trans(s59, s33)) | until2p29(s33) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.71 tff(7128,plain,
% 1.66/1.71 (~trans(s59, s33)),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7127, 6521, 6212])).
% 1.66/1.71 tff(7129,assumption,(~until2p29(s48)), introduced(assumption)).
% 1.66/1.71 tff(7130,assumption,(trans(s59, s48)), introduced(assumption)).
% 1.66/1.71 tff(7131,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s48) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s48)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s48) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s48)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7132,plain,
% 1.66/1.71 (((~trans(s59, s48)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s48)) <=> (until2p29(s48) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s48)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7133,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s48)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s48) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s48))))),
% 1.66/1.71 inference(monotonicity,[status(thm)],[7132])).
% 1.66/1.71 tff(7134,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s48)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s48) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s48)))),
% 1.66/1.71 inference(transitivity,[status(thm)],[7133, 7131])).
% 1.66/1.71 tff(7135,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s48)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s48))),
% 1.66/1.71 inference(quant_inst,[status(thm)],[])).
% 1.66/1.71 tff(7136,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s48) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s48))),
% 1.66/1.71 inference(modus_ponens,[status(thm)],[7135, 7134])).
% 1.66/1.71 tff(7137,plain,
% 1.66/1.71 ($false),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7136, 6222, 7130, 6361, 7129, 6582])).
% 1.66/1.71 tff(7138,plain,((~trans(s59, s48)) | until2p29(s48) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.71 tff(7139,plain,
% 1.66/1.71 (~trans(s59, s48)),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7138, 6371, 6212])).
% 1.66/1.71 tff(7140,assumption,(~until2p29(s42)), introduced(assumption)).
% 1.66/1.71 tff(7141,assumption,(trans(s59, s42)), introduced(assumption)).
% 1.66/1.71 tff(7142,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s42) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s42)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s42) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s42)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7143,plain,
% 1.66/1.71 (((~trans(s59, s42)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s42)) <=> (until2p29(s42) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s42)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7144,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s42)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s42) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s42))))),
% 1.66/1.71 inference(monotonicity,[status(thm)],[7143])).
% 1.66/1.71 tff(7145,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s42)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s42) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s42)))),
% 1.66/1.71 inference(transitivity,[status(thm)],[7144, 7142])).
% 1.66/1.71 tff(7146,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s42)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s42))),
% 1.66/1.71 inference(quant_inst,[status(thm)],[])).
% 1.66/1.71 tff(7147,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s42) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s42))),
% 1.66/1.71 inference(modus_ponens,[status(thm)],[7146, 7145])).
% 1.66/1.71 tff(7148,plain,
% 1.66/1.71 ($false),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7147, 6222, 7141, 6361, 7140, 6582])).
% 1.66/1.71 tff(7149,plain,((~trans(s59, s42)) | until2p29(s42) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.71 tff(7150,plain,
% 1.66/1.71 (~trans(s59, s42)),
% 1.66/1.71 inference(unit_resolution,[status(thm)],[7149, 6431, 6212])).
% 1.66/1.71 tff(7151,assumption,(~until2p29(s20)), introduced(assumption)).
% 1.66/1.71 tff(7152,assumption,(trans(s59, s20)), introduced(assumption)).
% 1.66/1.71 tff(7153,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s20) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s20)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s20) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s20)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7154,plain,
% 1.66/1.71 (((~trans(s59, s20)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s20)) <=> (until2p29(s20) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s20)))),
% 1.66/1.71 inference(rewrite,[status(thm)],[])).
% 1.66/1.71 tff(7155,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s20)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s20) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s20))))),
% 1.66/1.71 inference(monotonicity,[status(thm)],[7154])).
% 1.66/1.71 tff(7156,plain,
% 1.66/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s20)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s20) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s20)))),
% 1.66/1.71 inference(transitivity,[status(thm)],[7155, 7153])).
% 1.66/1.71 tff(7157,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s20)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s20))),
% 1.66/1.71 inference(quant_inst,[status(thm)],[])).
% 1.66/1.71 tff(7158,plain,
% 1.66/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s20) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s20))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7157, 7156])).
% 1.66/1.72 tff(7159,plain,
% 1.66/1.72 ($false),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7158, 6222, 7152, 6361, 7151, 6582])).
% 1.66/1.72 tff(7160,plain,((~trans(s59, s20)) | until2p29(s20) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.72 tff(7161,plain,
% 1.66/1.72 (~trans(s59, s20)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7160, 6674, 6212])).
% 1.66/1.72 tff(7162,plain,
% 1.66/1.72 (((~![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)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7163,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7164,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 1.66/1.72 tff(7165,plain,
% 1.66/1.72 (until2p29(s1) | (~xuntil2p30(s0))),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7164, 35, 6251])).
% 1.66/1.72 tff(7166,plain,
% 1.66/1.72 (~xuntil2p30(s0)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7165, 7095])).
% 1.66/1.72 tff(7167,plain,
% 1.66/1.72 (((~![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)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7168,plain,
% 1.66/1.72 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7169,plain,
% 1.66/1.72 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7168, 7167])).
% 1.66/1.72 tff(7170,plain,
% 1.66/1.72 (xuntil2p30(s0) | (~until2p29(s0))),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7169, 6236, 5379])).
% 1.66/1.72 tff(7171,plain,
% 1.66/1.72 (~until2p29(s0)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7170, 7166])).
% 1.66/1.72 tff(7172,assumption,(~until2p29(s0)), introduced(assumption)).
% 1.66/1.72 tff(7173,assumption,(trans(s59, s0)), introduced(assumption)).
% 1.66/1.72 tff(7174,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~last(s59)) | (~xuntil28(s59)) | until2p29(s0) | (~trans(s59, s0)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s0) | (~trans(s59, s0)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7175,plain,
% 1.66/1.72 (((~trans(s59, s0)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s0)) <=> ((~last(s59)) | (~xuntil28(s59)) | until2p29(s0) | (~trans(s59, s0)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7176,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s0)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~last(s59)) | (~xuntil28(s59)) | until2p29(s0) | (~trans(s59, s0))))),
% 1.66/1.72 inference(monotonicity,[status(thm)],[7175])).
% 1.66/1.72 tff(7177,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s0)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s0) | (~trans(s59, s0)))),
% 1.66/1.72 inference(transitivity,[status(thm)],[7176, 7174])).
% 1.66/1.72 tff(7178,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s0)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s0))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7179,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s0) | (~trans(s59, s0))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7178, 7177])).
% 1.66/1.72 tff(7180,plain,
% 1.66/1.72 ($false),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7179, 6222, 7173, 6361, 6582, 7172])).
% 1.66/1.72 tff(7181,plain,((~trans(s59, s0)) | (~xuntil28(s59)) | until2p29(s0)), inference(lemma,lemma(discharge,[]))).
% 1.66/1.72 tff(7182,plain,
% 1.66/1.72 (~trans(s59, s0)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7181, 6212, 7171])).
% 1.66/1.72 tff(7183,assumption,(~until2p29(s22)), introduced(assumption)).
% 1.66/1.72 tff(7184,assumption,(trans(s59, s22)), introduced(assumption)).
% 1.66/1.72 tff(7185,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s22) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s22)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s22) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s22)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7186,plain,
% 1.66/1.72 (((~trans(s59, s22)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s22)) <=> (until2p29(s22) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s22)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7187,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s22)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s22) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s22))))),
% 1.66/1.72 inference(monotonicity,[status(thm)],[7186])).
% 1.66/1.72 tff(7188,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s22)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s22) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s22)))),
% 1.66/1.72 inference(transitivity,[status(thm)],[7187, 7185])).
% 1.66/1.72 tff(7189,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s22)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s22))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7190,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s22) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s22))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7189, 7188])).
% 1.66/1.72 tff(7191,plain,
% 1.66/1.72 ($false),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7190, 6222, 7184, 6361, 7183, 6582])).
% 1.66/1.72 tff(7192,plain,((~trans(s59, s22)) | until2p29(s22) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.72 tff(7193,plain,
% 1.66/1.72 (~trans(s59, s22)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7192, 6654, 6212])).
% 1.66/1.72 tff(7194,assumption,(~until2p29(s29)), introduced(assumption)).
% 1.66/1.72 tff(7195,assumption,(trans(s59, s29)), introduced(assumption)).
% 1.66/1.72 tff(7196,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s29) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s29)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s29) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s29)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7197,plain,
% 1.66/1.72 (((~trans(s59, s29)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s29)) <=> (until2p29(s29) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s29)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7198,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s29)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s29) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s29))))),
% 1.66/1.72 inference(monotonicity,[status(thm)],[7197])).
% 1.66/1.72 tff(7199,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s29)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s29) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s29)))),
% 1.66/1.72 inference(transitivity,[status(thm)],[7198, 7196])).
% 1.66/1.72 tff(7200,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s29)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s29))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7201,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s29) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s29))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7200, 7199])).
% 1.66/1.72 tff(7202,plain,
% 1.66/1.72 ($false),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7201, 6222, 7195, 6361, 7194, 6582])).
% 1.66/1.72 tff(7203,plain,((~trans(s59, s29)) | until2p29(s29) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.72 tff(7204,plain,
% 1.66/1.72 (~trans(s59, s29)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7203, 6561, 6212])).
% 1.66/1.72 tff(7205,assumption,(~until2p29(s41)), introduced(assumption)).
% 1.66/1.72 tff(7206,assumption,(trans(s59, s41)), introduced(assumption)).
% 1.66/1.72 tff(7207,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s41) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s41)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s41) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s41)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7208,plain,
% 1.66/1.72 (((~trans(s59, s41)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s41)) <=> (until2p29(s41) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s41)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7209,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s41)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s41) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s41))))),
% 1.66/1.72 inference(monotonicity,[status(thm)],[7208])).
% 1.66/1.72 tff(7210,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s41)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s41) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s41)))),
% 1.66/1.72 inference(transitivity,[status(thm)],[7209, 7207])).
% 1.66/1.72 tff(7211,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s41)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s41))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7212,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s41) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s41))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7211, 7210])).
% 1.66/1.72 tff(7213,plain,
% 1.66/1.72 ($false),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7212, 6222, 7206, 6361, 7205, 6582])).
% 1.66/1.72 tff(7214,plain,((~trans(s59, s41)) | until2p29(s41) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.72 tff(7215,plain,
% 1.66/1.72 (~trans(s59, s41)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7214, 6441, 6212])).
% 1.66/1.72 tff(7216,assumption,(~until2p29(s10)), introduced(assumption)).
% 1.66/1.72 tff(7217,assumption,(trans(s59, s10)), introduced(assumption)).
% 1.66/1.72 tff(7218,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s10) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s10)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s10) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s10)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7219,plain,
% 1.66/1.72 (((~trans(s59, s10)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s10)) <=> (until2p29(s10) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s10)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7220,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s10)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s10) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s10))))),
% 1.66/1.72 inference(monotonicity,[status(thm)],[7219])).
% 1.66/1.72 tff(7221,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s10)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s10) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s10)))),
% 1.66/1.72 inference(transitivity,[status(thm)],[7220, 7218])).
% 1.66/1.72 tff(7222,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s10)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s10))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7223,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s10) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s10))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7222, 7221])).
% 1.66/1.72 tff(7224,plain,
% 1.66/1.72 ($false),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7223, 6222, 7217, 6361, 7216, 6582])).
% 1.66/1.72 tff(7225,plain,((~trans(s59, s10)) | until2p29(s10) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.72 tff(7226,plain,
% 1.66/1.72 (~trans(s59, s10)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7225, 6774, 6212])).
% 1.66/1.72 tff(7227,assumption,(~until2p29(s47)), introduced(assumption)).
% 1.66/1.72 tff(7228,assumption,(trans(s59, s47)), introduced(assumption)).
% 1.66/1.72 tff(7229,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s47) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s47)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s47) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s47)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7230,plain,
% 1.66/1.72 (((~trans(s59, s47)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s47)) <=> (until2p29(s47) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s47)))),
% 1.66/1.72 inference(rewrite,[status(thm)],[])).
% 1.66/1.72 tff(7231,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s47)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s47) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s47))))),
% 1.66/1.72 inference(monotonicity,[status(thm)],[7230])).
% 1.66/1.72 tff(7232,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s47)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s47) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s47)))),
% 1.66/1.72 inference(transitivity,[status(thm)],[7231, 7229])).
% 1.66/1.72 tff(7233,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s47)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s47))),
% 1.66/1.72 inference(quant_inst,[status(thm)],[])).
% 1.66/1.72 tff(7234,plain,
% 1.66/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s47) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s47))),
% 1.66/1.72 inference(modus_ponens,[status(thm)],[7233, 7232])).
% 1.66/1.72 tff(7235,plain,
% 1.66/1.72 ($false),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7234, 6222, 7228, 6361, 7227, 6582])).
% 1.66/1.72 tff(7236,plain,((~trans(s59, s47)) | until2p29(s47) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.72 tff(7237,plain,
% 1.66/1.72 (~trans(s59, s47)),
% 1.66/1.72 inference(unit_resolution,[status(thm)],[7236, 6381, 6212])).
% 1.66/1.72 tff(7238,assumption,(~until2p29(s5)), introduced(assumption)).
% 1.66/1.72 tff(7239,assumption,(trans(s59, s5)), introduced(assumption)).
% 1.66/1.72 tff(7240,plain,
% 1.66/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s5) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s5)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s5) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s5)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7241,plain,
% 1.66/1.73 (((~trans(s59, s5)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s5)) <=> (until2p29(s5) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s5)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7242,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s5)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s5) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s5))))),
% 1.66/1.73 inference(monotonicity,[status(thm)],[7241])).
% 1.66/1.73 tff(7243,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s5)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s5) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s5)))),
% 1.66/1.73 inference(transitivity,[status(thm)],[7242, 7240])).
% 1.66/1.73 tff(7244,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s5)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s5))),
% 1.66/1.73 inference(quant_inst,[status(thm)],[])).
% 1.66/1.73 tff(7245,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s5) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s5))),
% 1.66/1.73 inference(modus_ponens,[status(thm)],[7244, 7243])).
% 1.66/1.73 tff(7246,plain,
% 1.66/1.73 ($false),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7245, 6222, 7239, 6361, 7238, 6582])).
% 1.66/1.73 tff(7247,plain,((~trans(s59, s5)) | until2p29(s5) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.73 tff(7248,plain,
% 1.66/1.73 (~trans(s59, s5)),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7247, 6824, 6212])).
% 1.66/1.73 tff(7249,assumption,(~until2p29(s59)), introduced(assumption)).
% 1.66/1.73 tff(7250,assumption,(trans(s59, s59)), introduced(assumption)).
% 1.66/1.73 tff(7251,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s59) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s59)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s59) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s59)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7252,plain,
% 1.66/1.73 (((~trans(s59, s59)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s59)) <=> (until2p29(s59) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s59)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7253,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s59)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s59) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s59))))),
% 1.66/1.73 inference(monotonicity,[status(thm)],[7252])).
% 1.66/1.73 tff(7254,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s59)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s59) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s59)))),
% 1.66/1.73 inference(transitivity,[status(thm)],[7253, 7251])).
% 1.66/1.73 tff(7255,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s59)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s59))),
% 1.66/1.73 inference(quant_inst,[status(thm)],[])).
% 1.66/1.73 tff(7256,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s59) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s59))),
% 1.66/1.73 inference(modus_ponens,[status(thm)],[7255, 7254])).
% 1.66/1.73 tff(7257,plain,
% 1.66/1.73 ($false),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7256, 6222, 7250, 6361, 7249, 6582])).
% 1.66/1.73 tff(7258,plain,((~trans(s59, s59)) | until2p29(s59) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.73 tff(7259,plain,
% 1.66/1.73 (~trans(s59, s59)),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7258, 6241, 6212])).
% 1.66/1.73 tff(7260,assumption,(~until2p29(s23)), introduced(assumption)).
% 1.66/1.73 tff(7261,assumption,(trans(s59, s23)), introduced(assumption)).
% 1.66/1.73 tff(7262,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s23) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s23)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s23) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s23)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7263,plain,
% 1.66/1.73 (((~trans(s59, s23)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s23)) <=> (until2p29(s23) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s23)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7264,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s23)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s23) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s23))))),
% 1.66/1.73 inference(monotonicity,[status(thm)],[7263])).
% 1.66/1.73 tff(7265,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s23)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s23) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s23)))),
% 1.66/1.73 inference(transitivity,[status(thm)],[7264, 7262])).
% 1.66/1.73 tff(7266,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s23)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s23))),
% 1.66/1.73 inference(quant_inst,[status(thm)],[])).
% 1.66/1.73 tff(7267,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s23) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s23))),
% 1.66/1.73 inference(modus_ponens,[status(thm)],[7266, 7265])).
% 1.66/1.73 tff(7268,plain,
% 1.66/1.73 ($false),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7267, 6222, 7261, 6361, 7260, 6582])).
% 1.66/1.73 tff(7269,plain,((~trans(s59, s23)) | until2p29(s23) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.73 tff(7270,plain,
% 1.66/1.73 (~trans(s59, s23)),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7269, 6644, 6212])).
% 1.66/1.73 tff(7271,assumption,(~until2p29(s40)), introduced(assumption)).
% 1.66/1.73 tff(7272,assumption,(trans(s59, s40)), introduced(assumption)).
% 1.66/1.73 tff(7273,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s40) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s40)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s40) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s40)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7274,plain,
% 1.66/1.73 (((~trans(s59, s40)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s40)) <=> (until2p29(s40) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s40)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7275,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s40)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s40) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s40))))),
% 1.66/1.73 inference(monotonicity,[status(thm)],[7274])).
% 1.66/1.73 tff(7276,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s40)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s40) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s40)))),
% 1.66/1.73 inference(transitivity,[status(thm)],[7275, 7273])).
% 1.66/1.73 tff(7277,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s40)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s40))),
% 1.66/1.73 inference(quant_inst,[status(thm)],[])).
% 1.66/1.73 tff(7278,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s40) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s40))),
% 1.66/1.73 inference(modus_ponens,[status(thm)],[7277, 7276])).
% 1.66/1.73 tff(7279,plain,
% 1.66/1.73 ($false),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7278, 6222, 7272, 6361, 7271, 6582])).
% 1.66/1.73 tff(7280,plain,((~trans(s59, s40)) | until2p29(s40) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.73 tff(7281,plain,
% 1.66/1.73 (~trans(s59, s40)),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7280, 6451, 6212])).
% 1.66/1.73 tff(7282,assumption,(~until2p29(s46)), introduced(assumption)).
% 1.66/1.73 tff(7283,assumption,(trans(s59, s46)), introduced(assumption)).
% 1.66/1.73 tff(7284,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s46) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s46)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s46) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s46)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7285,plain,
% 1.66/1.73 (((~trans(s59, s46)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s46)) <=> (until2p29(s46) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s46)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7286,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s46)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s46) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s46))))),
% 1.66/1.73 inference(monotonicity,[status(thm)],[7285])).
% 1.66/1.73 tff(7287,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s46)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s46) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s46)))),
% 1.66/1.73 inference(transitivity,[status(thm)],[7286, 7284])).
% 1.66/1.73 tff(7288,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s46)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s46))),
% 1.66/1.73 inference(quant_inst,[status(thm)],[])).
% 1.66/1.73 tff(7289,plain,
% 1.66/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s46) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s46))),
% 1.66/1.73 inference(modus_ponens,[status(thm)],[7288, 7287])).
% 1.66/1.73 tff(7290,plain,
% 1.66/1.73 ($false),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7289, 6222, 7283, 6361, 7282, 6582])).
% 1.66/1.73 tff(7291,plain,((~trans(s59, s46)) | until2p29(s46) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.73 tff(7292,plain,
% 1.66/1.73 (~trans(s59, s46)),
% 1.66/1.73 inference(unit_resolution,[status(thm)],[7291, 6391, 6212])).
% 1.66/1.73 tff(7293,assumption,(~until2p29(s45)), introduced(assumption)).
% 1.66/1.73 tff(7294,assumption,(trans(s59, s45)), introduced(assumption)).
% 1.66/1.73 tff(7295,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s45) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s45)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s45) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s45)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7296,plain,
% 1.66/1.73 (((~trans(s59, s45)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s45)) <=> (until2p29(s45) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s45)))),
% 1.66/1.73 inference(rewrite,[status(thm)],[])).
% 1.66/1.73 tff(7297,plain,
% 1.66/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s45)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s45) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s45))))),
% 1.66/1.74 inference(monotonicity,[status(thm)],[7296])).
% 1.66/1.74 tff(7298,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s45)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s45) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s45)))),
% 1.66/1.74 inference(transitivity,[status(thm)],[7297, 7295])).
% 1.66/1.74 tff(7299,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s45)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s45))),
% 1.66/1.74 inference(quant_inst,[status(thm)],[])).
% 1.66/1.74 tff(7300,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s45) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s45))),
% 1.66/1.74 inference(modus_ponens,[status(thm)],[7299, 7298])).
% 1.66/1.74 tff(7301,plain,
% 1.66/1.74 ($false),
% 1.66/1.74 inference(unit_resolution,[status(thm)],[7300, 6222, 7294, 6361, 7293, 6582])).
% 1.66/1.74 tff(7302,plain,((~trans(s59, s45)) | until2p29(s45) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.74 tff(7303,plain,
% 1.66/1.74 (~trans(s59, s45)),
% 1.66/1.74 inference(unit_resolution,[status(thm)],[7302, 6401, 6212])).
% 1.66/1.74 tff(7304,assumption,(~until2p29(s44)), introduced(assumption)).
% 1.66/1.74 tff(7305,assumption,(trans(s59, s44)), introduced(assumption)).
% 1.66/1.74 tff(7306,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s44) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s44)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s44) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s44)))),
% 1.66/1.74 inference(rewrite,[status(thm)],[])).
% 1.66/1.74 tff(7307,plain,
% 1.66/1.74 (((~trans(s59, s44)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s44)) <=> (until2p29(s44) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s44)))),
% 1.66/1.74 inference(rewrite,[status(thm)],[])).
% 1.66/1.74 tff(7308,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s44)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s44) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s44))))),
% 1.66/1.74 inference(monotonicity,[status(thm)],[7307])).
% 1.66/1.74 tff(7309,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s44)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s44) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s44)))),
% 1.66/1.74 inference(transitivity,[status(thm)],[7308, 7306])).
% 1.66/1.74 tff(7310,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s44)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s44))),
% 1.66/1.74 inference(quant_inst,[status(thm)],[])).
% 1.66/1.74 tff(7311,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s44) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s44))),
% 1.66/1.74 inference(modus_ponens,[status(thm)],[7310, 7309])).
% 1.66/1.74 tff(7312,plain,
% 1.66/1.74 ($false),
% 1.66/1.74 inference(unit_resolution,[status(thm)],[7311, 6222, 7305, 6361, 7304, 6582])).
% 1.66/1.74 tff(7313,plain,((~trans(s59, s44)) | until2p29(s44) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.74 tff(7314,plain,
% 1.66/1.74 (~trans(s59, s44)),
% 1.66/1.74 inference(unit_resolution,[status(thm)],[7313, 6411, 6212])).
% 1.66/1.74 tff(7315,assumption,(~until2p29(s24)), introduced(assumption)).
% 1.66/1.74 tff(7316,assumption,(trans(s59, s24)), introduced(assumption)).
% 1.66/1.74 tff(7317,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s24) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s24)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s24) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s24)))),
% 1.66/1.74 inference(rewrite,[status(thm)],[])).
% 1.66/1.74 tff(7318,plain,
% 1.66/1.74 (((~trans(s59, s24)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s24)) <=> (until2p29(s24) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s24)))),
% 1.66/1.74 inference(rewrite,[status(thm)],[])).
% 1.66/1.74 tff(7319,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s24)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s24) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s24))))),
% 1.66/1.74 inference(monotonicity,[status(thm)],[7318])).
% 1.66/1.74 tff(7320,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s24)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s24) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s24)))),
% 1.66/1.74 inference(transitivity,[status(thm)],[7319, 7317])).
% 1.66/1.74 tff(7321,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s24)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s24))),
% 1.66/1.74 inference(quant_inst,[status(thm)],[])).
% 1.66/1.74 tff(7322,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s24) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s24))),
% 1.66/1.74 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 1.66/1.74 tff(7323,plain,
% 1.66/1.74 ($false),
% 1.66/1.74 inference(unit_resolution,[status(thm)],[7322, 6222, 7316, 6361, 7315, 6582])).
% 1.66/1.74 tff(7324,plain,((~trans(s59, s24)) | until2p29(s24) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.74 tff(7325,plain,
% 1.66/1.74 (~trans(s59, s24)),
% 1.66/1.74 inference(unit_resolution,[status(thm)],[7324, 6634, 6212])).
% 1.66/1.74 tff(7326,assumption,(~until2p29(s30)), introduced(assumption)).
% 1.66/1.74 tff(7327,assumption,(trans(s59, s30)), introduced(assumption)).
% 1.66/1.74 tff(7328,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s30) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s30)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s30) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s30)))),
% 1.66/1.74 inference(rewrite,[status(thm)],[])).
% 1.66/1.74 tff(7329,plain,
% 1.66/1.74 (((~trans(s59, s30)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s30)) <=> (until2p29(s30) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s30)))),
% 1.66/1.74 inference(rewrite,[status(thm)],[])).
% 1.66/1.74 tff(7330,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s30)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s30) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s30))))),
% 1.66/1.74 inference(monotonicity,[status(thm)],[7329])).
% 1.66/1.74 tff(7331,plain,
% 1.66/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s30)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s30) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s30)))),
% 1.66/1.74 inference(transitivity,[status(thm)],[7330, 7328])).
% 1.66/1.74 tff(7332,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s30)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s30))),
% 1.66/1.74 inference(quant_inst,[status(thm)],[])).
% 1.66/1.74 tff(7333,plain,
% 1.66/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s30) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s30))),
% 1.66/1.74 inference(modus_ponens,[status(thm)],[7332, 7331])).
% 1.66/1.74 tff(7334,plain,
% 1.66/1.74 ($false),
% 1.66/1.74 inference(unit_resolution,[status(thm)],[7333, 6222, 7327, 6361, 7326, 6582])).
% 1.66/1.74 tff(7335,plain,((~trans(s59, s30)) | until2p29(s30) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.66/1.74 tff(7336,plain,
% 1.66/1.74 (~trans(s59, s30)),
% 1.72/1.74 inference(unit_resolution,[status(thm)],[7335, 6551, 6212])).
% 1.72/1.74 tff(7337,assumption,(~until2p29(s37)), introduced(assumption)).
% 1.72/1.74 tff(7338,assumption,(trans(s59, s37)), introduced(assumption)).
% 1.72/1.74 tff(7339,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s37) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s37)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s37) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s37)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7340,plain,
% 1.72/1.74 (((~trans(s59, s37)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s37)) <=> (until2p29(s37) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s37)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7341,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s37)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s37) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s37))))),
% 1.72/1.74 inference(monotonicity,[status(thm)],[7340])).
% 1.72/1.74 tff(7342,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s37)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s37) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s37)))),
% 1.72/1.74 inference(transitivity,[status(thm)],[7341, 7339])).
% 1.72/1.74 tff(7343,plain,
% 1.72/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s37)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s37))),
% 1.72/1.74 inference(quant_inst,[status(thm)],[])).
% 1.72/1.74 tff(7344,plain,
% 1.72/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s37) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s37))),
% 1.72/1.74 inference(modus_ponens,[status(thm)],[7343, 7342])).
% 1.72/1.74 tff(7345,plain,
% 1.72/1.74 ($false),
% 1.72/1.74 inference(unit_resolution,[status(thm)],[7344, 6222, 7338, 6361, 7337, 6582])).
% 1.72/1.74 tff(7346,plain,((~trans(s59, s37)) | until2p29(s37) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.74 tff(7347,plain,
% 1.72/1.74 (~trans(s59, s37)),
% 1.72/1.74 inference(unit_resolution,[status(thm)],[7346, 6481, 6212])).
% 1.72/1.74 tff(7348,assumption,(~until2p29(s28)), introduced(assumption)).
% 1.72/1.74 tff(7349,assumption,(trans(s59, s28)), introduced(assumption)).
% 1.72/1.74 tff(7350,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s28) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s28)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s28) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s28)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7351,plain,
% 1.72/1.74 (((~trans(s59, s28)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s28)) <=> (until2p29(s28) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s28)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7352,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s28)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s28) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s28))))),
% 1.72/1.74 inference(monotonicity,[status(thm)],[7351])).
% 1.72/1.74 tff(7353,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s28)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s28) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s28)))),
% 1.72/1.74 inference(transitivity,[status(thm)],[7352, 7350])).
% 1.72/1.74 tff(7354,plain,
% 1.72/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s28)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s28))),
% 1.72/1.74 inference(quant_inst,[status(thm)],[])).
% 1.72/1.74 tff(7355,plain,
% 1.72/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s28) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s28))),
% 1.72/1.74 inference(modus_ponens,[status(thm)],[7354, 7353])).
% 1.72/1.74 tff(7356,plain,
% 1.72/1.74 ($false),
% 1.72/1.74 inference(unit_resolution,[status(thm)],[7355, 6222, 7349, 6361, 7348, 6582])).
% 1.72/1.74 tff(7357,plain,((~trans(s59, s28)) | until2p29(s28) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.74 tff(7358,plain,
% 1.72/1.74 (~trans(s59, s28)),
% 1.72/1.74 inference(unit_resolution,[status(thm)],[7357, 6571, 6212])).
% 1.72/1.74 tff(7359,assumption,(~until2p29(s6)), introduced(assumption)).
% 1.72/1.74 tff(7360,assumption,(trans(s59, s6)), introduced(assumption)).
% 1.72/1.74 tff(7361,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s6) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s6)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s6) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s6)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7362,plain,
% 1.72/1.74 (((~trans(s59, s6)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s6)) <=> (until2p29(s6) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s6)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7363,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s6)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s6) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s6))))),
% 1.72/1.74 inference(monotonicity,[status(thm)],[7362])).
% 1.72/1.74 tff(7364,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s6)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s6) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s6)))),
% 1.72/1.74 inference(transitivity,[status(thm)],[7363, 7361])).
% 1.72/1.74 tff(7365,plain,
% 1.72/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s6)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s6))),
% 1.72/1.74 inference(quant_inst,[status(thm)],[])).
% 1.72/1.74 tff(7366,plain,
% 1.72/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s6) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s6))),
% 1.72/1.74 inference(modus_ponens,[status(thm)],[7365, 7364])).
% 1.72/1.74 tff(7367,plain,
% 1.72/1.74 ($false),
% 1.72/1.74 inference(unit_resolution,[status(thm)],[7366, 6222, 7360, 6361, 7359, 6582])).
% 1.72/1.74 tff(7368,plain,((~trans(s59, s6)) | until2p29(s6) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.74 tff(7369,plain,
% 1.72/1.74 (~trans(s59, s6)),
% 1.72/1.74 inference(unit_resolution,[status(thm)],[7368, 6814, 6212])).
% 1.72/1.74 tff(7370,assumption,(~until2p29(s14)), introduced(assumption)).
% 1.72/1.74 tff(7371,assumption,(trans(s59, s14)), introduced(assumption)).
% 1.72/1.74 tff(7372,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s14) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s14)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s14) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s14)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7373,plain,
% 1.72/1.74 (((~trans(s59, s14)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s14)) <=> (until2p29(s14) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s14)))),
% 1.72/1.74 inference(rewrite,[status(thm)],[])).
% 1.72/1.74 tff(7374,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s14)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s14) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s14))))),
% 1.72/1.74 inference(monotonicity,[status(thm)],[7373])).
% 1.72/1.74 tff(7375,plain,
% 1.72/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s14)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s14) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s14)))),
% 1.72/1.75 inference(transitivity,[status(thm)],[7374, 7372])).
% 1.72/1.75 tff(7376,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s14)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s14))),
% 1.72/1.75 inference(quant_inst,[status(thm)],[])).
% 1.72/1.75 tff(7377,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s14) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s14))),
% 1.72/1.75 inference(modus_ponens,[status(thm)],[7376, 7375])).
% 1.72/1.75 tff(7378,plain,
% 1.72/1.75 ($false),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7377, 6222, 7371, 6361, 7370, 6582])).
% 1.72/1.75 tff(7379,plain,((~trans(s59, s14)) | until2p29(s14) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.75 tff(7380,plain,
% 1.72/1.75 (~trans(s59, s14)),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7379, 6734, 6212])).
% 1.72/1.75 tff(7381,assumption,(~until2p29(s39)), introduced(assumption)).
% 1.72/1.75 tff(7382,assumption,(trans(s59, s39)), introduced(assumption)).
% 1.72/1.75 tff(7383,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s39) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s39)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s39) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s39)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7384,plain,
% 1.72/1.75 (((~trans(s59, s39)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s39)) <=> (until2p29(s39) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s39)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7385,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s39)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s39) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s39))))),
% 1.72/1.75 inference(monotonicity,[status(thm)],[7384])).
% 1.72/1.75 tff(7386,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s39)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s39) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s39)))),
% 1.72/1.75 inference(transitivity,[status(thm)],[7385, 7383])).
% 1.72/1.75 tff(7387,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s39)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s39))),
% 1.72/1.75 inference(quant_inst,[status(thm)],[])).
% 1.72/1.75 tff(7388,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s39) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s39))),
% 1.72/1.75 inference(modus_ponens,[status(thm)],[7387, 7386])).
% 1.72/1.75 tff(7389,plain,
% 1.72/1.75 ($false),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7388, 6222, 7382, 6361, 7381, 6582])).
% 1.72/1.75 tff(7390,plain,((~trans(s59, s39)) | until2p29(s39) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.75 tff(7391,plain,
% 1.72/1.75 (~trans(s59, s39)),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7390, 6461, 6212])).
% 1.72/1.75 tff(7392,assumption,(~until2p29(s13)), introduced(assumption)).
% 1.72/1.75 tff(7393,assumption,(trans(s59, s13)), introduced(assumption)).
% 1.72/1.75 tff(7394,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s13) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s13)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s13) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s13)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7395,plain,
% 1.72/1.75 (((~trans(s59, s13)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s13)) <=> (until2p29(s13) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s13)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7396,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s13)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s13) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s13))))),
% 1.72/1.75 inference(monotonicity,[status(thm)],[7395])).
% 1.72/1.75 tff(7397,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s13)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s13) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s13)))),
% 1.72/1.75 inference(transitivity,[status(thm)],[7396, 7394])).
% 1.72/1.75 tff(7398,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s13)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s13))),
% 1.72/1.75 inference(quant_inst,[status(thm)],[])).
% 1.72/1.75 tff(7399,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s13) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s13))),
% 1.72/1.75 inference(modus_ponens,[status(thm)],[7398, 7397])).
% 1.72/1.75 tff(7400,plain,
% 1.72/1.75 ($false),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7399, 6222, 7393, 6361, 7392, 6582])).
% 1.72/1.75 tff(7401,plain,((~trans(s59, s13)) | until2p29(s13) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.75 tff(7402,plain,
% 1.72/1.75 (~trans(s59, s13)),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7401, 6744, 6212])).
% 1.72/1.75 tff(7403,assumption,(~until2p29(s11)), introduced(assumption)).
% 1.72/1.75 tff(7404,assumption,(trans(s59, s11)), introduced(assumption)).
% 1.72/1.75 tff(7405,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s11) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s11)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s11) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s11)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7406,plain,
% 1.72/1.75 (((~trans(s59, s11)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s11)) <=> (until2p29(s11) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s11)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7407,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s11)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s11) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s11))))),
% 1.72/1.75 inference(monotonicity,[status(thm)],[7406])).
% 1.72/1.75 tff(7408,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s11)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s11) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s11)))),
% 1.72/1.75 inference(transitivity,[status(thm)],[7407, 7405])).
% 1.72/1.75 tff(7409,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s11)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s11))),
% 1.72/1.75 inference(quant_inst,[status(thm)],[])).
% 1.72/1.75 tff(7410,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s11) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s11))),
% 1.72/1.75 inference(modus_ponens,[status(thm)],[7409, 7408])).
% 1.72/1.75 tff(7411,plain,
% 1.72/1.75 ($false),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7410, 6222, 7404, 6361, 7403, 6582])).
% 1.72/1.75 tff(7412,plain,((~trans(s59, s11)) | until2p29(s11) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.75 tff(7413,plain,
% 1.72/1.75 (~trans(s59, s11)),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7412, 6764, 6212])).
% 1.72/1.75 tff(7414,assumption,(~until2p29(s9)), introduced(assumption)).
% 1.72/1.75 tff(7415,assumption,(trans(s59, s9)), introduced(assumption)).
% 1.72/1.75 tff(7416,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s9) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s9)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s9) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s9)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7417,plain,
% 1.72/1.75 (((~trans(s59, s9)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s9)) <=> (until2p29(s9) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s9)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7418,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s9)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s9) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s9))))),
% 1.72/1.75 inference(monotonicity,[status(thm)],[7417])).
% 1.72/1.75 tff(7419,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s9)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s9) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s9)))),
% 1.72/1.75 inference(transitivity,[status(thm)],[7418, 7416])).
% 1.72/1.75 tff(7420,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s9)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s9))),
% 1.72/1.75 inference(quant_inst,[status(thm)],[])).
% 1.72/1.75 tff(7421,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s9) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s9))),
% 1.72/1.75 inference(modus_ponens,[status(thm)],[7420, 7419])).
% 1.72/1.75 tff(7422,plain,
% 1.72/1.75 ($false),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7421, 6222, 7415, 6361, 7414, 6582])).
% 1.72/1.75 tff(7423,plain,((~trans(s59, s9)) | until2p29(s9) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.75 tff(7424,plain,
% 1.72/1.75 (~trans(s59, s9)),
% 1.72/1.75 inference(unit_resolution,[status(thm)],[7423, 6784, 6212])).
% 1.72/1.75 tff(7425,assumption,(~until2p29(s15)), introduced(assumption)).
% 1.72/1.75 tff(7426,assumption,(trans(s59, s15)), introduced(assumption)).
% 1.72/1.75 tff(7427,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s15) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s15)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s15) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s15)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7428,plain,
% 1.72/1.75 (((~trans(s59, s15)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s15)) <=> (until2p29(s15) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s15)))),
% 1.72/1.75 inference(rewrite,[status(thm)],[])).
% 1.72/1.75 tff(7429,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s15)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s15) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s15))))),
% 1.72/1.75 inference(monotonicity,[status(thm)],[7428])).
% 1.72/1.75 tff(7430,plain,
% 1.72/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s15)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s15) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s15)))),
% 1.72/1.75 inference(transitivity,[status(thm)],[7429, 7427])).
% 1.72/1.75 tff(7431,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s15)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s15))),
% 1.72/1.75 inference(quant_inst,[status(thm)],[])).
% 1.72/1.75 tff(7432,plain,
% 1.72/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s15) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s15))),
% 1.72/1.75 inference(modus_ponens,[status(thm)],[7431, 7430])).
% 1.74/1.76 tff(7433,plain,
% 1.74/1.76 ($false),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7432, 6222, 7426, 6361, 7425, 6582])).
% 1.74/1.76 tff(7434,plain,((~trans(s59, s15)) | until2p29(s15) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.76 tff(7435,plain,
% 1.74/1.76 (~trans(s59, s15)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7434, 6724, 6212])).
% 1.74/1.76 tff(7436,assumption,(~until2p29(s7)), introduced(assumption)).
% 1.74/1.76 tff(7437,assumption,(trans(s59, s7)), introduced(assumption)).
% 1.74/1.76 tff(7438,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s7) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s7)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s7) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s7)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7439,plain,
% 1.74/1.76 (((~trans(s59, s7)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s7)) <=> (until2p29(s7) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s7)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7440,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s7)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s7) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s7))))),
% 1.74/1.76 inference(monotonicity,[status(thm)],[7439])).
% 1.74/1.76 tff(7441,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s7)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s7) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s7)))),
% 1.74/1.76 inference(transitivity,[status(thm)],[7440, 7438])).
% 1.74/1.76 tff(7442,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s7)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s7))),
% 1.74/1.76 inference(quant_inst,[status(thm)],[])).
% 1.74/1.76 tff(7443,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s7) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s7))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7442, 7441])).
% 1.74/1.76 tff(7444,plain,
% 1.74/1.76 ($false),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7443, 6222, 7437, 6361, 7436, 6582])).
% 1.74/1.76 tff(7445,plain,((~trans(s59, s7)) | until2p29(s7) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.76 tff(7446,plain,
% 1.74/1.76 (~trans(s59, s7)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7445, 6804, 6212])).
% 1.74/1.76 tff(7447,assumption,(~until2p29(s58)), introduced(assumption)).
% 1.74/1.76 tff(7448,assumption,(trans(s59, s58)), introduced(assumption)).
% 1.74/1.76 tff(7449,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s58) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s58)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s58) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s58)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7450,plain,
% 1.74/1.76 (((~trans(s59, s58)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s58)) <=> (until2p29(s58) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s58)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7451,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s58)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s58) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s58))))),
% 1.74/1.76 inference(monotonicity,[status(thm)],[7450])).
% 1.74/1.76 tff(7452,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s58)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s58) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s58)))),
% 1.74/1.76 inference(transitivity,[status(thm)],[7451, 7449])).
% 1.74/1.76 tff(7453,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s58)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s58))),
% 1.74/1.76 inference(quant_inst,[status(thm)],[])).
% 1.74/1.76 tff(7454,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s58) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s58))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7453, 7452])).
% 1.74/1.76 tff(7455,plain,
% 1.74/1.76 ($false),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7454, 6222, 7448, 6361, 7447, 6582])).
% 1.74/1.76 tff(7456,plain,((~trans(s59, s58)) | until2p29(s58) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.76 tff(7457,plain,
% 1.74/1.76 (~trans(s59, s58)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7456, 6261, 6212])).
% 1.74/1.76 tff(7458,assumption,(~until2p29(s53)), introduced(assumption)).
% 1.74/1.76 tff(7459,assumption,(trans(s59, s53)), introduced(assumption)).
% 1.74/1.76 tff(7460,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s53) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s53)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s53) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s53)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7461,plain,
% 1.74/1.76 (((~trans(s59, s53)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s53)) <=> (until2p29(s53) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s53)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7462,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s53)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s53) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s53))))),
% 1.74/1.76 inference(monotonicity,[status(thm)],[7461])).
% 1.74/1.76 tff(7463,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s53)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s53) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s53)))),
% 1.74/1.76 inference(transitivity,[status(thm)],[7462, 7460])).
% 1.74/1.76 tff(7464,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s53)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s53))),
% 1.74/1.76 inference(quant_inst,[status(thm)],[])).
% 1.74/1.76 tff(7465,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s53) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s53))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7464, 7463])).
% 1.74/1.76 tff(7466,plain,
% 1.74/1.76 ($false),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7465, 6222, 7459, 6361, 7458, 6582])).
% 1.74/1.76 tff(7467,plain,((~trans(s59, s53)) | until2p29(s53) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.76 tff(7468,plain,
% 1.74/1.76 (~trans(s59, s53)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7467, 6311, 6212])).
% 1.74/1.76 tff(7469,assumption,(~until2p29(s56)), introduced(assumption)).
% 1.74/1.76 tff(7470,assumption,(trans(s59, s56)), introduced(assumption)).
% 1.74/1.76 tff(7471,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s56) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s56)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s56) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s56)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7472,plain,
% 1.74/1.76 (((~trans(s59, s56)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s56)) <=> (until2p29(s56) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s56)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7473,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s56)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s56) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s56))))),
% 1.74/1.76 inference(monotonicity,[status(thm)],[7472])).
% 1.74/1.76 tff(7474,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s56)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s56) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s56)))),
% 1.74/1.76 inference(transitivity,[status(thm)],[7473, 7471])).
% 1.74/1.76 tff(7475,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s56)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s56))),
% 1.74/1.76 inference(quant_inst,[status(thm)],[])).
% 1.74/1.76 tff(7476,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s56) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s56))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7475, 7474])).
% 1.74/1.76 tff(7477,plain,
% 1.74/1.76 ($false),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7476, 6222, 7470, 6361, 7469, 6582])).
% 1.74/1.76 tff(7478,plain,((~trans(s59, s56)) | until2p29(s56) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.76 tff(7479,plain,
% 1.74/1.76 (~trans(s59, s56)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7478, 6281, 6212])).
% 1.74/1.76 tff(7480,assumption,(~until2p29(s57)), introduced(assumption)).
% 1.74/1.76 tff(7481,assumption,(trans(s59, s57)), introduced(assumption)).
% 1.74/1.76 tff(7482,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s57) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s57)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s57) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s57)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7483,plain,
% 1.74/1.76 (((~trans(s59, s57)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s57)) <=> (until2p29(s57) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s57)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7484,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s57)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s57) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s57))))),
% 1.74/1.76 inference(monotonicity,[status(thm)],[7483])).
% 1.74/1.76 tff(7485,plain,
% 1.74/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s57)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s57) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s57)))),
% 1.74/1.76 inference(transitivity,[status(thm)],[7484, 7482])).
% 1.74/1.76 tff(7486,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s57)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s57))),
% 1.74/1.76 inference(quant_inst,[status(thm)],[])).
% 1.74/1.76 tff(7487,plain,
% 1.74/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s57) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s57))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7486, 7485])).
% 1.74/1.76 tff(7488,plain,
% 1.74/1.76 ($false),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7487, 6222, 7481, 6361, 7480, 6582])).
% 1.74/1.76 tff(7489,plain,((~trans(s59, s57)) | until2p29(s57) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.76 tff(7490,plain,
% 1.74/1.76 (~trans(s59, s57)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7489, 6271, 6212])).
% 1.74/1.76 tff(7491,assumption,(~loop), introduced(assumption)).
% 1.74/1.76 tff(7492,plain,
% 1.74/1.76 (^[X: $i] : refl((loop | (~always25(X)) | (~last(X))) <=> (loop | (~always25(X)) | (~last(X))))),
% 1.74/1.76 inference(bind,[status(th)],[])).
% 1.74/1.76 tff(7493,plain,
% 1.74/1.76 (![X: $i] : (loop | (~always25(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.74/1.76 inference(quant_intro,[status(thm)],[7492])).
% 1.74/1.76 tff(7494,plain,
% 1.74/1.76 (![X: $i] : (loop | (~always25(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7495,plain,
% 1.74/1.76 (^[X: $i] : rewrite(((loop | (~always25(X))) | (~last(X))) <=> (loop | (~always25(X)) | (~last(X))))),
% 1.74/1.76 inference(bind,[status(th)],[])).
% 1.74/1.76 tff(7496,plain,
% 1.74/1.76 (![X: $i] : ((loop | (~always25(X))) | (~last(X))) <=> ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.74/1.76 inference(quant_intro,[status(thm)],[7495])).
% 1.74/1.76 tff(7497,axiom,(![X: $i] : ((loop | (~always25(X))) | (~last(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty16')).
% 1.74/1.76 tff(7498,plain,
% 1.74/1.76 (![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7497, 7496])).
% 1.74/1.76 tff(7499,plain,
% 1.74/1.76 (![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7498, 7494])).
% 1.74/1.76 tff(7500,plain,(
% 1.74/1.76 ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.74/1.76 inference(skolemize,[status(sab)],[7499])).
% 1.74/1.76 tff(7501,plain,
% 1.74/1.76 (![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7500, 7493])).
% 1.74/1.76 tff(7502,plain,
% 1.74/1.76 (((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | (loop | (~always25(s59)) | (~last(s59)))) <=> ((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | loop | (~always25(s59)) | (~last(s59)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7503,plain,
% 1.74/1.76 ((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | (loop | (~always25(s59)) | (~last(s59)))),
% 1.74/1.76 inference(quant_inst,[status(thm)],[])).
% 1.74/1.76 tff(7504,plain,
% 1.74/1.76 ((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | loop | (~always25(s59)) | (~last(s59))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7503, 7502])).
% 1.74/1.76 tff(7505,plain,
% 1.74/1.76 (loop | (~always25(s59))),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7504, 6222, 7501])).
% 1.74/1.76 tff(7506,plain,
% 1.74/1.76 (~always25(s59)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7505, 7491])).
% 1.74/1.76 tff(7507,plain,
% 1.74/1.76 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s59) | (~node26(s59)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s59) | (~node26(s59)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7508,plain,
% 1.74/1.76 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s59) | (~node26(s59)))),
% 1.74/1.76 inference(quant_inst,[status(thm)],[])).
% 1.74/1.76 tff(7509,plain,
% 1.74/1.76 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s59) | (~node26(s59))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7508, 7507])).
% 1.74/1.76 tff(7510,plain,
% 1.74/1.76 (~node26(s59)),
% 1.74/1.76 inference(unit_resolution,[status(thm)],[7509, 2069, 7506])).
% 1.74/1.76 tff(7511,plain,
% 1.74/1.76 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 1.74/1.76 inference(bind,[status(th)],[])).
% 1.74/1.76 tff(7512,plain,
% 1.74/1.76 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.74/1.76 inference(quant_intro,[status(thm)],[7511])).
% 1.74/1.76 tff(7513,plain,
% 1.74/1.76 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.74/1.76 inference(rewrite,[status(thm)],[])).
% 1.74/1.76 tff(7514,plain,
% 1.74/1.76 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 1.74/1.76 inference(bind,[status(th)],[])).
% 1.74/1.76 tff(7515,plain,
% 1.74/1.76 (![X: $i] : ((loop | (~last(X))) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.74/1.76 inference(quant_intro,[status(thm)],[7514])).
% 1.74/1.76 tff(7516,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty21')).
% 1.74/1.76 tff(7517,plain,
% 1.74/1.76 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7516, 7515])).
% 1.74/1.76 tff(7518,plain,
% 1.74/1.76 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7517, 7513])).
% 1.74/1.76 tff(7519,plain,(
% 1.74/1.76 ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.74/1.76 inference(skolemize,[status(sab)],[7518])).
% 1.74/1.76 tff(7520,plain,
% 1.74/1.76 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.74/1.76 inference(modus_ponens,[status(thm)],[7519, 7512])).
% 1.74/1.76 tff(7521,plain,
% 1.74/1.76 (((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s59)) | (~xuntil28(s59)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s59)) | (~xuntil28(s59)))),
% 1.74/1.77 inference(rewrite,[status(thm)],[])).
% 1.74/1.77 tff(7522,plain,
% 1.74/1.77 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s59)) | (~xuntil28(s59)))),
% 1.74/1.77 inference(quant_inst,[status(thm)],[])).
% 1.74/1.77 tff(7523,plain,
% 1.74/1.77 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s59)) | (~xuntil28(s59))),
% 1.74/1.77 inference(modus_ponens,[status(thm)],[7522, 7521])).
% 1.74/1.77 tff(7524,plain,
% 1.74/1.77 (loop | (~xuntil28(s59))),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[7523, 6222, 7520])).
% 1.74/1.77 tff(7525,plain,
% 1.74/1.77 (~xuntil28(s59)),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[7524, 7491])).
% 1.74/1.77 tff(7526,plain,
% 1.74/1.77 (~until27(s59)),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[6210, 5392, 7525, 7510])).
% 1.74/1.77 tff(7527,plain,
% 1.74/1.77 (~always25(s58)),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[2061, 7506])).
% 1.74/1.77 tff(7528,plain,
% 1.74/1.77 (~node26(s58)),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[2072, 2069, 7527])).
% 1.74/1.77 tff(7529,plain,
% 1.74/1.77 (xuntil28(s58)),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[6198, 7528])).
% 1.74/1.77 tff(7530,plain,
% 1.74/1.77 ($false),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[6203, 7529, 7526])).
% 1.74/1.77 tff(7531,plain,(loop), inference(lemma,lemma(discharge,[]))).
% 1.74/1.77 tff(7532,assumption,(~until2p29(s19)), introduced(assumption)).
% 1.74/1.77 tff(7533,assumption,(trans(s59, s19)), introduced(assumption)).
% 1.74/1.77 tff(7534,plain,
% 1.74/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s19) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s19)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s19) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s19)))),
% 1.74/1.77 inference(rewrite,[status(thm)],[])).
% 1.74/1.77 tff(7535,plain,
% 1.74/1.77 (((~trans(s59, s19)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s19)) <=> (until2p29(s19) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s19)))),
% 1.74/1.77 inference(rewrite,[status(thm)],[])).
% 1.74/1.77 tff(7536,plain,
% 1.74/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s19)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s19) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s19))))),
% 1.74/1.77 inference(monotonicity,[status(thm)],[7535])).
% 1.74/1.77 tff(7537,plain,
% 1.74/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s19)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s19) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s19)))),
% 1.74/1.77 inference(transitivity,[status(thm)],[7536, 7534])).
% 1.74/1.77 tff(7538,plain,
% 1.74/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s19)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s19))),
% 1.74/1.77 inference(quant_inst,[status(thm)],[])).
% 1.74/1.77 tff(7539,plain,
% 1.74/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s19) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s19))),
% 1.74/1.77 inference(modus_ponens,[status(thm)],[7538, 7537])).
% 1.74/1.77 tff(7540,plain,
% 1.74/1.77 ($false),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[7539, 6222, 7533, 6361, 7532, 6582])).
% 1.74/1.77 tff(7541,plain,((~trans(s59, s19)) | until2p29(s19) | (~xuntil28(s59))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.77 tff(7542,plain,
% 1.74/1.77 (~trans(s59, s19)),
% 1.74/1.77 inference(unit_resolution,[status(thm)],[7541, 6684, 6212])).
% 1.74/1.77 tff(7543,plain,
% 1.74/1.77 (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59))),
% 1.74/1.78 inference(rewrite,[status(thm)],[])).
% 1.74/1.78 tff(7544,plain,
% 1.74/1.78 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)) | trans(s59, s59)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59))),
% 1.74/1.78 inference(rewrite,[status(thm)],[])).
% 1.74/1.78 tff(7545,plain,
% 1.74/1.78 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57)) | trans(s59, s58)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58))),
% 1.74/1.78 inference(rewrite,[status(thm)],[])).
% 1.74/1.78 tff(7546,plain,
% 1.74/1.78 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56)) | trans(s59, s57)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57))),
% 1.74/1.79 inference(rewrite,[status(thm)],[])).
% 1.74/1.79 tff(7547,plain,
% 1.74/1.79 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55)) | trans(s59, s56)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56))),
% 1.74/1.79 inference(rewrite,[status(thm)],[])).
% 1.74/1.79 tff(7548,plain,
% 1.74/1.79 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54)) | trans(s59, s55)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55))),
% 1.74/1.80 inference(rewrite,[status(thm)],[])).
% 1.74/1.80 tff(7549,plain,
% 1.74/1.80 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53)) | trans(s59, s54)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54))),
% 1.74/1.80 inference(rewrite,[status(thm)],[])).
% 1.74/1.80 tff(7550,plain,
% 1.74/1.80 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52)) | trans(s59, s53)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53))),
% 1.74/1.81 inference(rewrite,[status(thm)],[])).
% 1.74/1.81 tff(7551,plain,
% 1.74/1.81 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51)) | trans(s59, s52)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52))),
% 1.74/1.81 inference(rewrite,[status(thm)],[])).
% 1.74/1.81 tff(7552,plain,
% 1.74/1.81 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50)) | trans(s59, s51)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51))),
% 1.79/1.81 inference(rewrite,[status(thm)],[])).
% 1.79/1.81 tff(7553,plain,
% 1.79/1.81 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49)) | trans(s59, s50)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50))),
% 1.79/1.81 inference(rewrite,[status(thm)],[])).
% 1.79/1.81 tff(7554,plain,
% 1.79/1.81 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48)) | trans(s59, s49)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49))),
% 1.79/1.81 inference(rewrite,[status(thm)],[])).
% 1.79/1.81 tff(7555,plain,
% 1.79/1.81 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47)) | trans(s59, s48)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48))),
% 1.79/1.82 inference(rewrite,[status(thm)],[])).
% 1.79/1.82 tff(7556,plain,
% 1.79/1.82 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46)) | trans(s59, s47)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47))),
% 1.79/1.82 inference(rewrite,[status(thm)],[])).
% 1.79/1.82 tff(7557,plain,
% 1.79/1.82 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45)) | trans(s59, s46)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46))),
% 1.79/1.83 inference(rewrite,[status(thm)],[])).
% 1.79/1.83 tff(7558,plain,
% 1.79/1.83 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44)) | trans(s59, s45)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45))),
% 1.79/1.83 inference(rewrite,[status(thm)],[])).
% 1.79/1.83 tff(7559,plain,
% 1.79/1.83 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43)) | trans(s59, s44)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44))),
% 1.79/1.84 inference(rewrite,[status(thm)],[])).
% 1.79/1.84 tff(7560,plain,
% 1.79/1.84 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42)) | trans(s59, s43)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43))),
% 1.79/1.84 inference(rewrite,[status(thm)],[])).
% 1.79/1.84 tff(7561,plain,
% 1.79/1.84 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41)) | trans(s59, s42)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42))),
% 1.79/1.84 inference(rewrite,[status(thm)],[])).
% 1.79/1.84 tff(7562,plain,
% 1.79/1.84 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40)) | trans(s59, s41)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41))),
% 1.79/1.84 inference(rewrite,[status(thm)],[])).
% 1.79/1.84 tff(7563,plain,
% 1.79/1.84 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39)) | trans(s59, s40)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40))),
% 1.79/1.84 inference(rewrite,[status(thm)],[])).
% 1.79/1.84 tff(7564,plain,
% 1.79/1.84 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38)) | trans(s59, s39)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39))),
% 1.79/1.85 inference(rewrite,[status(thm)],[])).
% 1.79/1.85 tff(7565,plain,
% 1.79/1.85 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37)) | trans(s59, s38)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38))),
% 1.79/1.85 inference(rewrite,[status(thm)],[])).
% 1.79/1.85 tff(7566,plain,
% 1.79/1.85 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36)) | trans(s59, s37)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37))),
% 1.79/1.85 inference(rewrite,[status(thm)],[])).
% 1.79/1.85 tff(7567,plain,
% 1.79/1.85 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35)) | trans(s59, s36)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36))),
% 1.83/1.86 inference(rewrite,[status(thm)],[])).
% 1.83/1.86 tff(7568,plain,
% 1.83/1.86 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34)) | trans(s59, s35)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35))),
% 1.83/1.86 inference(rewrite,[status(thm)],[])).
% 1.83/1.86 tff(7569,plain,
% 1.83/1.86 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33)) | trans(s59, s34)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34))),
% 1.83/1.86 inference(rewrite,[status(thm)],[])).
% 1.83/1.86 tff(7570,plain,
% 1.83/1.86 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32)) | trans(s59, s33)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33))),
% 1.83/1.87 inference(rewrite,[status(thm)],[])).
% 1.83/1.87 tff(7571,plain,
% 1.83/1.87 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31)) | trans(s59, s32)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32))),
% 1.83/1.87 inference(rewrite,[status(thm)],[])).
% 1.83/1.87 tff(7572,plain,
% 1.83/1.87 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30)) | trans(s59, s31)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31))),
% 1.83/1.87 inference(rewrite,[status(thm)],[])).
% 1.83/1.87 tff(7573,plain,
% 1.83/1.87 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29)) | trans(s59, s30)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30))),
% 1.83/1.87 inference(rewrite,[status(thm)],[])).
% 1.83/1.87 tff(7574,plain,
% 1.83/1.87 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28)) | trans(s59, s29)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29))),
% 1.83/1.87 inference(rewrite,[status(thm)],[])).
% 1.83/1.87 tff(7575,plain,
% 1.83/1.87 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27)) | trans(s59, s28)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28))),
% 1.83/1.87 inference(rewrite,[status(thm)],[])).
% 1.83/1.87 tff(7576,plain,
% 1.83/1.87 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26)) | trans(s59, s27)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27))),
% 1.83/1.87 inference(rewrite,[status(thm)],[])).
% 1.83/1.87 tff(7577,plain,
% 1.83/1.87 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25)) | trans(s59, s26)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26))),
% 1.83/1.88 inference(rewrite,[status(thm)],[])).
% 1.83/1.88 tff(7578,plain,
% 1.83/1.88 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24)) | trans(s59, s25)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25))),
% 1.83/1.88 inference(rewrite,[status(thm)],[])).
% 1.83/1.88 tff(7579,plain,
% 1.83/1.88 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23)) | trans(s59, s24)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24))),
% 1.83/1.88 inference(rewrite,[status(thm)],[])).
% 1.83/1.88 tff(7580,plain,
% 1.83/1.88 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22)) | trans(s59, s23)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23))),
% 1.83/1.88 inference(rewrite,[status(thm)],[])).
% 1.83/1.88 tff(7581,plain,
% 1.83/1.88 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21)) | trans(s59, s22)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22))),
% 1.83/1.88 inference(rewrite,[status(thm)],[])).
% 1.83/1.88 tff(7582,plain,
% 1.83/1.88 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20)) | trans(s59, s21)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7583,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19)) | trans(s59, s20)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7584,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18)) | trans(s59, s19)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7585,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17)) | trans(s59, s18)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7586,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16)) | trans(s59, s17)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7587,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15)) | trans(s59, s16)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7588,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14)) | trans(s59, s15)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7589,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13)) | trans(s59, s14)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7590,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12)) | trans(s59, s13)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7591,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11)) | trans(s59, s12)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7592,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10)) | trans(s59, s11)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7593,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9)) | trans(s59, s10)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.89 tff(7594,plain,
% 1.83/1.89 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8)) | trans(s59, s9)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9))),
% 1.83/1.89 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7595,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7)) | trans(s59, s8)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7596,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6)) | trans(s59, s7)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7597,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5)) | trans(s59, s6)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7598,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4)) | trans(s59, s5)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7599,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3)) | trans(s59, s4)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7600,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2)) | trans(s59, s3)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7601,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0) | trans(s59, s1)) | trans(s59, s2)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7602,plain,
% 1.83/1.90 ((((~loop) | trans(s59, s0)) | trans(s59, s1)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1))),
% 1.83/1.90 inference(rewrite,[status(thm)],[])).
% 1.83/1.90 tff(7603,plain,
% 1.83/1.90 (((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1)) | trans(s59, s2))),
% 1.83/1.90 inference(monotonicity,[status(thm)],[7602])).
% 1.83/1.90 tff(7604,plain,
% 1.83/1.90 (((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2))),
% 1.83/1.90 inference(transitivity,[status(thm)],[7603, 7601])).
% 1.83/1.90 tff(7605,plain,
% 1.83/1.90 ((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2)) | trans(s59, s3))),
% 1.83/1.90 inference(monotonicity,[status(thm)],[7604])).
% 1.83/1.90 tff(7606,plain,
% 1.83/1.90 ((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3))),
% 1.83/1.90 inference(transitivity,[status(thm)],[7605, 7600])).
% 1.83/1.90 tff(7607,plain,
% 1.83/1.90 (((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3)) | trans(s59, s4))),
% 1.83/1.90 inference(monotonicity,[status(thm)],[7606])).
% 1.83/1.90 tff(7608,plain,
% 1.83/1.90 (((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4))),
% 1.83/1.90 inference(transitivity,[status(thm)],[7607, 7599])).
% 1.83/1.90 tff(7609,plain,
% 1.83/1.90 ((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4)) | trans(s59, s5))),
% 1.83/1.90 inference(monotonicity,[status(thm)],[7608])).
% 1.83/1.90 tff(7610,plain,
% 1.83/1.90 ((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7609, 7598])).
% 1.83/1.91 tff(7611,plain,
% 1.83/1.91 (((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5)) | trans(s59, s6))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7610])).
% 1.83/1.91 tff(7612,plain,
% 1.83/1.91 (((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7611, 7597])).
% 1.83/1.91 tff(7613,plain,
% 1.83/1.91 ((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6)) | trans(s59, s7))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7612])).
% 1.83/1.91 tff(7614,plain,
% 1.83/1.91 ((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7613, 7596])).
% 1.83/1.91 tff(7615,plain,
% 1.83/1.91 (((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7)) | trans(s59, s8))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7614])).
% 1.83/1.91 tff(7616,plain,
% 1.83/1.91 (((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7615, 7595])).
% 1.83/1.91 tff(7617,plain,
% 1.83/1.91 ((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8)) | trans(s59, s9))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7616])).
% 1.83/1.91 tff(7618,plain,
% 1.83/1.91 ((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7617, 7594])).
% 1.83/1.91 tff(7619,plain,
% 1.83/1.91 (((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9)) | trans(s59, s10))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7618])).
% 1.83/1.91 tff(7620,plain,
% 1.83/1.91 (((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7619, 7593])).
% 1.83/1.91 tff(7621,plain,
% 1.83/1.91 ((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10)) | trans(s59, s11))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7620])).
% 1.83/1.91 tff(7622,plain,
% 1.83/1.91 ((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7621, 7592])).
% 1.83/1.91 tff(7623,plain,
% 1.83/1.91 (((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11)) | trans(s59, s12))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7622])).
% 1.83/1.91 tff(7624,plain,
% 1.83/1.91 (((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7623, 7591])).
% 1.83/1.91 tff(7625,plain,
% 1.83/1.91 ((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12)) | trans(s59, s13))),
% 1.83/1.91 inference(monotonicity,[status(thm)],[7624])).
% 1.83/1.91 tff(7626,plain,
% 1.83/1.91 ((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13))),
% 1.83/1.91 inference(transitivity,[status(thm)],[7625, 7590])).
% 1.83/1.91 tff(7627,plain,
% 1.83/1.91 (((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13)) | trans(s59, s14))),
% 1.83/1.92 inference(monotonicity,[status(thm)],[7626])).
% 1.83/1.92 tff(7628,plain,
% 1.83/1.92 (((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14))),
% 1.83/1.92 inference(transitivity,[status(thm)],[7627, 7589])).
% 1.83/1.92 tff(7629,plain,
% 1.83/1.92 ((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14)) | trans(s59, s15))),
% 1.83/1.92 inference(monotonicity,[status(thm)],[7628])).
% 1.83/1.92 tff(7630,plain,
% 1.83/1.92 ((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15))),
% 1.83/1.92 inference(transitivity,[status(thm)],[7629, 7588])).
% 1.83/1.92 tff(7631,plain,
% 1.83/1.92 (((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15)) | trans(s59, s16))),
% 1.83/1.92 inference(monotonicity,[status(thm)],[7630])).
% 1.83/1.92 tff(7632,plain,
% 1.83/1.92 (((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16))),
% 1.83/1.92 inference(transitivity,[status(thm)],[7631, 7587])).
% 1.83/1.92 tff(7633,plain,
% 1.83/1.92 ((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16)) | trans(s59, s17))),
% 1.83/1.93 inference(monotonicity,[status(thm)],[7632])).
% 1.83/1.93 tff(7634,plain,
% 1.83/1.93 ((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17))),
% 1.83/1.93 inference(transitivity,[status(thm)],[7633, 7586])).
% 1.83/1.93 tff(7635,plain,
% 1.83/1.93 (((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17)) | trans(s59, s18))),
% 1.83/1.93 inference(monotonicity,[status(thm)],[7634])).
% 1.83/1.93 tff(7636,plain,
% 1.83/1.93 (((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18))),
% 1.83/1.93 inference(transitivity,[status(thm)],[7635, 7585])).
% 1.83/1.93 tff(7637,plain,
% 1.83/1.93 ((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18)) | trans(s59, s19))),
% 1.83/1.93 inference(monotonicity,[status(thm)],[7636])).
% 1.83/1.93 tff(7638,plain,
% 1.83/1.93 ((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19))),
% 1.83/1.93 inference(transitivity,[status(thm)],[7637, 7584])).
% 1.83/1.93 tff(7639,plain,
% 1.83/1.93 (((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19)) | trans(s59, s20))),
% 1.83/1.93 inference(monotonicity,[status(thm)],[7638])).
% 1.83/1.93 tff(7640,plain,
% 1.83/1.93 (((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20))),
% 1.83/1.93 inference(transitivity,[status(thm)],[7639, 7583])).
% 1.83/1.93 tff(7641,plain,
% 1.83/1.93 ((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20)) | trans(s59, s21))),
% 1.83/1.93 inference(monotonicity,[status(thm)],[7640])).
% 1.83/1.93 tff(7642,plain,
% 1.83/1.93 ((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21))),
% 1.83/1.93 inference(transitivity,[status(thm)],[7641, 7582])).
% 1.83/1.93 tff(7643,plain,
% 1.92/1.94 (((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21)) | trans(s59, s22))),
% 1.92/1.94 inference(monotonicity,[status(thm)],[7642])).
% 1.92/1.94 tff(7644,plain,
% 1.92/1.94 (((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22))),
% 1.92/1.94 inference(transitivity,[status(thm)],[7643, 7581])).
% 1.92/1.94 tff(7645,plain,
% 1.92/1.94 ((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22)) | trans(s59, s23))),
% 1.92/1.94 inference(monotonicity,[status(thm)],[7644])).
% 1.92/1.94 tff(7646,plain,
% 1.92/1.94 ((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23))),
% 1.92/1.94 inference(transitivity,[status(thm)],[7645, 7580])).
% 1.92/1.94 tff(7647,plain,
% 1.92/1.94 (((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23)) | trans(s59, s24))),
% 1.92/1.95 inference(monotonicity,[status(thm)],[7646])).
% 1.92/1.95 tff(7648,plain,
% 1.92/1.95 (((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24))),
% 1.92/1.95 inference(transitivity,[status(thm)],[7647, 7579])).
% 1.92/1.95 tff(7649,plain,
% 1.92/1.95 ((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24)) | trans(s59, s25))),
% 1.92/1.95 inference(monotonicity,[status(thm)],[7648])).
% 1.92/1.95 tff(7650,plain,
% 1.92/1.95 ((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25))),
% 1.92/1.95 inference(transitivity,[status(thm)],[7649, 7578])).
% 1.92/1.95 tff(7651,plain,
% 1.92/1.95 (((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25)) | trans(s59, s26))),
% 1.92/1.95 inference(monotonicity,[status(thm)],[7650])).
% 1.92/1.95 tff(7652,plain,
% 1.92/1.95 (((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26))),
% 1.92/1.95 inference(transitivity,[status(thm)],[7651, 7577])).
% 1.92/1.95 tff(7653,plain,
% 1.92/1.95 ((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26)) | trans(s59, s27))),
% 1.92/1.95 inference(monotonicity,[status(thm)],[7652])).
% 1.92/1.95 tff(7654,plain,
% 1.92/1.95 ((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27))),
% 1.92/1.96 inference(transitivity,[status(thm)],[7653, 7576])).
% 1.92/1.96 tff(7655,plain,
% 1.92/1.96 (((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27)) | trans(s59, s28))),
% 1.92/1.96 inference(monotonicity,[status(thm)],[7654])).
% 1.92/1.96 tff(7656,plain,
% 1.92/1.96 (((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28))),
% 1.92/1.96 inference(transitivity,[status(thm)],[7655, 7575])).
% 1.92/1.96 tff(7657,plain,
% 1.92/1.96 ((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28)) | trans(s59, s29))),
% 1.92/1.96 inference(monotonicity,[status(thm)],[7656])).
% 1.92/1.96 tff(7658,plain,
% 1.92/1.96 ((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29))),
% 1.92/1.97 inference(transitivity,[status(thm)],[7657, 7574])).
% 1.92/1.97 tff(7659,plain,
% 1.92/1.97 (((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29)) | trans(s59, s30))),
% 1.92/1.97 inference(monotonicity,[status(thm)],[7658])).
% 1.92/1.97 tff(7660,plain,
% 1.92/1.97 (((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30))),
% 1.92/1.97 inference(transitivity,[status(thm)],[7659, 7573])).
% 1.92/1.97 tff(7661,plain,
% 1.92/1.97 ((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30)) | trans(s59, s31))),
% 1.92/1.98 inference(monotonicity,[status(thm)],[7660])).
% 1.92/1.98 tff(7662,plain,
% 1.92/1.98 ((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31))),
% 1.92/1.98 inference(transitivity,[status(thm)],[7661, 7572])).
% 1.92/1.98 tff(7663,plain,
% 1.92/1.98 (((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31)) | trans(s59, s32))),
% 1.92/1.98 inference(monotonicity,[status(thm)],[7662])).
% 1.92/1.98 tff(7664,plain,
% 1.92/1.98 (((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32))),
% 1.96/1.98 inference(transitivity,[status(thm)],[7663, 7571])).
% 1.96/1.98 tff(7665,plain,
% 1.96/1.98 ((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32)) | trans(s59, s33))),
% 1.96/1.98 inference(monotonicity,[status(thm)],[7664])).
% 1.96/1.98 tff(7666,plain,
% 1.96/1.98 ((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33))),
% 1.96/1.98 inference(transitivity,[status(thm)],[7665, 7570])).
% 1.96/1.98 tff(7667,plain,
% 1.96/1.98 (((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33)) | trans(s59, s34))),
% 1.96/1.99 inference(monotonicity,[status(thm)],[7666])).
% 1.96/1.99 tff(7668,plain,
% 1.96/1.99 (((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34))),
% 1.96/1.99 inference(transitivity,[status(thm)],[7667, 7569])).
% 1.96/1.99 tff(7669,plain,
% 1.96/1.99 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34)) | trans(s59, s35))),
% 1.96/1.99 inference(monotonicity,[status(thm)],[7668])).
% 1.96/1.99 tff(7670,plain,
% 1.96/1.99 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35))),
% 1.96/2.00 inference(transitivity,[status(thm)],[7669, 7568])).
% 1.96/2.00 tff(7671,plain,
% 1.96/2.00 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35)) | trans(s59, s36))),
% 1.96/2.00 inference(monotonicity,[status(thm)],[7670])).
% 1.96/2.00 tff(7672,plain,
% 1.96/2.00 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36))),
% 1.96/2.00 inference(transitivity,[status(thm)],[7671, 7567])).
% 1.96/2.00 tff(7673,plain,
% 1.96/2.00 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36)) | trans(s59, s37))),
% 1.96/2.01 inference(monotonicity,[status(thm)],[7672])).
% 1.96/2.01 tff(7674,plain,
% 1.96/2.01 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37))),
% 1.96/2.01 inference(transitivity,[status(thm)],[7673, 7566])).
% 1.96/2.01 tff(7675,plain,
% 1.96/2.01 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37)) | trans(s59, s38))),
% 1.96/2.01 inference(monotonicity,[status(thm)],[7674])).
% 1.96/2.01 tff(7676,plain,
% 1.96/2.01 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38))),
% 1.96/2.01 inference(transitivity,[status(thm)],[7675, 7565])).
% 1.96/2.01 tff(7677,plain,
% 1.96/2.01 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38)) | trans(s59, s39))),
% 1.96/2.01 inference(monotonicity,[status(thm)],[7676])).
% 1.96/2.01 tff(7678,plain,
% 1.96/2.01 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39))),
% 1.96/2.02 inference(transitivity,[status(thm)],[7677, 7564])).
% 1.96/2.02 tff(7679,plain,
% 1.96/2.02 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39)) | trans(s59, s40))),
% 1.96/2.02 inference(monotonicity,[status(thm)],[7678])).
% 1.96/2.02 tff(7680,plain,
% 1.96/2.02 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40))),
% 1.96/2.03 inference(transitivity,[status(thm)],[7679, 7563])).
% 1.96/2.03 tff(7681,plain,
% 1.96/2.03 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40)) | trans(s59, s41))),
% 1.96/2.03 inference(monotonicity,[status(thm)],[7680])).
% 1.96/2.03 tff(7682,plain,
% 1.96/2.03 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41))),
% 1.96/2.03 inference(transitivity,[status(thm)],[7681, 7562])).
% 1.96/2.03 tff(7683,plain,
% 1.96/2.03 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41)) | trans(s59, s42))),
% 1.96/2.03 inference(monotonicity,[status(thm)],[7682])).
% 1.96/2.03 tff(7684,plain,
% 1.96/2.03 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42))),
% 1.96/2.03 inference(transitivity,[status(thm)],[7683, 7561])).
% 1.96/2.03 tff(7685,plain,
% 1.96/2.03 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42)) | trans(s59, s43))),
% 2.02/2.04 inference(monotonicity,[status(thm)],[7684])).
% 2.02/2.04 tff(7686,plain,
% 2.02/2.04 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43))),
% 2.02/2.04 inference(transitivity,[status(thm)],[7685, 7560])).
% 2.02/2.04 tff(7687,plain,
% 2.02/2.04 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43)) | trans(s59, s44))),
% 2.02/2.04 inference(monotonicity,[status(thm)],[7686])).
% 2.02/2.04 tff(7688,plain,
% 2.02/2.04 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44))),
% 2.02/2.05 inference(transitivity,[status(thm)],[7687, 7559])).
% 2.02/2.05 tff(7689,plain,
% 2.02/2.05 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44)) | trans(s59, s45))),
% 2.02/2.05 inference(monotonicity,[status(thm)],[7688])).
% 2.02/2.05 tff(7690,plain,
% 2.02/2.05 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45))),
% 2.04/2.06 inference(transitivity,[status(thm)],[7689, 7558])).
% 2.04/2.06 tff(7691,plain,
% 2.04/2.06 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45)) | trans(s59, s46))),
% 2.04/2.06 inference(monotonicity,[status(thm)],[7690])).
% 2.04/2.06 tff(7692,plain,
% 2.04/2.06 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46))),
% 2.04/2.06 inference(transitivity,[status(thm)],[7691, 7557])).
% 2.04/2.06 tff(7693,plain,
% 2.04/2.06 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46)) | trans(s59, s47))),
% 2.04/2.06 inference(monotonicity,[status(thm)],[7692])).
% 2.04/2.06 tff(7694,plain,
% 2.04/2.06 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47))),
% 2.04/2.07 inference(transitivity,[status(thm)],[7693, 7556])).
% 2.04/2.07 tff(7695,plain,
% 2.04/2.07 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47)) | trans(s59, s48))),
% 2.04/2.07 inference(monotonicity,[status(thm)],[7694])).
% 2.04/2.07 tff(7696,plain,
% 2.04/2.07 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48))),
% 2.04/2.08 inference(transitivity,[status(thm)],[7695, 7555])).
% 2.04/2.08 tff(7697,plain,
% 2.04/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48)) | trans(s59, s49))),
% 2.04/2.08 inference(monotonicity,[status(thm)],[7696])).
% 2.04/2.08 tff(7698,plain,
% 2.04/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49))),
% 2.04/2.08 inference(transitivity,[status(thm)],[7697, 7554])).
% 2.04/2.08 tff(7699,plain,
% 2.04/2.08 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49)) | trans(s59, s50))),
% 2.04/2.08 inference(monotonicity,[status(thm)],[7698])).
% 2.04/2.08 tff(7700,plain,
% 2.04/2.08 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50))),
% 2.04/2.09 inference(transitivity,[status(thm)],[7699, 7553])).
% 2.04/2.09 tff(7701,plain,
% 2.04/2.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50)) | trans(s59, s51))),
% 2.04/2.09 inference(monotonicity,[status(thm)],[7700])).
% 2.04/2.09 tff(7702,plain,
% 2.04/2.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51))),
% 2.04/2.10 inference(transitivity,[status(thm)],[7701, 7552])).
% 2.04/2.10 tff(7703,plain,
% 2.04/2.10 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51)) | trans(s59, s52))),
% 2.04/2.10 inference(monotonicity,[status(thm)],[7702])).
% 2.04/2.10 tff(7704,plain,
% 2.04/2.10 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52))),
% 2.04/2.11 inference(transitivity,[status(thm)],[7703, 7551])).
% 2.04/2.11 tff(7705,plain,
% 2.04/2.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52)) | trans(s59, s53))),
% 2.04/2.11 inference(monotonicity,[status(thm)],[7704])).
% 2.04/2.11 tff(7706,plain,
% 2.04/2.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53))),
% 2.09/2.11 inference(transitivity,[status(thm)],[7705, 7550])).
% 2.09/2.11 tff(7707,plain,
% 2.09/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53)) | trans(s59, s54))),
% 2.09/2.11 inference(monotonicity,[status(thm)],[7706])).
% 2.09/2.11 tff(7708,plain,
% 2.09/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54))),
% 2.09/2.12 inference(transitivity,[status(thm)],[7707, 7549])).
% 2.09/2.12 tff(7709,plain,
% 2.09/2.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54)) | trans(s59, s55))),
% 2.09/2.12 inference(monotonicity,[status(thm)],[7708])).
% 2.09/2.12 tff(7710,plain,
% 2.09/2.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55))),
% 2.09/2.13 inference(transitivity,[status(thm)],[7709, 7548])).
% 2.09/2.13 tff(7711,plain,
% 2.09/2.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55)) | trans(s59, s56))),
% 2.09/2.13 inference(monotonicity,[status(thm)],[7710])).
% 2.09/2.13 tff(7712,plain,
% 2.09/2.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56))),
% 2.09/2.13 inference(transitivity,[status(thm)],[7711, 7547])).
% 2.09/2.13 tff(7713,plain,
% 2.09/2.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56)) | trans(s59, s57))),
% 2.09/2.13 inference(monotonicity,[status(thm)],[7712])).
% 2.09/2.13 tff(7714,plain,
% 2.09/2.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57))),
% 2.09/2.14 inference(transitivity,[status(thm)],[7713, 7546])).
% 2.09/2.14 tff(7715,plain,
% 2.09/2.14 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57)) | trans(s59, s58))),
% 2.09/2.15 inference(monotonicity,[status(thm)],[7714])).
% 2.09/2.15 tff(7716,plain,
% 2.09/2.15 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58))),
% 2.09/2.15 inference(transitivity,[status(thm)],[7715, 7545])).
% 2.09/2.15 tff(7717,plain,
% 2.09/2.15 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) | trans(s59, s59)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58)) | trans(s59, s59))),
% 2.09/2.15 inference(monotonicity,[status(thm)],[7716])).
% 2.09/2.15 tff(7718,plain,
% 2.09/2.15 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) | trans(s59, s59)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59))),
% 2.09/2.15 inference(transitivity,[status(thm)],[7717, 7544])).
% 2.09/2.15 tff(7719,axiom,(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | trans(s59, s11)) | trans(s59, s12)) | trans(s59, s13)) | trans(s59, s14)) | trans(s59, s15)) | trans(s59, s16)) | trans(s59, s17)) | trans(s59, s18)) | trans(s59, s19)) | trans(s59, s20)) | trans(s59, s21)) | trans(s59, s22)) | trans(s59, s23)) | trans(s59, s24)) | trans(s59, s25)) | trans(s59, s26)) | trans(s59, s27)) | trans(s59, s28)) | trans(s59, s29)) | trans(s59, s30)) | trans(s59, s31)) | trans(s59, s32)) | trans(s59, s33)) | trans(s59, s34)) | trans(s59, s35)) | trans(s59, s36)) | trans(s59, s37)) | trans(s59, s38)) | trans(s59, s39)) | trans(s59, s40)) | trans(s59, s41)) | trans(s59, s42)) | trans(s59, s43)) | trans(s59, s44)) | trans(s59, s45)) | trans(s59, s46)) | trans(s59, s47)) | trans(s59, s48)) | trans(s59, s49)) | trans(s59, s50)) | trans(s59, s51)) | trans(s59, s52)) | trans(s59, s53)) | trans(s59, s54)) | trans(s59, s55)) | trans(s59, s56)) | trans(s59, s57)) | trans(s59, s58)) | trans(s59, s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound62')).
% 2.09/2.16 tff(7720,plain,
% 2.09/2.16 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.09/2.16 inference(modus_ponens,[status(thm)],[7719, 7718])).
% 2.09/2.16 tff(7721,plain,
% 2.09/2.16 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.09/2.16 inference(modus_ponens,[status(thm)],[7720, 7543])).
% 2.09/2.16 tff(7722,plain,
% 2.09/2.16 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.09/2.16 inference(modus_ponens,[status(thm)],[7721, 7543])).
% 2.09/2.16 tff(7723,plain,
% 2.09/2.16 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.15/2.17 inference(modus_ponens,[status(thm)],[7722, 7543])).
% 2.15/2.17 tff(7724,plain,
% 2.15/2.17 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.15/2.17 inference(modus_ponens,[status(thm)],[7723, 7543])).
% 2.15/2.17 tff(7725,plain,
% 2.15/2.17 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.15/2.17 inference(modus_ponens,[status(thm)],[7724, 7543])).
% 2.15/2.17 tff(7726,plain,
% 2.15/2.17 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.15/2.17 inference(modus_ponens,[status(thm)],[7725, 7543])).
% 2.15/2.17 tff(7727,plain,
% 2.15/2.17 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.15/2.17 inference(modus_ponens,[status(thm)],[7726, 7543])).
% 2.15/2.17 tff(7728,plain,
% 2.15/2.17 (trans(s59, s49)),
% 2.15/2.17 inference(unit_resolution,[status(thm)],[7727, 7542, 7531, 7490, 7479, 7468, 7457, 7446, 7435, 7424, 7413, 7402, 7391, 7380, 7369, 7358, 7347, 7336, 7325, 7314, 7303, 7292, 7281, 7270, 7259, 7248, 7237, 7226, 7215, 7204, 7193, 7182, 7161, 7150, 7139, 7128, 7117, 7106, 7085, 7074, 7063, 7052, 7041, 7030, 7019, 7008, 6997, 6986, 6975, 6964, 6953, 6942, 6931, 6920, 6909, 6888, 6877, 6866, 6855, 6604, 6593])).
% 2.15/2.17 tff(7729,plain,
% 2.15/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s49) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s49)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s49) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s49)))),
% 2.15/2.17 inference(rewrite,[status(thm)],[])).
% 2.15/2.17 tff(7730,plain,
% 2.15/2.17 (((~trans(s59, s49)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s49)) <=> (until2p29(s49) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s49)))),
% 2.15/2.17 inference(rewrite,[status(thm)],[])).
% 2.15/2.17 tff(7731,plain,
% 2.15/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s49)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s49) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s49))))),
% 2.15/2.17 inference(monotonicity,[status(thm)],[7730])).
% 2.15/2.17 tff(7732,plain,
% 2.15/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s49)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s49) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s49)))),
% 2.15/2.17 inference(transitivity,[status(thm)],[7731, 7729])).
% 2.15/2.17 tff(7733,plain,
% 2.15/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s59, s49)) | (~last(s59)) | (~xuntil28(s59)) | until2p29(s49))),
% 2.15/2.17 inference(quant_inst,[status(thm)],[])).
% 2.15/2.17 tff(7734,plain,
% 2.15/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s49) | (~last(s59)) | (~xuntil28(s59)) | (~trans(s59, s49))),
% 2.15/2.17 inference(modus_ponens,[status(thm)],[7733, 7732])).
% 2.15/2.17 tff(7735,plain,
% 2.15/2.17 ($false),
% 2.15/2.17 inference(unit_resolution,[status(thm)],[7734, 6222, 7728, 6361, 6351, 6212])).
% 2.15/2.17 tff(7736,plain,(node26(s59) | node26(s58)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.17 tff(7737,plain,
% 2.15/2.17 (node26(s59)),
% 2.15/2.17 inference(unit_resolution,[status(thm)],[7736, 2073])).
% 2.15/2.17 tff(7738,plain,
% 2.15/2.17 ($false),
% 2.15/2.17 inference(unit_resolution,[status(thm)],[7509, 2069, 2047, 7737])).
% 2.15/2.17 tff(7739,plain,(always25(s59)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.17 tff(7740,plain,
% 2.15/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s54) | (~trans(s59, s54)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s54) | (~trans(s59, s54)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7741,plain,
% 2.15/2.18 (((~trans(s59, s54)) | (~always25(s59)) | always25(s54)) <=> ((~always25(s59)) | always25(s54) | (~trans(s59, s54)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7742,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s54)) | (~always25(s59)) | always25(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s54) | (~trans(s59, s54))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7741])).
% 2.15/2.18 tff(7743,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s54)) | (~always25(s59)) | always25(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s54) | (~trans(s59, s54)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7742, 7740])).
% 2.15/2.18 tff(7744,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s54)) | (~always25(s59)) | always25(s54))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7745,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s54) | (~trans(s59, s54))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7744, 7743])).
% 2.15/2.18 tff(7746,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7745, 6595, 2041, 7739, 5001])).
% 2.15/2.18 tff(7747,plain,(~trans(s59, s54)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7748,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s3) | (~trans(s59, s3)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s3) | (~trans(s59, s3)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7749,plain,
% 2.15/2.18 (((~trans(s59, s3)) | (~always25(s59)) | always25(s3)) <=> ((~always25(s59)) | always25(s3) | (~trans(s59, s3)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7750,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s3)) | (~always25(s59)) | always25(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s3) | (~trans(s59, s3))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7749])).
% 2.15/2.18 tff(7751,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s3)) | (~always25(s59)) | always25(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s3) | (~trans(s59, s3)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7750, 7748])).
% 2.15/2.18 tff(7752,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s3)) | (~always25(s59)) | always25(s3))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7753,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s3) | (~trans(s59, s3))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7752, 7751])).
% 2.15/2.18 tff(7754,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7753, 6846, 2041, 7739, 5357])).
% 2.15/2.18 tff(7755,plain,(~trans(s59, s3)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7756,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s43) | (~trans(s59, s43)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s43) | (~trans(s59, s43)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7757,plain,
% 2.15/2.18 (((~trans(s59, s43)) | (~always25(s59)) | always25(s43)) <=> ((~always25(s59)) | always25(s43) | (~trans(s59, s43)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7758,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s43)) | (~always25(s59)) | always25(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s43) | (~trans(s59, s43))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7757])).
% 2.15/2.18 tff(7759,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s43)) | (~always25(s59)) | always25(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s43) | (~trans(s59, s43)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7758, 7756])).
% 2.15/2.18 tff(7760,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s43)) | (~always25(s59)) | always25(s43))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7761,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s43) | (~trans(s59, s43))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7760, 7759])).
% 2.15/2.18 tff(7762,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7761, 6857, 2041, 7739, 5079])).
% 2.15/2.18 tff(7763,plain,(~trans(s59, s43)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7764,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s27) | (~trans(s59, s27)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s27) | (~trans(s59, s27)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7765,plain,
% 2.15/2.18 (((~trans(s59, s27)) | (~always25(s59)) | always25(s27)) <=> ((~always25(s59)) | always25(s27) | (~trans(s59, s27)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7766,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s27)) | (~always25(s59)) | always25(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s27) | (~trans(s59, s27))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7765])).
% 2.15/2.18 tff(7767,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s27)) | (~always25(s59)) | always25(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s27) | (~trans(s59, s27)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7766, 7764])).
% 2.15/2.18 tff(7768,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s27)) | (~always25(s59)) | always25(s27))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7769,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s27) | (~trans(s59, s27))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7768, 7767])).
% 2.15/2.18 tff(7770,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7769, 6584, 2041, 7739, 5195])).
% 2.15/2.18 tff(7771,plain,(~trans(s59, s27)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7772,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s4) | (~trans(s59, s4)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s4) | (~trans(s59, s4)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7773,plain,
% 2.15/2.18 (((~trans(s59, s4)) | (~always25(s59)) | always25(s4)) <=> ((~always25(s59)) | always25(s4) | (~trans(s59, s4)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7774,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s4)) | (~always25(s59)) | always25(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s4) | (~trans(s59, s4))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7773])).
% 2.15/2.18 tff(7775,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s4)) | (~always25(s59)) | always25(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s4) | (~trans(s59, s4)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7774, 7772])).
% 2.15/2.18 tff(7776,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s4)) | (~always25(s59)) | always25(s4))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7777,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s4) | (~trans(s59, s4))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7776, 7775])).
% 2.15/2.18 tff(7778,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7777, 6868, 2041, 7739, 5352])).
% 2.15/2.18 tff(7779,plain,(~trans(s59, s4)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7780,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s17, s18)) | (~always25(s17)) | always25(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s17, s18)) | (~always25(s17)) | always25(s18))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7781,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s17, s18)) | (~always25(s17)) | always25(s18))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7782,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s17, s18)) | (~always25(s17)) | always25(s18)),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7781, 7780])).
% 2.15/2.18 tff(7783,plain,
% 2.15/2.18 ((~always25(s17)) | always25(s18)),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7782, 2041, 1831])).
% 2.15/2.18 tff(7784,plain,
% 2.15/2.18 (~always25(s17)),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7783, 5250])).
% 2.15/2.18 tff(7785,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s17) | (~trans(s59, s17)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s17) | (~trans(s59, s17)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7786,plain,
% 2.15/2.18 (((~trans(s59, s17)) | (~always25(s59)) | always25(s17)) <=> ((~always25(s59)) | always25(s17) | (~trans(s59, s17)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7787,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s17)) | (~always25(s59)) | always25(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s17) | (~trans(s59, s17))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7786])).
% 2.15/2.18 tff(7788,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s17)) | (~always25(s59)) | always25(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s17) | (~trans(s59, s17)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7787, 7785])).
% 2.15/2.18 tff(7789,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s17)) | (~always25(s59)) | always25(s17))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7790,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s17) | (~trans(s59, s17))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7789, 7788])).
% 2.15/2.18 tff(7791,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7790, 6879, 2041, 7739, 7784])).
% 2.15/2.18 tff(7792,plain,(~trans(s59, s17)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7793,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s2) | (~trans(s59, s2)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s2) | (~trans(s59, s2)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7794,plain,
% 2.15/2.18 (((~trans(s59, s2)) | (~always25(s59)) | always25(s2)) <=> ((~always25(s59)) | always25(s2) | (~trans(s59, s2)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7795,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s2)) | (~always25(s59)) | always25(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s2) | (~trans(s59, s2))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7794])).
% 2.15/2.18 tff(7796,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s2)) | (~always25(s59)) | always25(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s2) | (~trans(s59, s2)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7795, 7793])).
% 2.15/2.18 tff(7797,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s2)) | (~always25(s59)) | always25(s2))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7798,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s2) | (~trans(s59, s2))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7797, 7796])).
% 2.15/2.18 tff(7799,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7798, 6900, 2041, 7739, 5362])).
% 2.15/2.18 tff(7800,plain,(~trans(s59, s2)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7801,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s8) | (~trans(s59, s8)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s8) | (~trans(s59, s8)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7802,plain,
% 2.15/2.18 (((~trans(s59, s8)) | (~always25(s59)) | always25(s8)) <=> ((~always25(s59)) | always25(s8) | (~trans(s59, s8)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7803,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s8)) | (~always25(s59)) | always25(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s8) | (~trans(s59, s8))))),
% 2.15/2.18 inference(monotonicity,[status(thm)],[7802])).
% 2.15/2.18 tff(7804,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s8)) | (~always25(s59)) | always25(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s8) | (~trans(s59, s8)))),
% 2.15/2.18 inference(transitivity,[status(thm)],[7803, 7801])).
% 2.15/2.18 tff(7805,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s8)) | (~always25(s59)) | always25(s8))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7806,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s8) | (~trans(s59, s8))),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7805, 7804])).
% 2.15/2.18 tff(7807,plain,
% 2.15/2.18 ($false),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7806, 6911, 2041, 7739, 5323])).
% 2.15/2.18 tff(7808,plain,(~trans(s59, s8)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.18 tff(7809,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s25, s26)) | (~always25(s25)) | always25(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s25, s26)) | (~always25(s25)) | always25(s26))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7810,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s25, s26)) | (~always25(s25)) | always25(s26))),
% 2.15/2.18 inference(quant_inst,[status(thm)],[])).
% 2.15/2.18 tff(7811,plain,
% 2.15/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s25, s26)) | (~always25(s25)) | always25(s26)),
% 2.15/2.18 inference(modus_ponens,[status(thm)],[7810, 7809])).
% 2.15/2.18 tff(7812,plain,
% 2.15/2.18 ((~always25(s25)) | always25(s26)),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7811, 2041, 2536])).
% 2.15/2.18 tff(7813,plain,
% 2.15/2.18 (~always25(s25)),
% 2.15/2.18 inference(unit_resolution,[status(thm)],[7812, 5204])).
% 2.15/2.18 tff(7814,plain,
% 2.15/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s25) | (~trans(s59, s25)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s25) | (~trans(s59, s25)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.18 tff(7815,plain,
% 2.15/2.18 (((~trans(s59, s25)) | (~always25(s59)) | always25(s25)) <=> ((~always25(s59)) | always25(s25) | (~trans(s59, s25)))),
% 2.15/2.18 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7816,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s25)) | (~always25(s59)) | always25(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s25) | (~trans(s59, s25))))),
% 2.15/2.19 inference(monotonicity,[status(thm)],[7815])).
% 2.15/2.19 tff(7817,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s25)) | (~always25(s59)) | always25(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s25) | (~trans(s59, s25)))),
% 2.15/2.19 inference(transitivity,[status(thm)],[7816, 7814])).
% 2.15/2.19 tff(7818,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s25)) | (~always25(s59)) | always25(s25))),
% 2.15/2.19 inference(quant_inst,[status(thm)],[])).
% 2.15/2.19 tff(7819,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s25) | (~trans(s59, s25))),
% 2.15/2.19 inference(modus_ponens,[status(thm)],[7818, 7817])).
% 2.15/2.19 tff(7820,plain,
% 2.15/2.19 ($false),
% 2.15/2.19 inference(unit_resolution,[status(thm)],[7819, 6922, 2041, 7739, 7813])).
% 2.15/2.19 tff(7821,plain,(~trans(s59, s25)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.19 tff(7822,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s35) | (~trans(s59, s35)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s35) | (~trans(s59, s35)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7823,plain,
% 2.15/2.19 (((~trans(s59, s35)) | (~always25(s59)) | always25(s35)) <=> ((~always25(s59)) | always25(s35) | (~trans(s59, s35)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7824,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s35)) | (~always25(s59)) | always25(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s35) | (~trans(s59, s35))))),
% 2.15/2.19 inference(monotonicity,[status(thm)],[7823])).
% 2.15/2.19 tff(7825,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s35)) | (~always25(s59)) | always25(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s35) | (~trans(s59, s35)))),
% 2.15/2.19 inference(transitivity,[status(thm)],[7824, 7822])).
% 2.15/2.19 tff(7826,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s35)) | (~always25(s59)) | always25(s35))),
% 2.15/2.19 inference(quant_inst,[status(thm)],[])).
% 2.15/2.19 tff(7827,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s35) | (~trans(s59, s35))),
% 2.15/2.19 inference(modus_ponens,[status(thm)],[7826, 7825])).
% 2.15/2.19 tff(7828,plain,
% 2.15/2.19 ($false),
% 2.15/2.19 inference(unit_resolution,[status(thm)],[7827, 6933, 2041, 7739, 5137])).
% 2.15/2.19 tff(7829,plain,(~trans(s59, s35)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.19 tff(7830,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s36) | (~trans(s59, s36)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s36) | (~trans(s59, s36)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7831,plain,
% 2.15/2.19 (((~trans(s59, s36)) | (~always25(s59)) | always25(s36)) <=> ((~always25(s59)) | always25(s36) | (~trans(s59, s36)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7832,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s36)) | (~always25(s59)) | always25(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s36) | (~trans(s59, s36))))),
% 2.15/2.19 inference(monotonicity,[status(thm)],[7831])).
% 2.15/2.19 tff(7833,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s36)) | (~always25(s59)) | always25(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s36) | (~trans(s59, s36)))),
% 2.15/2.19 inference(transitivity,[status(thm)],[7832, 7830])).
% 2.15/2.19 tff(7834,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s36)) | (~always25(s59)) | always25(s36))),
% 2.15/2.19 inference(quant_inst,[status(thm)],[])).
% 2.15/2.19 tff(7835,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s36) | (~trans(s59, s36))),
% 2.15/2.19 inference(modus_ponens,[status(thm)],[7834, 7833])).
% 2.15/2.19 tff(7836,plain,
% 2.15/2.19 ($false),
% 2.15/2.19 inference(unit_resolution,[status(thm)],[7835, 6944, 2041, 7739, 5132])).
% 2.15/2.19 tff(7837,plain,(~trans(s59, s36)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.19 tff(7838,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s38) | (~trans(s59, s38)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s38) | (~trans(s59, s38)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7839,plain,
% 2.15/2.19 (((~trans(s59, s38)) | (~always25(s59)) | always25(s38)) <=> ((~always25(s59)) | always25(s38) | (~trans(s59, s38)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7840,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s38)) | (~always25(s59)) | always25(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s38) | (~trans(s59, s38))))),
% 2.15/2.19 inference(monotonicity,[status(thm)],[7839])).
% 2.15/2.19 tff(7841,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s38)) | (~always25(s59)) | always25(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s38) | (~trans(s59, s38)))),
% 2.15/2.19 inference(transitivity,[status(thm)],[7840, 7838])).
% 2.15/2.19 tff(7842,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s38)) | (~always25(s59)) | always25(s38))),
% 2.15/2.19 inference(quant_inst,[status(thm)],[])).
% 2.15/2.19 tff(7843,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s38) | (~trans(s59, s38))),
% 2.15/2.19 inference(modus_ponens,[status(thm)],[7842, 7841])).
% 2.15/2.19 tff(7844,plain,
% 2.15/2.19 ($false),
% 2.15/2.19 inference(unit_resolution,[status(thm)],[7843, 6955, 2041, 7739, 5117])).
% 2.15/2.19 tff(7845,plain,(~trans(s59, s38)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.19 tff(7846,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s26) | (~trans(s59, s26)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s26) | (~trans(s59, s26)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7847,plain,
% 2.15/2.19 (((~trans(s59, s26)) | (~always25(s59)) | always25(s26)) <=> ((~always25(s59)) | always25(s26) | (~trans(s59, s26)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7848,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s26)) | (~always25(s59)) | always25(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s26) | (~trans(s59, s26))))),
% 2.15/2.19 inference(monotonicity,[status(thm)],[7847])).
% 2.15/2.19 tff(7849,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s26)) | (~always25(s59)) | always25(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s26) | (~trans(s59, s26)))),
% 2.15/2.19 inference(transitivity,[status(thm)],[7848, 7846])).
% 2.15/2.19 tff(7850,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s26)) | (~always25(s59)) | always25(s26))),
% 2.15/2.19 inference(quant_inst,[status(thm)],[])).
% 2.15/2.19 tff(7851,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s26) | (~trans(s59, s26))),
% 2.15/2.19 inference(modus_ponens,[status(thm)],[7850, 7849])).
% 2.15/2.19 tff(7852,plain,
% 2.15/2.19 ($false),
% 2.15/2.19 inference(unit_resolution,[status(thm)],[7851, 6966, 2041, 7739, 5204])).
% 2.15/2.19 tff(7853,plain,(~trans(s59, s26)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.19 tff(7854,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s18) | (~trans(s59, s18)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s18) | (~trans(s59, s18)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7855,plain,
% 2.15/2.19 (((~trans(s59, s18)) | (~always25(s59)) | always25(s18)) <=> ((~always25(s59)) | always25(s18) | (~trans(s59, s18)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7856,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s18)) | (~always25(s59)) | always25(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s18) | (~trans(s59, s18))))),
% 2.15/2.19 inference(monotonicity,[status(thm)],[7855])).
% 2.15/2.19 tff(7857,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s18)) | (~always25(s59)) | always25(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s18) | (~trans(s59, s18)))),
% 2.15/2.19 inference(transitivity,[status(thm)],[7856, 7854])).
% 2.15/2.19 tff(7858,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s18)) | (~always25(s59)) | always25(s18))),
% 2.15/2.19 inference(quant_inst,[status(thm)],[])).
% 2.15/2.19 tff(7859,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s18) | (~trans(s59, s18))),
% 2.15/2.19 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 2.15/2.19 tff(7860,plain,
% 2.15/2.19 ($false),
% 2.15/2.19 inference(unit_resolution,[status(thm)],[7859, 6977, 2041, 7739, 5250])).
% 2.15/2.19 tff(7861,plain,(~trans(s59, s18)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.19 tff(7862,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s52) | (~trans(s59, s52)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s52) | (~trans(s59, s52)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7863,plain,
% 2.15/2.19 (((~trans(s59, s52)) | (~always25(s59)) | always25(s52)) <=> ((~always25(s59)) | always25(s52) | (~trans(s59, s52)))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7864,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s52)) | (~always25(s59)) | always25(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s52) | (~trans(s59, s52))))),
% 2.15/2.19 inference(monotonicity,[status(thm)],[7863])).
% 2.15/2.19 tff(7865,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s52)) | (~always25(s59)) | always25(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s52) | (~trans(s59, s52)))),
% 2.15/2.19 inference(transitivity,[status(thm)],[7864, 7862])).
% 2.15/2.19 tff(7866,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s52)) | (~always25(s59)) | always25(s52))),
% 2.15/2.19 inference(quant_inst,[status(thm)],[])).
% 2.15/2.19 tff(7867,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s52) | (~trans(s59, s52))),
% 2.15/2.19 inference(modus_ponens,[status(thm)],[7866, 7865])).
% 2.15/2.19 tff(7868,plain,
% 2.15/2.19 ($false),
% 2.15/2.19 inference(unit_resolution,[status(thm)],[7867, 6988, 2041, 7739, 5016])).
% 2.15/2.19 tff(7869,plain,(~trans(s59, s52)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.19 tff(7870,plain,
% 2.15/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s21, s22)) | (~always25(s21)) | always25(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s21, s22)) | (~always25(s21)) | always25(s22))),
% 2.15/2.19 inference(rewrite,[status(thm)],[])).
% 2.15/2.19 tff(7871,plain,
% 2.15/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s21, s22)) | (~always25(s21)) | always25(s22))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7872,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s21, s22)) | (~always25(s21)) | always25(s22)),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7871, 7870])).
% 2.15/2.20 tff(7873,plain,
% 2.15/2.20 ((~always25(s21)) | always25(s22)),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7872, 2041, 2203])).
% 2.15/2.20 tff(7874,plain,
% 2.15/2.20 (~always25(s21)),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7873, 5233])).
% 2.15/2.20 tff(7875,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s21) | (~trans(s59, s21)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s21) | (~trans(s59, s21)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7876,plain,
% 2.15/2.20 (((~trans(s59, s21)) | (~always25(s59)) | always25(s21)) <=> ((~always25(s59)) | always25(s21) | (~trans(s59, s21)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7877,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s21)) | (~always25(s59)) | always25(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s21) | (~trans(s59, s21))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7876])).
% 2.15/2.20 tff(7878,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s21)) | (~always25(s59)) | always25(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s21) | (~trans(s59, s21)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7877, 7875])).
% 2.15/2.20 tff(7879,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s21)) | (~always25(s59)) | always25(s21))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7880,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s21) | (~trans(s59, s21))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7879, 7878])).
% 2.15/2.20 tff(7881,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7880, 6999, 2041, 7739, 7874])).
% 2.15/2.20 tff(7882,plain,(~trans(s59, s21)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7883,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s50) | (~trans(s59, s50)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s50) | (~trans(s59, s50)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7884,plain,
% 2.15/2.20 (((~trans(s59, s50)) | (~always25(s59)) | always25(s50)) <=> ((~always25(s59)) | always25(s50) | (~trans(s59, s50)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7885,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s50)) | (~always25(s59)) | always25(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s50) | (~trans(s59, s50))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7884])).
% 2.15/2.20 tff(7886,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s50)) | (~always25(s59)) | always25(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s50) | (~trans(s59, s50)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7885, 7883])).
% 2.15/2.20 tff(7887,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s50)) | (~always25(s59)) | always25(s50))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7888,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s50) | (~trans(s59, s50))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7887, 7886])).
% 2.15/2.20 tff(7889,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7888, 7010, 2041, 7739, 5030])).
% 2.15/2.20 tff(7890,plain,(~trans(s59, s50)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7891,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s31) | (~trans(s59, s31)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s31) | (~trans(s59, s31)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7892,plain,
% 2.15/2.20 (((~trans(s59, s31)) | (~always25(s59)) | always25(s31)) <=> ((~always25(s59)) | always25(s31) | (~trans(s59, s31)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7893,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s31)) | (~always25(s59)) | always25(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s31) | (~trans(s59, s31))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7892])).
% 2.15/2.20 tff(7894,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s31)) | (~always25(s59)) | always25(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s31) | (~trans(s59, s31)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7893, 7891])).
% 2.15/2.20 tff(7895,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s31)) | (~always25(s59)) | always25(s31))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7896,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s31) | (~trans(s59, s31))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7895, 7894])).
% 2.15/2.20 tff(7897,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7896, 7021, 2041, 7739, 5166])).
% 2.15/2.20 tff(7898,plain,(~trans(s59, s31)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7899,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s32) | (~trans(s59, s32)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s32) | (~trans(s59, s32)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7900,plain,
% 2.15/2.20 (((~trans(s59, s32)) | (~always25(s59)) | always25(s32)) <=> ((~always25(s59)) | always25(s32) | (~trans(s59, s32)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7901,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s32)) | (~always25(s59)) | always25(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s32) | (~trans(s59, s32))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7900])).
% 2.15/2.20 tff(7902,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s32)) | (~always25(s59)) | always25(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s32) | (~trans(s59, s32)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7901, 7899])).
% 2.15/2.20 tff(7903,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s32)) | (~always25(s59)) | always25(s32))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7904,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s32) | (~trans(s59, s32))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7903, 7902])).
% 2.15/2.20 tff(7905,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7904, 7032, 2041, 7739, 5161])).
% 2.15/2.20 tff(7906,plain,(~trans(s59, s32)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7907,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s34) | (~trans(s59, s34)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s34) | (~trans(s59, s34)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7908,plain,
% 2.15/2.20 (((~trans(s59, s34)) | (~always25(s59)) | always25(s34)) <=> ((~always25(s59)) | always25(s34) | (~trans(s59, s34)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7909,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s34)) | (~always25(s59)) | always25(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s34) | (~trans(s59, s34))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7908])).
% 2.15/2.20 tff(7910,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s34)) | (~always25(s59)) | always25(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s34) | (~trans(s59, s34)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7909, 7907])).
% 2.15/2.20 tff(7911,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s34)) | (~always25(s59)) | always25(s34))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7912,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s34) | (~trans(s59, s34))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7911, 7910])).
% 2.15/2.20 tff(7913,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7912, 7043, 2041, 7739, 5146])).
% 2.15/2.20 tff(7914,plain,(~trans(s59, s34)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7915,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s55) | (~trans(s59, s55)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s55) | (~trans(s59, s55)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7916,plain,
% 2.15/2.20 (((~trans(s59, s55)) | (~always25(s59)) | always25(s55)) <=> ((~always25(s59)) | always25(s55) | (~trans(s59, s55)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7917,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s55)) | (~always25(s59)) | always25(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s55) | (~trans(s59, s55))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7916])).
% 2.15/2.20 tff(7918,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s55)) | (~always25(s59)) | always25(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s55) | (~trans(s59, s55)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7917, 7915])).
% 2.15/2.20 tff(7919,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s55)) | (~always25(s59)) | always25(s55))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7920,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s55) | (~trans(s59, s55))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7919, 7918])).
% 2.15/2.20 tff(7921,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7920, 7054, 2041, 7739, 4992])).
% 2.15/2.20 tff(7922,plain,(~trans(s59, s55)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7923,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s16) | (~trans(s59, s16)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s16) | (~trans(s59, s16)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7924,plain,
% 2.15/2.20 (((~trans(s59, s16)) | (~always25(s59)) | always25(s16)) <=> ((~always25(s59)) | always25(s16) | (~trans(s59, s16)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7925,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s16)) | (~always25(s59)) | always25(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s16) | (~trans(s59, s16))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7924])).
% 2.15/2.20 tff(7926,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s16)) | (~always25(s59)) | always25(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s16) | (~trans(s59, s16)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7925, 7923])).
% 2.15/2.20 tff(7927,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s16)) | (~always25(s59)) | always25(s16))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7928,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s16) | (~trans(s59, s16))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7927, 7926])).
% 2.15/2.20 tff(7929,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7928, 7065, 2041, 7739, 5265])).
% 2.15/2.20 tff(7930,plain,(~trans(s59, s16)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7931,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s12) | (~trans(s59, s12)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s12) | (~trans(s59, s12)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7932,plain,
% 2.15/2.20 (((~trans(s59, s12)) | (~always25(s59)) | always25(s12)) <=> ((~always25(s59)) | always25(s12) | (~trans(s59, s12)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7933,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s12)) | (~always25(s59)) | always25(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s12) | (~trans(s59, s12))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7932])).
% 2.15/2.20 tff(7934,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s12)) | (~always25(s59)) | always25(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s12) | (~trans(s59, s12)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7933, 7931])).
% 2.15/2.20 tff(7935,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s12)) | (~always25(s59)) | always25(s12))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7936,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s12) | (~trans(s59, s12))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7935, 7934])).
% 2.15/2.20 tff(7937,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7936, 7076, 2041, 7739, 5294])).
% 2.15/2.20 tff(7938,plain,(~trans(s59, s12)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7939,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s1) | (~trans(s59, s1)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s1) | (~trans(s59, s1)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7940,plain,
% 2.15/2.20 (((~trans(s59, s1)) | (~always25(s59)) | always25(s1)) <=> ((~always25(s59)) | always25(s1) | (~trans(s59, s1)))),
% 2.15/2.20 inference(rewrite,[status(thm)],[])).
% 2.15/2.20 tff(7941,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s1)) | (~always25(s59)) | always25(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s1) | (~trans(s59, s1))))),
% 2.15/2.20 inference(monotonicity,[status(thm)],[7940])).
% 2.15/2.20 tff(7942,plain,
% 2.15/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s1)) | (~always25(s59)) | always25(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s1) | (~trans(s59, s1)))),
% 2.15/2.20 inference(transitivity,[status(thm)],[7941, 7939])).
% 2.15/2.20 tff(7943,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s1)) | (~always25(s59)) | always25(s1))),
% 2.15/2.20 inference(quant_inst,[status(thm)],[])).
% 2.15/2.20 tff(7944,plain,
% 2.15/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s1) | (~trans(s59, s1))),
% 2.15/2.20 inference(modus_ponens,[status(thm)],[7943, 7942])).
% 2.15/2.20 tff(7945,plain,
% 2.15/2.20 ($false),
% 2.15/2.20 inference(unit_resolution,[status(thm)],[7944, 7097, 2041, 7739, 5371])).
% 2.15/2.20 tff(7946,plain,(~trans(s59, s1)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.20 tff(7947,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s51) | (~trans(s59, s51)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s51) | (~trans(s59, s51)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7948,plain,
% 2.15/2.21 (((~trans(s59, s51)) | (~always25(s59)) | always25(s51)) <=> ((~always25(s59)) | always25(s51) | (~trans(s59, s51)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7949,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s51)) | (~always25(s59)) | always25(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s51) | (~trans(s59, s51))))),
% 2.15/2.21 inference(monotonicity,[status(thm)],[7948])).
% 2.15/2.21 tff(7950,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s51)) | (~always25(s59)) | always25(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s51) | (~trans(s59, s51)))),
% 2.15/2.21 inference(transitivity,[status(thm)],[7949, 7947])).
% 2.15/2.21 tff(7951,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s51)) | (~always25(s59)) | always25(s51))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(7952,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s51) | (~trans(s59, s51))),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[7951, 7950])).
% 2.15/2.21 tff(7953,plain,
% 2.15/2.21 ($false),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7952, 7108, 2041, 7739, 5021])).
% 2.15/2.21 tff(7954,plain,(~trans(s59, s51)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.21 tff(7955,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s33, s34)) | (~always25(s33)) | always25(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s33, s34)) | (~always25(s33)) | always25(s34))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7956,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s33, s34)) | (~always25(s33)) | always25(s34))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(7957,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s33, s34)) | (~always25(s33)) | always25(s34)),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[7956, 7955])).
% 2.15/2.21 tff(7958,plain,
% 2.15/2.21 ((~always25(s33)) | always25(s34)),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7957, 2041, 3164])).
% 2.15/2.21 tff(7959,plain,
% 2.15/2.21 (~always25(s33)),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7958, 5146])).
% 2.15/2.21 tff(7960,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s33) | (~trans(s59, s33)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s33) | (~trans(s59, s33)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7961,plain,
% 2.15/2.21 (((~trans(s59, s33)) | (~always25(s59)) | always25(s33)) <=> ((~always25(s59)) | always25(s33) | (~trans(s59, s33)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7962,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s33)) | (~always25(s59)) | always25(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s33) | (~trans(s59, s33))))),
% 2.15/2.21 inference(monotonicity,[status(thm)],[7961])).
% 2.15/2.21 tff(7963,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s33)) | (~always25(s59)) | always25(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s33) | (~trans(s59, s33)))),
% 2.15/2.21 inference(transitivity,[status(thm)],[7962, 7960])).
% 2.15/2.21 tff(7964,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s33)) | (~always25(s59)) | always25(s33))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(7965,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s33) | (~trans(s59, s33))),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[7964, 7963])).
% 2.15/2.21 tff(7966,plain,
% 2.15/2.21 ($false),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7965, 7119, 2041, 7739, 7959])).
% 2.15/2.21 tff(7967,plain,(~trans(s59, s33)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.21 tff(7968,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s48) | (~trans(s59, s48)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s48) | (~trans(s59, s48)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7969,plain,
% 2.15/2.21 (((~trans(s59, s48)) | (~always25(s59)) | always25(s48)) <=> ((~always25(s59)) | always25(s48) | (~trans(s59, s48)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7970,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s48)) | (~always25(s59)) | always25(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s48) | (~trans(s59, s48))))),
% 2.15/2.21 inference(monotonicity,[status(thm)],[7969])).
% 2.15/2.21 tff(7971,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s48)) | (~always25(s59)) | always25(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s48) | (~trans(s59, s48)))),
% 2.15/2.21 inference(transitivity,[status(thm)],[7970, 7968])).
% 2.15/2.21 tff(7972,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s48)) | (~always25(s59)) | always25(s48))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(7973,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s48) | (~trans(s59, s48))),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[7972, 7971])).
% 2.15/2.21 tff(7974,plain,
% 2.15/2.21 ($false),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7973, 7130, 2041, 7739, 5045])).
% 2.15/2.21 tff(7975,plain,(~trans(s59, s48)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.21 tff(7976,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s42) | (~trans(s59, s42)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s42) | (~trans(s59, s42)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7977,plain,
% 2.15/2.21 (((~trans(s59, s42)) | (~always25(s59)) | always25(s42)) <=> ((~always25(s59)) | always25(s42) | (~trans(s59, s42)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7978,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s42)) | (~always25(s59)) | always25(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s42) | (~trans(s59, s42))))),
% 2.15/2.21 inference(monotonicity,[status(thm)],[7977])).
% 2.15/2.21 tff(7979,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s42)) | (~always25(s59)) | always25(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s42) | (~trans(s59, s42)))),
% 2.15/2.21 inference(transitivity,[status(thm)],[7978, 7976])).
% 2.15/2.21 tff(7980,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s42)) | (~always25(s59)) | always25(s42))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(7981,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s42) | (~trans(s59, s42))),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[7980, 7979])).
% 2.15/2.21 tff(7982,plain,
% 2.15/2.21 ($false),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7981, 7141, 2041, 7739, 5088])).
% 2.15/2.21 tff(7983,plain,(~trans(s59, s42)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.21 tff(7984,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s20) | (~trans(s59, s20)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s20) | (~trans(s59, s20)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7985,plain,
% 2.15/2.21 (((~trans(s59, s20)) | (~always25(s59)) | always25(s20)) <=> ((~always25(s59)) | always25(s20) | (~trans(s59, s20)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7986,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s20)) | (~always25(s59)) | always25(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s20) | (~trans(s59, s20))))),
% 2.15/2.21 inference(monotonicity,[status(thm)],[7985])).
% 2.15/2.21 tff(7987,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s20)) | (~always25(s59)) | always25(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s20) | (~trans(s59, s20)))),
% 2.15/2.21 inference(transitivity,[status(thm)],[7986, 7984])).
% 2.15/2.21 tff(7988,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s20)) | (~always25(s59)) | always25(s20))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(7989,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s20) | (~trans(s59, s20))),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[7988, 7987])).
% 2.15/2.21 tff(7990,plain,
% 2.15/2.21 ($false),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7989, 7152, 2041, 7739, 2031])).
% 2.15/2.21 tff(7991,plain,(~trans(s59, s20)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.21 tff(7992,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s0, s1)) | (~always25(s0)) | always25(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s0, s1)) | (~always25(s0)) | always25(s1))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7993,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s0, s1)) | (~always25(s0)) | always25(s1))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(7994,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s0, s1)) | (~always25(s0)) | always25(s1)),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[7993, 7992])).
% 2.15/2.21 tff(7995,plain,
% 2.15/2.21 ((~always25(s0)) | always25(s1)),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7994, 2041, 39])).
% 2.15/2.21 tff(7996,plain,
% 2.15/2.21 (~always25(s0)),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[7995, 5371])).
% 2.15/2.21 tff(7997,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s0) | (~trans(s59, s0)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s0) | (~trans(s59, s0)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7998,plain,
% 2.15/2.21 (((~trans(s59, s0)) | (~always25(s59)) | always25(s0)) <=> ((~always25(s59)) | always25(s0) | (~trans(s59, s0)))),
% 2.15/2.21 inference(rewrite,[status(thm)],[])).
% 2.15/2.21 tff(7999,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s0)) | (~always25(s59)) | always25(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s0) | (~trans(s59, s0))))),
% 2.15/2.21 inference(monotonicity,[status(thm)],[7998])).
% 2.15/2.21 tff(8000,plain,
% 2.15/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s0)) | (~always25(s59)) | always25(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s0) | (~trans(s59, s0)))),
% 2.15/2.21 inference(transitivity,[status(thm)],[7999, 7997])).
% 2.15/2.21 tff(8001,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s0)) | (~always25(s59)) | always25(s0))),
% 2.15/2.21 inference(quant_inst,[status(thm)],[])).
% 2.15/2.21 tff(8002,plain,
% 2.15/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s0) | (~trans(s59, s0))),
% 2.15/2.21 inference(modus_ponens,[status(thm)],[8001, 8000])).
% 2.15/2.21 tff(8003,plain,
% 2.15/2.21 ($false),
% 2.15/2.21 inference(unit_resolution,[status(thm)],[8002, 7173, 2041, 7739, 7996])).
% 2.15/2.22 tff(8004,plain,(~trans(s59, s0)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.22 tff(8005,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s22) | (~trans(s59, s22)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s22) | (~trans(s59, s22)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8006,plain,
% 2.15/2.22 (((~trans(s59, s22)) | (~always25(s59)) | always25(s22)) <=> ((~always25(s59)) | always25(s22) | (~trans(s59, s22)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8007,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s22)) | (~always25(s59)) | always25(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s22) | (~trans(s59, s22))))),
% 2.15/2.22 inference(monotonicity,[status(thm)],[8006])).
% 2.15/2.22 tff(8008,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s22)) | (~always25(s59)) | always25(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s22) | (~trans(s59, s22)))),
% 2.15/2.22 inference(transitivity,[status(thm)],[8007, 8005])).
% 2.15/2.22 tff(8009,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s22)) | (~always25(s59)) | always25(s22))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8010,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s22) | (~trans(s59, s22))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8009, 8008])).
% 2.15/2.22 tff(8011,plain,
% 2.15/2.22 ($false),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8010, 7184, 2041, 7739, 5233])).
% 2.15/2.22 tff(8012,plain,(~trans(s59, s22)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.22 tff(8013,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s29, s30)) | (~always25(s29)) | always25(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s29, s30)) | (~always25(s29)) | always25(s30))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8014,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s29, s30)) | (~always25(s29)) | always25(s30))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8015,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s29, s30)) | (~always25(s29)) | always25(s30)),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8014, 8013])).
% 2.15/2.22 tff(8016,plain,
% 2.15/2.22 ((~always25(s29)) | always25(s30)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8015, 2041, 2831])).
% 2.15/2.22 tff(8017,plain,
% 2.15/2.22 (~always25(s29)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8016, 5175])).
% 2.15/2.22 tff(8018,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s29) | (~trans(s59, s29)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s29) | (~trans(s59, s29)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8019,plain,
% 2.15/2.22 (((~trans(s59, s29)) | (~always25(s59)) | always25(s29)) <=> ((~always25(s59)) | always25(s29) | (~trans(s59, s29)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8020,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s29)) | (~always25(s59)) | always25(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s29) | (~trans(s59, s29))))),
% 2.15/2.22 inference(monotonicity,[status(thm)],[8019])).
% 2.15/2.22 tff(8021,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s29)) | (~always25(s59)) | always25(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s29) | (~trans(s59, s29)))),
% 2.15/2.22 inference(transitivity,[status(thm)],[8020, 8018])).
% 2.15/2.22 tff(8022,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s29)) | (~always25(s59)) | always25(s29))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8023,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s29) | (~trans(s59, s29))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 2.15/2.22 tff(8024,plain,
% 2.15/2.22 ($false),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8023, 7195, 2041, 7739, 8017])).
% 2.15/2.22 tff(8025,plain,(~trans(s59, s29)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.22 tff(8026,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s41, s42)) | (~always25(s41)) | always25(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s41, s42)) | (~always25(s41)) | always25(s42))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8027,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s41, s42)) | (~always25(s41)) | always25(s42))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8028,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s41, s42)) | (~always25(s41)) | always25(s42)),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 2.15/2.22 tff(8029,plain,
% 2.15/2.22 ((~always25(s41)) | always25(s42)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8028, 2041, 3792])).
% 2.15/2.22 tff(8030,plain,
% 2.15/2.22 (~always25(s41)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8029, 5088])).
% 2.15/2.22 tff(8031,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s41) | (~trans(s59, s41)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s41) | (~trans(s59, s41)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8032,plain,
% 2.15/2.22 (((~trans(s59, s41)) | (~always25(s59)) | always25(s41)) <=> ((~always25(s59)) | always25(s41) | (~trans(s59, s41)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8033,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s41)) | (~always25(s59)) | always25(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s41) | (~trans(s59, s41))))),
% 2.15/2.22 inference(monotonicity,[status(thm)],[8032])).
% 2.15/2.22 tff(8034,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s41)) | (~always25(s59)) | always25(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s41) | (~trans(s59, s41)))),
% 2.15/2.22 inference(transitivity,[status(thm)],[8033, 8031])).
% 2.15/2.22 tff(8035,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s41)) | (~always25(s59)) | always25(s41))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8036,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s41) | (~trans(s59, s41))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8035, 8034])).
% 2.15/2.22 tff(8037,plain,
% 2.15/2.22 ($false),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8036, 7206, 2041, 7739, 8030])).
% 2.15/2.22 tff(8038,plain,(~trans(s59, s41)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.22 tff(8039,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s10) | (~trans(s59, s10)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s10) | (~trans(s59, s10)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8040,plain,
% 2.15/2.22 (((~trans(s59, s10)) | (~always25(s59)) | always25(s10)) <=> ((~always25(s59)) | always25(s10) | (~trans(s59, s10)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8041,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s10)) | (~always25(s59)) | always25(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s10) | (~trans(s59, s10))))),
% 2.15/2.22 inference(monotonicity,[status(thm)],[8040])).
% 2.15/2.22 tff(8042,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s10)) | (~always25(s59)) | always25(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s10) | (~trans(s59, s10)))),
% 2.15/2.22 inference(transitivity,[status(thm)],[8041, 8039])).
% 2.15/2.22 tff(8043,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s10)) | (~always25(s59)) | always25(s10))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8044,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s10) | (~trans(s59, s10))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8043, 8042])).
% 2.15/2.22 tff(8045,plain,
% 2.15/2.22 ($false),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8044, 7217, 2041, 7739, 5308])).
% 2.15/2.22 tff(8046,plain,(~trans(s59, s10)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.22 tff(8047,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s47) | (~trans(s59, s47)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s47) | (~trans(s59, s47)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8048,plain,
% 2.15/2.22 (((~trans(s59, s47)) | (~always25(s59)) | always25(s47)) <=> ((~always25(s59)) | always25(s47) | (~trans(s59, s47)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8049,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s47)) | (~always25(s59)) | always25(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s47) | (~trans(s59, s47))))),
% 2.15/2.22 inference(monotonicity,[status(thm)],[8048])).
% 2.15/2.22 tff(8050,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s47)) | (~always25(s59)) | always25(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s47) | (~trans(s59, s47)))),
% 2.15/2.22 inference(transitivity,[status(thm)],[8049, 8047])).
% 2.15/2.22 tff(8051,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s47)) | (~always25(s59)) | always25(s47))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8052,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s47) | (~trans(s59, s47))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8051, 8050])).
% 2.15/2.22 tff(8053,plain,
% 2.15/2.22 ($false),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8052, 7228, 2041, 7739, 5050])).
% 2.15/2.22 tff(8054,plain,(~trans(s59, s47)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.22 tff(8055,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s5, s6)) | (~always25(s5)) | always25(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s5, s6)) | (~always25(s5)) | always25(s6))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8056,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s5, s6)) | (~always25(s5)) | always25(s6))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8057,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s5, s6)) | (~always25(s5)) | always25(s6)),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8056, 8055])).
% 2.15/2.22 tff(8058,plain,
% 2.15/2.22 ((~always25(s5)) | always25(s6)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8057, 2041, 878])).
% 2.15/2.22 tff(8059,plain,
% 2.15/2.22 (~always25(s5)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8058, 5337])).
% 2.15/2.22 tff(8060,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s5) | (~trans(s59, s5)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s5) | (~trans(s59, s5)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8061,plain,
% 2.15/2.22 (((~trans(s59, s5)) | (~always25(s59)) | always25(s5)) <=> ((~always25(s59)) | always25(s5) | (~trans(s59, s5)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8062,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s5)) | (~always25(s59)) | always25(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s5) | (~trans(s59, s5))))),
% 2.15/2.22 inference(monotonicity,[status(thm)],[8061])).
% 2.15/2.22 tff(8063,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s5)) | (~always25(s59)) | always25(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s5) | (~trans(s59, s5)))),
% 2.15/2.22 inference(transitivity,[status(thm)],[8062, 8060])).
% 2.15/2.22 tff(8064,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s5)) | (~always25(s59)) | always25(s5))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8065,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s5) | (~trans(s59, s5))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8064, 8063])).
% 2.15/2.22 tff(8066,plain,
% 2.15/2.22 ($false),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8065, 7239, 2041, 7739, 8059])).
% 2.15/2.22 tff(8067,plain,(~trans(s59, s5)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.22 tff(8068,assumption,(node18(s59, s59)), introduced(assumption)).
% 2.15/2.22 tff(8069,plain,
% 2.15/2.22 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_c2)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8070,plain,
% 2.15/2.22 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_c2)))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8071,plain,
% 2.15/2.22 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s57, c_n2)) | (~m_main_v_state2(s57, c_c2))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8070, 8069])).
% 2.15/2.22 tff(8072,plain,
% 2.15/2.22 (~m_main_v_state2(s57, c_c2)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8071, 697, 4965])).
% 2.15/2.22 tff(8073,plain,
% 2.15/2.22 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s57, c_c2) | (~node3(s57)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s57, c_c2) | (~node3(s57)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8074,plain,
% 2.15/2.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s57, c_c2) | (~node3(s57)))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8075,plain,
% 2.15/2.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s57, c_c2) | (~node3(s57))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8074, 8073])).
% 2.15/2.22 tff(8076,plain,
% 2.15/2.22 (~node3(s57)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8075, 399, 8072])).
% 2.15/2.22 tff(8077,plain,
% 2.15/2.22 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s56, c_n1) | (~node1(s56)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s56, c_n1) | (~node1(s56)))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8078,plain,
% 2.15/2.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s56, c_n1) | (~node1(s56)))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8079,plain,
% 2.15/2.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s56, c_n1) | (~node1(s56))),
% 2.15/2.22 inference(modus_ponens,[status(thm)],[8078, 8077])).
% 2.15/2.22 tff(8080,plain,
% 2.15/2.22 (~node1(s56)),
% 2.15/2.22 inference(unit_resolution,[status(thm)],[8079, 421, 4922])).
% 2.15/2.22 tff(8081,plain,
% 2.15/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s55, s56)) | node18(s55, s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s55, s56)) | node18(s55, s56))),
% 2.15/2.22 inference(rewrite,[status(thm)],[])).
% 2.15/2.22 tff(8082,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s55, s56)) | node18(s55, s56))),
% 2.15/2.22 inference(quant_inst,[status(thm)],[])).
% 2.15/2.22 tff(8083,plain,
% 2.15/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s55, s56)) | node18(s55, s56)),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8082, 8081])).
% 2.15/2.23 tff(8084,plain,
% 2.15/2.23 (node18(s55, s56)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8083, 125, 4892])).
% 2.15/2.23 tff(8085,plain,
% 2.15/2.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node18(s55, s56)) | m_main_v_turn(s56, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node18(s55, s56)) | m_main_v_turn(s56, c_2))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8086,plain,
% 2.15/2.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node18(s55, s56)) | m_main_v_turn(s56, c_2))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8087,plain,
% 2.15/2.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node18(s55, s56)) | m_main_v_turn(s56, c_2)),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8086, 8085])).
% 2.15/2.23 tff(8088,plain,
% 2.15/2.23 ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | m_main_v_turn(s56, c_2)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8087, 760, 8084])).
% 2.15/2.23 tff(8089,plain,
% 2.15/2.23 (m_main_v_turn(s56, c_2)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8088, 4845, 4881])).
% 2.15/2.23 tff(8090,plain,
% 2.15/2.23 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s56, c_1)) | (~m_main_v_turn(s56, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s56, c_1)) | (~m_main_v_turn(s56, c_2)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8091,plain,
% 2.15/2.23 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s56, c_1)) | (~m_main_v_turn(s56, c_2)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8092,plain,
% 2.15/2.23 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s56, c_1)) | (~m_main_v_turn(s56, c_2))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8091, 8090])).
% 2.15/2.23 tff(8093,plain,
% 2.15/2.23 (~m_main_v_turn(s56, c_1)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8092, 156, 8089])).
% 2.15/2.23 tff(8094,plain,
% 2.15/2.23 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s56, c_1) | (~node5(s56)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s56, c_1) | (~node5(s56)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8095,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s56, c_1) | (~node5(s56)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8096,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s56, c_1) | (~node5(s56))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8095, 8094])).
% 2.15/2.23 tff(8097,plain,
% 2.15/2.23 (~node5(s56)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8096, 776, 8093])).
% 2.15/2.23 tff(8098,plain,
% 2.15/2.23 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s56, c_n1) | (~node2(s56)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s56, c_n1) | (~node2(s56)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8099,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s56, c_n1) | (~node2(s56)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8100,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s56, c_n1) | (~node2(s56))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8099, 8098])).
% 2.15/2.23 tff(8101,plain,
% 2.15/2.23 (~node2(s56)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8100, 787, 4922])).
% 2.15/2.23 tff(8102,plain,
% 2.15/2.23 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s56, c_n1) | (~node3(s56)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s56, c_n1) | (~node3(s56)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8103,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s56, c_n1) | (~node3(s56)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8104,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s56, c_n1) | (~node3(s56))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8103, 8102])).
% 2.15/2.23 tff(8105,plain,
% 2.15/2.23 (~node3(s56)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8104, 798, 4922])).
% 2.15/2.23 tff(8106,plain,
% 2.15/2.23 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s56, c_n2) | (~node4(s56)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s56, c_n2) | (~node4(s56)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8107,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s56, c_n2) | (~node4(s56)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8108,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s56, c_n2) | (~node4(s56))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8107, 8106])).
% 2.15/2.23 tff(8109,plain,
% 2.15/2.23 (~node4(s56)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8108, 388, 4942])).
% 2.15/2.23 tff(8110,plain,
% 2.15/2.23 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s56, s57)) | node7(s56, s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s56, s57)) | node7(s56, s57))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8111,plain,
% 2.15/2.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s56, s57)) | node7(s56, s57))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8112,plain,
% 2.15/2.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s56, s57)) | node7(s56, s57)),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8111, 8110])).
% 2.15/2.23 tff(8113,plain,
% 2.15/2.23 (node7(s56, s57)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8112, 206, 4953])).
% 2.15/2.23 tff(8114,plain,
% 2.15/2.23 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57) | (~node7(s56, s57)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57) | (~node7(s56, s57)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8115,plain,
% 2.15/2.23 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57) | (~node7(s56, s57)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8116,plain,
% 2.15/2.23 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57) | (~node7(s56, s57))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8115, 8114])).
% 2.15/2.23 tff(8117,plain,
% 2.15/2.23 (m_main_v_state1(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8116, 820, 8113])).
% 2.15/2.23 tff(8118,plain,
% 2.15/2.23 (node6(s56, s57)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8117, 8109, 4930, 8105, 8101, 8097, 8080])).
% 2.15/2.23 tff(8119,plain,
% 2.15/2.23 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8120,plain,
% 2.15/2.23 (((~node6(s56, s57)) | m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1))) <=> (m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8121,plain,
% 2.15/2.23 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s56, s57)) | m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57))))),
% 2.15/2.23 inference(monotonicity,[status(thm)],[8120])).
% 2.15/2.23 tff(8122,plain,
% 2.15/2.23 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s56, s57)) | m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57)))),
% 2.15/2.23 inference(transitivity,[status(thm)],[8121, 8119])).
% 2.15/2.23 tff(8123,plain,
% 2.15/2.23 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s56, s57)) | m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8124,plain,
% 2.15/2.23 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s56, c_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8123, 8122])).
% 2.15/2.23 tff(8125,plain,
% 2.15/2.23 (~m_main_v_state1(s57, c_n1)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8124, 835, 4922, 8118])).
% 2.15/2.23 tff(8126,plain,
% 2.15/2.23 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s57, c_n1) | (~node2(s57)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s57, c_n1) | (~node2(s57)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8127,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s57, c_n1) | (~node2(s57)))),
% 2.15/2.23 inference(quant_inst,[status(thm)],[])).
% 2.15/2.23 tff(8128,plain,
% 2.15/2.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s57, c_n1) | (~node2(s57))),
% 2.15/2.23 inference(modus_ponens,[status(thm)],[8127, 8126])).
% 2.15/2.23 tff(8129,plain,
% 2.15/2.23 (~node2(s57)),
% 2.15/2.23 inference(unit_resolution,[status(thm)],[8128, 787, 8125])).
% 2.15/2.23 tff(8130,plain,
% 2.15/2.23 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1) | (~node6(s56, s57)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1) | (~node6(s56, s57)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8131,plain,
% 2.15/2.23 (((~node6(s56, s57)) | (~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1)) <=> ((~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1) | (~node6(s56, s57)))),
% 2.15/2.23 inference(rewrite,[status(thm)],[])).
% 2.15/2.23 tff(8132,plain,
% 2.15/2.23 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s56, s57)) | (~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1) | (~node6(s56, s57))))),
% 2.15/2.23 inference(monotonicity,[status(thm)],[8131])).
% 2.15/2.23 tff(8133,plain,
% 2.15/2.23 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s56, s57)) | (~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1) | (~node6(s56, s57)))),
% 2.15/2.23 inference(transitivity,[status(thm)],[8132, 8130])).
% 2.15/2.23 tff(8134,plain,
% 2.15/2.23 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s56, s57)) | (~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8135,plain,
% 2.15/2.24 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s56, c_t1)) | m_main_v_state1(s57, c_t1) | (~node6(s56, s57))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8134, 8133])).
% 2.15/2.24 tff(8136,plain,
% 2.15/2.24 (m_main_v_state1(s57, c_t1)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8135, 856, 4918, 8118])).
% 2.15/2.24 tff(8137,plain,
% 2.15/2.24 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s57, c_t2) | (~node1(s57)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s57, c_t2) | (~node1(s57)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8138,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s57, c_t2) | (~node1(s57)))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8139,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s57, c_t2) | (~node1(s57))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8138, 8137])).
% 2.15/2.24 tff(8140,plain,
% 2.15/2.24 (~node1(s57)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8139, 195, 4969])).
% 2.15/2.24 tff(8141,plain,
% 2.15/2.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8142,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8143,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58)),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8142, 8141])).
% 2.15/2.24 tff(8144,plain,
% 2.15/2.24 (trans(s57, s58)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8143, 6186, 32])).
% 2.15/2.24 tff(8145,plain,
% 2.15/2.24 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s57, s58)) | node7(s57, s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s57, s58)) | node7(s57, s58))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8146,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s57, s58)) | node7(s57, s58))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8147,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s57, s58)) | node7(s57, s58)),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8146, 8145])).
% 2.15/2.24 tff(8148,plain,
% 2.15/2.24 (node7(s57, s58)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8147, 206, 8144])).
% 2.15/2.24 tff(8149,plain,
% 2.15/2.24 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state1(s58, c_c1) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state1(s58, c_c1) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8150,plain,
% 2.15/2.24 (((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)) | m_main_v_state1(s58, c_c1)) <=> ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state1(s58, c_c1) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8151,plain,
% 2.15/2.24 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)) | m_main_v_state1(s58, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state1(s58, c_c1) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58))))),
% 2.15/2.24 inference(monotonicity,[status(thm)],[8150])).
% 2.15/2.24 tff(8152,plain,
% 2.15/2.24 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)) | m_main_v_state1(s58, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state1(s58, c_c1) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)))),
% 2.15/2.24 inference(transitivity,[status(thm)],[8151, 8149])).
% 2.15/2.24 tff(8153,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58)) | m_main_v_state1(s58, c_c1))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8154,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state1(s58, c_c1) | node1(s57) | node2(s57) | node3(s57) | (~node7(s57, s58))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8153, 8152])).
% 2.15/2.24 tff(8155,plain,
% 2.15/2.24 ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state1(s58, c_c1) | node1(s57) | node2(s57) | node3(s57)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8154, 892, 8148])).
% 2.15/2.24 tff(8156,plain,
% 2.15/2.24 (m_main_v_state1(s58, c_c1)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8155, 8140, 4965, 8136, 8129, 8076])).
% 2.15/2.24 tff(8157,plain,
% 2.15/2.24 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s58, c_t1)) | (~m_main_v_state1(s58, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s58, c_t1)) | (~m_main_v_state1(s58, c_c1)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8158,plain,
% 2.15/2.24 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s58, c_t1)) | (~m_main_v_state1(s58, c_c1)))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8159,plain,
% 2.15/2.24 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s58, c_t1)) | (~m_main_v_state1(s58, c_c1))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8158, 8157])).
% 2.15/2.24 tff(8160,plain,
% 2.15/2.24 (~m_main_v_state1(s58, c_t1)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8159, 539, 8156])).
% 2.15/2.24 tff(8161,plain,
% 2.15/2.24 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s58, c_t1) | (~node5(s58)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s58, c_t1) | (~node5(s58)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8162,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s58, c_t1) | (~node5(s58)))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8163,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s58, c_t1) | (~node5(s58))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8162, 8161])).
% 2.15/2.24 tff(8164,plain,
% 2.15/2.24 (~node5(s58)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8163, 550, 8160])).
% 2.15/2.24 tff(8165,plain,
% 2.15/2.24 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s57, s58)) | node14(s57, s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s57, s58)) | node14(s57, s58))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8166,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s57, s58)) | node14(s57, s58))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8167,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s57, s58)) | node14(s57, s58)),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8166, 8165])).
% 2.15/2.24 tff(8168,plain,
% 2.15/2.24 (node14(s57, s58)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8167, 46, 8144])).
% 2.15/2.24 tff(8169,plain,
% 2.15/2.24 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | (~node14(s57, s58)) | m_main_v_state2(s58, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | (~node14(s57, s58)) | m_main_v_state2(s58, c_t2))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8170,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | (~node14(s57, s58)) | m_main_v_state2(s58, c_t2))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8171,plain,
% 2.15/2.24 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | (~node14(s57, s58)) | m_main_v_state2(s58, c_t2)),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8170, 8169])).
% 2.15/2.24 tff(8172,plain,
% 2.15/2.24 ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state2(s58, c_t2)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8171, 922, 8168])).
% 2.15/2.24 tff(8173,plain,
% 2.15/2.24 (m_main_v_state2(s58, c_t2)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8172, 8136, 4965])).
% 2.15/2.24 tff(8174,plain,
% 2.15/2.24 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s58, c_n2)) | (~m_main_v_state2(s58, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s58, c_n2)) | (~m_main_v_state2(s58, c_t2)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8175,plain,
% 2.15/2.24 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s58, c_n2)) | (~m_main_v_state2(s58, c_t2)))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8176,plain,
% 2.15/2.24 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s58, c_n2)) | (~m_main_v_state2(s58, c_t2))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8175, 8174])).
% 2.15/2.24 tff(8177,plain,
% 2.15/2.24 (~m_main_v_state2(s58, c_n2)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8176, 77, 8173])).
% 2.15/2.24 tff(8178,plain,
% 2.15/2.24 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s58, c_n2) | (~node2(s58)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s58, c_n2) | (~node2(s58)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8179,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s58, c_n2) | (~node2(s58)))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8180,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s58, c_n2) | (~node2(s58))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8179, 8178])).
% 2.15/2.24 tff(8181,plain,
% 2.15/2.24 (~node2(s58)),
% 2.15/2.24 inference(unit_resolution,[status(thm)],[8180, 410, 8177])).
% 2.15/2.24 tff(8182,plain,
% 2.15/2.24 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s58, c_n2) | (~node4(s58)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s58, c_n2) | (~node4(s58)))),
% 2.15/2.24 inference(rewrite,[status(thm)],[])).
% 2.15/2.24 tff(8183,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s58, c_n2) | (~node4(s58)))),
% 2.15/2.24 inference(quant_inst,[status(thm)],[])).
% 2.15/2.24 tff(8184,plain,
% 2.15/2.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s58, c_n2) | (~node4(s58))),
% 2.15/2.24 inference(modus_ponens,[status(thm)],[8183, 8182])).
% 2.15/2.24 tff(8185,plain,
% 2.15/2.25 (~node4(s58)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8184, 388, 8177])).
% 2.15/2.25 tff(8186,plain,
% 2.15/2.25 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s58, c_t2)) | (~m_main_v_state2(s58, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s58, c_t2)) | (~m_main_v_state2(s58, c_c2)))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8187,plain,
% 2.15/2.25 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s58, c_t2)) | (~m_main_v_state2(s58, c_c2)))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8188,plain,
% 2.15/2.25 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s58, c_t2)) | (~m_main_v_state2(s58, c_c2))),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8187, 8186])).
% 2.15/2.25 tff(8189,plain,
% 2.15/2.25 (~m_main_v_state2(s58, c_c2)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8188, 260, 8173])).
% 2.15/2.25 tff(8190,plain,
% 2.15/2.25 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s58, c_c2) | (~node3(s58)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s58, c_c2) | (~node3(s58)))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8191,plain,
% 2.15/2.25 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s58, c_c2) | (~node3(s58)))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8192,plain,
% 2.15/2.25 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s58, c_c2) | (~node3(s58))),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8191, 8190])).
% 2.15/2.25 tff(8193,plain,
% 2.15/2.25 (~node3(s58)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8192, 399, 8189])).
% 2.15/2.25 tff(8194,plain,
% 2.15/2.25 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s58, c_n1)) | (~m_main_v_state1(s58, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s58, c_n1)) | (~m_main_v_state1(s58, c_c1)))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8195,plain,
% 2.15/2.25 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s58, c_n1)) | (~m_main_v_state1(s58, c_c1)))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8196,plain,
% 2.15/2.25 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s58, c_n1)) | (~m_main_v_state1(s58, c_c1))),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8195, 8194])).
% 2.15/2.25 tff(8197,plain,
% 2.15/2.25 (~m_main_v_state1(s58, c_n1)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8196, 454, 8156])).
% 2.15/2.25 tff(8198,plain,
% 2.15/2.25 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s58, c_n1) | (~node1(s58)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s58, c_n1) | (~node1(s58)))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8199,plain,
% 2.15/2.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s58, c_n1) | (~node1(s58)))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8200,plain,
% 2.15/2.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s58, c_n1) | (~node1(s58))),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8199, 8198])).
% 2.15/2.25 tff(8201,plain,
% 2.15/2.25 (~node1(s58)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8200, 421, 8197])).
% 2.15/2.25 tff(8202,plain,
% 2.15/2.25 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s58, s59)) | node7(s58, s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s58, s59)) | node7(s58, s59))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8203,plain,
% 2.15/2.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s58, s59)) | node7(s58, s59))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8204,plain,
% 2.15/2.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s58, s59)) | node7(s58, s59)),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8203, 8202])).
% 2.15/2.25 tff(8205,plain,
% 2.15/2.25 (node7(s58, s59)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8204, 206, 2054])).
% 2.15/2.25 tff(8206,plain,
% 2.15/2.25 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)) | m_main_v_state1(s59, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)) | m_main_v_state1(s59, c_n1))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8207,plain,
% 2.15/2.25 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)) | m_main_v_state1(s59, c_n1))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8208,plain,
% 2.15/2.25 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)) | m_main_v_state1(s59, c_n1)),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8207, 8206])).
% 2.15/2.25 tff(8209,plain,
% 2.15/2.25 ((~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | m_main_v_state1(s59, c_n1)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8208, 584, 8205])).
% 2.15/2.25 tff(8210,plain,
% 2.15/2.25 (m_main_v_state1(s59, c_n1)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8209, 8201, 8156, 8193, 8185, 8181, 8164])).
% 2.15/2.25 tff(8211,plain,
% 2.15/2.25 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s57, c_t2) | (~node15(s57)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s57, c_t2) | (~node15(s57)))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8212,plain,
% 2.15/2.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s57, c_t2) | (~node15(s57)))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8213,plain,
% 2.15/2.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s57, c_t2) | (~node15(s57))),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8212, 8211])).
% 2.15/2.25 tff(8214,plain,
% 2.15/2.25 (~node15(s57)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8213, 103, 4969])).
% 2.15/2.25 tff(8215,plain,
% 2.15/2.25 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s57, s58)) | node18(s57, s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s57, s58)) | node18(s57, s58))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8216,plain,
% 2.15/2.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s57, s58)) | node18(s57, s58))),
% 2.15/2.25 inference(quant_inst,[status(thm)],[])).
% 2.15/2.25 tff(8217,plain,
% 2.15/2.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s57, s58)) | node18(s57, s58)),
% 2.15/2.25 inference(modus_ponens,[status(thm)],[8216, 8215])).
% 2.15/2.25 tff(8218,plain,
% 2.15/2.25 (node18(s57, s58)),
% 2.15/2.25 inference(unit_resolution,[status(thm)],[8217, 125, 8144])).
% 2.15/2.25 tff(8219,plain,
% 2.15/2.25 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s57) | (~node18(s57, s58)) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s57) | (~node18(s57, s58)) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8220,plain,
% 2.15/2.25 (((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node15(s57) | (~node18(s57, s58)) | m_main_v_turn(s58, c_1)) <=> (node15(s57) | (~node18(s57, s58)) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1))),
% 2.15/2.25 inference(rewrite,[status(thm)],[])).
% 2.15/2.25 tff(8221,plain,
% 2.15/2.25 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node15(s57) | (~node18(s57, s58)) | m_main_v_turn(s58, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s57) | (~node18(s57, s58)) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1)))),
% 2.23/2.25 inference(monotonicity,[status(thm)],[8220])).
% 2.23/2.25 tff(8222,plain,
% 2.23/2.25 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node15(s57) | (~node18(s57, s58)) | m_main_v_turn(s58, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s57) | (~node18(s57, s58)) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1))),
% 2.23/2.25 inference(transitivity,[status(thm)],[8221, 8219])).
% 2.23/2.25 tff(8223,plain,
% 2.23/2.25 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node15(s57) | (~node18(s57, s58)) | m_main_v_turn(s58, c_1))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8224,plain,
% 2.23/2.25 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s57) | (~node18(s57, s58)) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1)),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 2.23/2.25 tff(8225,plain,
% 2.23/2.25 (node15(s57) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8224, 992, 8218])).
% 2.23/2.25 tff(8226,plain,
% 2.23/2.25 (m_main_v_turn(s58, c_1)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8225, 8214, 4965, 8136])).
% 2.23/2.25 tff(8227,plain,
% 2.23/2.25 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s58, c_1)) | (~m_main_v_turn(s58, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s58, c_1)) | (~m_main_v_turn(s58, c_2)))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8228,plain,
% 2.23/2.25 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s58, c_1)) | (~m_main_v_turn(s58, c_2)))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8229,plain,
% 2.23/2.25 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s58, c_1)) | (~m_main_v_turn(s58, c_2))),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8228, 8227])).
% 2.23/2.25 tff(8230,plain,
% 2.23/2.25 (~m_main_v_turn(s58, c_2)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8229, 156, 8226])).
% 2.23/2.25 tff(8231,plain,
% 2.23/2.25 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s58, c_2) | (~node12(s58)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s58, c_2) | (~node12(s58)))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8232,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s58, c_2) | (~node12(s58)))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8233,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s58, c_2) | (~node12(s58))),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8232, 8231])).
% 2.23/2.25 tff(8234,plain,
% 2.23/2.25 (~node12(s58)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8233, 184, 8230])).
% 2.23/2.25 tff(8235,plain,
% 2.23/2.25 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s58, c_n2) | (~node8(s58)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s58, c_n2) | (~node8(s58)))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8236,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s58, c_n2) | (~node8(s58)))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8237,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s58, c_n2) | (~node8(s58))),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8236, 8235])).
% 2.23/2.25 tff(8238,plain,
% 2.23/2.25 (~node8(s58)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8237, 271, 8177])).
% 2.23/2.25 tff(8239,plain,
% 2.23/2.25 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s58, c_n2) | (~node9(s58)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s58, c_n2) | (~node9(s58)))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8240,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s58, c_n2) | (~node9(s58)))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8241,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s58, c_n2) | (~node9(s58))),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8240, 8239])).
% 2.23/2.25 tff(8242,plain,
% 2.23/2.25 (~node9(s58)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8241, 88, 8177])).
% 2.23/2.25 tff(8243,plain,
% 2.23/2.25 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s58, c_n2) | (~node10(s58)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s58, c_n2) | (~node10(s58)))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8244,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s58, c_n2) | (~node10(s58)))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8245,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s58, c_n2) | (~node10(s58))),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8244, 8243])).
% 2.23/2.25 tff(8246,plain,
% 2.23/2.25 (~node10(s58)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8245, 249, 8177])).
% 2.23/2.25 tff(8247,plain,
% 2.23/2.25 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s58, c_n1) | (~node11(s58)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s58, c_n1) | (~node11(s58)))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8248,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s58, c_n1) | (~node11(s58)))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8249,plain,
% 2.23/2.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s58, c_n1) | (~node11(s58))),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8248, 8247])).
% 2.23/2.25 tff(8250,plain,
% 2.23/2.25 (~node11(s58)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8249, 238, 8197])).
% 2.23/2.25 tff(8251,plain,
% 2.23/2.25 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s58, s59)) | node14(s58, s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s58, s59)) | node14(s58, s59))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8252,plain,
% 2.23/2.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s58, s59)) | node14(s58, s59))),
% 2.23/2.25 inference(quant_inst,[status(thm)],[])).
% 2.23/2.25 tff(8253,plain,
% 2.23/2.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s58, s59)) | node14(s58, s59)),
% 2.23/2.25 inference(modus_ponens,[status(thm)],[8252, 8251])).
% 2.23/2.25 tff(8254,plain,
% 2.23/2.25 (node14(s58, s59)),
% 2.23/2.25 inference(unit_resolution,[status(thm)],[8253, 46, 2054])).
% 2.23/2.25 tff(8255,plain,
% 2.23/2.25 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59) | (~node14(s58, s59)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59) | (~node14(s58, s59)))),
% 2.23/2.25 inference(rewrite,[status(thm)],[])).
% 2.23/2.25 tff(8256,plain,
% 2.23/2.25 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59) | (~node14(s58, s59)))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8257,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59) | (~node14(s58, s59))),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8256, 8255])).
% 2.23/2.26 tff(8258,plain,
% 2.23/2.26 (m_main_v_state2(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8257, 296, 8254])).
% 2.23/2.26 tff(8259,plain,
% 2.23/2.26 (node13(s58, s59)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8258, 8250, 8189, 8246, 8242, 8238, 8234])).
% 2.23/2.26 tff(8260,plain,
% 2.23/2.26 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2) | (~node13(s58, s59)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2) | (~node13(s58, s59)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8261,plain,
% 2.23/2.26 (((~node13(s58, s59)) | (~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2)) <=> ((~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2) | (~node13(s58, s59)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8262,plain,
% 2.23/2.26 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s58, s59)) | (~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2) | (~node13(s58, s59))))),
% 2.23/2.26 inference(monotonicity,[status(thm)],[8261])).
% 2.23/2.26 tff(8263,plain,
% 2.23/2.26 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s58, s59)) | (~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2) | (~node13(s58, s59)))),
% 2.23/2.26 inference(transitivity,[status(thm)],[8262, 8260])).
% 2.23/2.26 tff(8264,plain,
% 2.23/2.26 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s58, s59)) | (~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8265,plain,
% 2.23/2.26 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s58, c_t2)) | m_main_v_state2(s59, c_t2) | (~node13(s58, s59))),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8264, 8263])).
% 2.23/2.26 tff(8266,plain,
% 2.23/2.26 (m_main_v_state2(s59, c_t2)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8265, 518, 8173, 8259])).
% 2.23/2.26 tff(8267,plain,
% 2.23/2.26 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s58, c_n2) | (~node16(s58)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s58, c_n2) | (~node16(s58)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8268,plain,
% 2.23/2.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s58, c_n2) | (~node16(s58)))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8269,plain,
% 2.23/2.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s58, c_n2) | (~node16(s58))),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8268, 8267])).
% 2.23/2.26 tff(8270,plain,
% 2.23/2.26 (~node16(s58)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8269, 329, 8177])).
% 2.23/2.26 tff(8271,plain,
% 2.23/2.26 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s58, c_n1) | (~node15(s58)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s58, c_n1) | (~node15(s58)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8272,plain,
% 2.23/2.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s58, c_n1) | (~node15(s58)))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8273,plain,
% 2.23/2.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s58, c_n1) | (~node15(s58))),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8272, 8271])).
% 2.23/2.26 tff(8274,plain,
% 2.23/2.26 (~node15(s58)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8273, 340, 8197])).
% 2.23/2.26 tff(8275,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s58, s59)) | node18(s58, s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s58, s59)) | node18(s58, s59))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8276,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s58, s59)) | node18(s58, s59))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8277,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s58, s59)) | node18(s58, s59)),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8276, 8275])).
% 2.23/2.26 tff(8278,plain,
% 2.23/2.26 (node18(s58, s59)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8277, 125, 2054])).
% 2.23/2.26 tff(8279,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s58) | node16(s58) | node17(s58, s59) | (~node18(s58, s59)))) <=> ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s58) | node16(s58) | node17(s58, s59) | (~node18(s58, s59)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8280,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s58) | node16(s58) | node17(s58, s59) | (~node18(s58, s59)))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8281,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s58) | node16(s58) | node17(s58, s59) | (~node18(s58, s59))),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8280, 8279])).
% 2.23/2.26 tff(8282,plain,
% 2.23/2.26 (node15(s58) | node16(s58) | node17(s58, s59)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8281, 139, 8278])).
% 2.23/2.26 tff(8283,plain,
% 2.23/2.26 (node17(s58, s59)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8282, 8274, 8270])).
% 2.23/2.26 tff(8284,plain,
% 2.23/2.26 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | (m_main_v_turn(s58, c_2) | (~node17(s58, s59)) | (~m_main_v_turn(s59, c_2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s58, c_2) | (~node17(s58, s59)) | (~m_main_v_turn(s59, c_2)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8285,plain,
% 2.23/2.26 (((~node17(s58, s59)) | m_main_v_turn(s58, c_2) | (~m_main_v_turn(s59, c_2))) <=> (m_main_v_turn(s58, c_2) | (~node17(s58, s59)) | (~m_main_v_turn(s59, c_2)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8286,plain,
% 2.23/2.26 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s58, s59)) | m_main_v_turn(s58, c_2) | (~m_main_v_turn(s59, c_2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | (m_main_v_turn(s58, c_2) | (~node17(s58, s59)) | (~m_main_v_turn(s59, c_2))))),
% 2.23/2.26 inference(monotonicity,[status(thm)],[8285])).
% 2.23/2.26 tff(8287,plain,
% 2.23/2.26 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s58, s59)) | m_main_v_turn(s58, c_2) | (~m_main_v_turn(s59, c_2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s58, c_2) | (~node17(s58, s59)) | (~m_main_v_turn(s59, c_2)))),
% 2.23/2.26 inference(transitivity,[status(thm)],[8286, 8284])).
% 2.23/2.26 tff(8288,plain,
% 2.23/2.26 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s58, s59)) | m_main_v_turn(s58, c_2) | (~m_main_v_turn(s59, c_2)))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8289,plain,
% 2.23/2.26 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s58, c_2) | (~node17(s58, s59)) | (~m_main_v_turn(s59, c_2))),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8288, 8287])).
% 2.23/2.26 tff(8290,plain,
% 2.23/2.26 (~m_main_v_turn(s59, c_2)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8289, 170, 8230, 8283])).
% 2.23/2.26 tff(8291,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s59)) | m_main_v_turn(s59, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s59)) | m_main_v_turn(s59, c_2))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8292,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s59)) | m_main_v_turn(s59, c_2))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8293,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s59)) | m_main_v_turn(s59, c_2)),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8292, 8291])).
% 2.23/2.26 tff(8294,plain,
% 2.23/2.26 ($false),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8293, 760, 8290, 8266, 8210, 8068])).
% 2.23/2.26 tff(8295,plain,(~node18(s59, s59)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.26 tff(8296,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s59, s59)) | node18(s59, s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s59, s59)) | node18(s59, s59))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8297,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s59, s59)) | node18(s59, s59))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8298,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s59, s59)) | node18(s59, s59)),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8297, 8296])).
% 2.23/2.26 tff(8299,plain,
% 2.23/2.26 (~trans(s59, s59)),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8298, 125, 8295])).
% 2.23/2.26 tff(8300,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s23) | (~trans(s59, s23)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s23) | (~trans(s59, s23)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8301,plain,
% 2.23/2.26 (((~trans(s59, s23)) | (~always25(s59)) | always25(s23)) <=> ((~always25(s59)) | always25(s23) | (~trans(s59, s23)))),
% 2.23/2.26 inference(rewrite,[status(thm)],[])).
% 2.23/2.26 tff(8302,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s23)) | (~always25(s59)) | always25(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s23) | (~trans(s59, s23))))),
% 2.23/2.26 inference(monotonicity,[status(thm)],[8301])).
% 2.23/2.26 tff(8303,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s23)) | (~always25(s59)) | always25(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s23) | (~trans(s59, s23)))),
% 2.23/2.26 inference(transitivity,[status(thm)],[8302, 8300])).
% 2.23/2.26 tff(8304,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s23)) | (~always25(s59)) | always25(s23))),
% 2.23/2.26 inference(quant_inst,[status(thm)],[])).
% 2.23/2.26 tff(8305,plain,
% 2.23/2.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s23) | (~trans(s59, s23))),
% 2.23/2.26 inference(modus_ponens,[status(thm)],[8304, 8303])).
% 2.23/2.26 tff(8306,plain,
% 2.23/2.26 ($false),
% 2.23/2.26 inference(unit_resolution,[status(thm)],[8305, 7261, 2041, 7739, 5224])).
% 2.23/2.26 tff(8307,plain,(~trans(s59, s23)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.26 tff(8308,plain,
% 2.23/2.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s40) | (~trans(s59, s40)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s40) | (~trans(s59, s40)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8309,plain,
% 2.23/2.27 (((~trans(s59, s40)) | (~always25(s59)) | always25(s40)) <=> ((~always25(s59)) | always25(s40) | (~trans(s59, s40)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8310,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s40)) | (~always25(s59)) | always25(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s40) | (~trans(s59, s40))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8309])).
% 2.23/2.27 tff(8311,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s40)) | (~always25(s59)) | always25(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s40) | (~trans(s59, s40)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8310, 8308])).
% 2.23/2.27 tff(8312,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s40)) | (~always25(s59)) | always25(s40))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8313,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s40) | (~trans(s59, s40))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8312, 8311])).
% 2.23/2.27 tff(8314,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8313, 7272, 2041, 7739, 5103])).
% 2.23/2.27 tff(8315,plain,(~trans(s59, s40)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8316,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s46) | (~trans(s59, s46)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s46) | (~trans(s59, s46)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8317,plain,
% 2.23/2.27 (((~trans(s59, s46)) | (~always25(s59)) | always25(s46)) <=> ((~always25(s59)) | always25(s46) | (~trans(s59, s46)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8318,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s46)) | (~always25(s59)) | always25(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s46) | (~trans(s59, s46))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8317])).
% 2.23/2.27 tff(8319,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s46)) | (~always25(s59)) | always25(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s46) | (~trans(s59, s46)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8318, 8316])).
% 2.23/2.27 tff(8320,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s46)) | (~always25(s59)) | always25(s46))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8321,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s46) | (~trans(s59, s46))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8320, 8319])).
% 2.23/2.27 tff(8322,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8321, 7283, 2041, 7739, 5059])).
% 2.23/2.27 tff(8323,plain,(~trans(s59, s46)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8324,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s45, s46)) | (~always25(s45)) | always25(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s45, s46)) | (~always25(s45)) | always25(s46))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8325,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s45, s46)) | (~always25(s45)) | always25(s46))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8326,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s45, s46)) | (~always25(s45)) | always25(s46)),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8325, 8324])).
% 2.23/2.27 tff(8327,plain,
% 2.23/2.27 ((~always25(s45)) | always25(s46)),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8326, 2041, 4087])).
% 2.23/2.27 tff(8328,plain,
% 2.23/2.27 (~always25(s45)),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8327, 5059])).
% 2.23/2.27 tff(8329,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s45) | (~trans(s59, s45)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s45) | (~trans(s59, s45)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8330,plain,
% 2.23/2.27 (((~trans(s59, s45)) | (~always25(s59)) | always25(s45)) <=> ((~always25(s59)) | always25(s45) | (~trans(s59, s45)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8331,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s45)) | (~always25(s59)) | always25(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s45) | (~trans(s59, s45))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8330])).
% 2.23/2.27 tff(8332,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s45)) | (~always25(s59)) | always25(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s45) | (~trans(s59, s45)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8331, 8329])).
% 2.23/2.27 tff(8333,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s45)) | (~always25(s59)) | always25(s45))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8334,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s45) | (~trans(s59, s45))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8333, 8332])).
% 2.23/2.27 tff(8335,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8334, 7294, 2041, 7739, 8328])).
% 2.23/2.27 tff(8336,plain,(~trans(s59, s45)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8337,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s44) | (~trans(s59, s44)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s44) | (~trans(s59, s44)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8338,plain,
% 2.23/2.27 (((~trans(s59, s44)) | (~always25(s59)) | always25(s44)) <=> ((~always25(s59)) | always25(s44) | (~trans(s59, s44)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8339,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s44)) | (~always25(s59)) | always25(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s44) | (~trans(s59, s44))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8338])).
% 2.23/2.27 tff(8340,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s44)) | (~always25(s59)) | always25(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s44) | (~trans(s59, s44)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8339, 8337])).
% 2.23/2.27 tff(8341,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s44)) | (~always25(s59)) | always25(s44))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8342,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s44) | (~trans(s59, s44))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8341, 8340])).
% 2.23/2.27 tff(8343,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8342, 7305, 2041, 7739, 5074])).
% 2.23/2.27 tff(8344,plain,(~trans(s59, s44)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8345,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s24) | (~trans(s59, s24)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s24) | (~trans(s59, s24)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8346,plain,
% 2.23/2.27 (((~trans(s59, s24)) | (~always25(s59)) | always25(s24)) <=> ((~always25(s59)) | always25(s24) | (~trans(s59, s24)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8347,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s24)) | (~always25(s59)) | always25(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s24) | (~trans(s59, s24))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8346])).
% 2.23/2.27 tff(8348,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s24)) | (~always25(s59)) | always25(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s24) | (~trans(s59, s24)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8347, 8345])).
% 2.23/2.27 tff(8349,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s24)) | (~always25(s59)) | always25(s24))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8350,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s24) | (~trans(s59, s24))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8349, 8348])).
% 2.23/2.27 tff(8351,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8350, 7316, 2041, 7739, 5219])).
% 2.23/2.27 tff(8352,plain,(~trans(s59, s24)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8353,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s30) | (~trans(s59, s30)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s30) | (~trans(s59, s30)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8354,plain,
% 2.23/2.27 (((~trans(s59, s30)) | (~always25(s59)) | always25(s30)) <=> ((~always25(s59)) | always25(s30) | (~trans(s59, s30)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8355,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s30)) | (~always25(s59)) | always25(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s30) | (~trans(s59, s30))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8354])).
% 2.23/2.27 tff(8356,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s30)) | (~always25(s59)) | always25(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s30) | (~trans(s59, s30)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8355, 8353])).
% 2.23/2.27 tff(8357,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s30)) | (~always25(s59)) | always25(s30))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8358,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s30) | (~trans(s59, s30))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8357, 8356])).
% 2.23/2.27 tff(8359,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8358, 7327, 2041, 7739, 5175])).
% 2.23/2.27 tff(8360,plain,(~trans(s59, s30)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8361,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s37, s38)) | (~always25(s37)) | always25(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s37, s38)) | (~always25(s37)) | always25(s38))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8362,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s37, s38)) | (~always25(s37)) | always25(s38))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8363,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s37, s38)) | (~always25(s37)) | always25(s38)),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8362, 8361])).
% 2.23/2.27 tff(8364,plain,
% 2.23/2.27 ((~always25(s37)) | always25(s38)),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8363, 2041, 3459])).
% 2.23/2.27 tff(8365,plain,
% 2.23/2.27 (~always25(s37)),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8364, 5117])).
% 2.23/2.27 tff(8366,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s37) | (~trans(s59, s37)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s37) | (~trans(s59, s37)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8367,plain,
% 2.23/2.27 (((~trans(s59, s37)) | (~always25(s59)) | always25(s37)) <=> ((~always25(s59)) | always25(s37) | (~trans(s59, s37)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8368,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s37)) | (~always25(s59)) | always25(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s37) | (~trans(s59, s37))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8367])).
% 2.23/2.27 tff(8369,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s37)) | (~always25(s59)) | always25(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s37) | (~trans(s59, s37)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8368, 8366])).
% 2.23/2.27 tff(8370,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s37)) | (~always25(s59)) | always25(s37))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8371,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s37) | (~trans(s59, s37))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8370, 8369])).
% 2.23/2.27 tff(8372,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8371, 7338, 2041, 7739, 8365])).
% 2.23/2.27 tff(8373,plain,(~trans(s59, s37)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8374,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s28) | (~trans(s59, s28)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s28) | (~trans(s59, s28)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8375,plain,
% 2.23/2.27 (((~trans(s59, s28)) | (~always25(s59)) | always25(s28)) <=> ((~always25(s59)) | always25(s28) | (~trans(s59, s28)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8376,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s28)) | (~always25(s59)) | always25(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s28) | (~trans(s59, s28))))),
% 2.23/2.27 inference(monotonicity,[status(thm)],[8375])).
% 2.23/2.27 tff(8377,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s28)) | (~always25(s59)) | always25(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s28) | (~trans(s59, s28)))),
% 2.23/2.27 inference(transitivity,[status(thm)],[8376, 8374])).
% 2.23/2.27 tff(8378,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s28)) | (~always25(s59)) | always25(s28))),
% 2.23/2.27 inference(quant_inst,[status(thm)],[])).
% 2.23/2.27 tff(8379,plain,
% 2.23/2.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s28) | (~trans(s59, s28))),
% 2.23/2.27 inference(modus_ponens,[status(thm)],[8378, 8377])).
% 2.23/2.27 tff(8380,plain,
% 2.23/2.27 ($false),
% 2.23/2.27 inference(unit_resolution,[status(thm)],[8379, 7349, 2041, 7739, 5190])).
% 2.23/2.27 tff(8381,plain,(~trans(s59, s28)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.27 tff(8382,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s6) | (~trans(s59, s6)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s6) | (~trans(s59, s6)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8383,plain,
% 2.23/2.27 (((~trans(s59, s6)) | (~always25(s59)) | always25(s6)) <=> ((~always25(s59)) | always25(s6) | (~trans(s59, s6)))),
% 2.23/2.27 inference(rewrite,[status(thm)],[])).
% 2.23/2.27 tff(8384,plain,
% 2.23/2.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s6)) | (~always25(s59)) | always25(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s6) | (~trans(s59, s6))))),
% 2.23/2.28 inference(monotonicity,[status(thm)],[8383])).
% 2.23/2.28 tff(8385,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s6)) | (~always25(s59)) | always25(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s6) | (~trans(s59, s6)))),
% 2.23/2.28 inference(transitivity,[status(thm)],[8384, 8382])).
% 2.23/2.28 tff(8386,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s6)) | (~always25(s59)) | always25(s6))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8387,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s6) | (~trans(s59, s6))),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8386, 8385])).
% 2.23/2.28 tff(8388,plain,
% 2.23/2.28 ($false),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8387, 7360, 2041, 7739, 5337])).
% 2.23/2.28 tff(8389,plain,(~trans(s59, s6)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.28 tff(8390,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s14) | (~trans(s59, s14)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s14) | (~trans(s59, s14)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8391,plain,
% 2.23/2.28 (((~trans(s59, s14)) | (~always25(s59)) | always25(s14)) <=> ((~always25(s59)) | always25(s14) | (~trans(s59, s14)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8392,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s14)) | (~always25(s59)) | always25(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s14) | (~trans(s59, s14))))),
% 2.23/2.28 inference(monotonicity,[status(thm)],[8391])).
% 2.23/2.28 tff(8393,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s14)) | (~always25(s59)) | always25(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s14) | (~trans(s59, s14)))),
% 2.23/2.28 inference(transitivity,[status(thm)],[8392, 8390])).
% 2.23/2.28 tff(8394,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s14)) | (~always25(s59)) | always25(s14))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8395,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s14) | (~trans(s59, s14))),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8394, 8393])).
% 2.23/2.28 tff(8396,plain,
% 2.23/2.28 ($false),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8395, 7371, 2041, 7739, 5279])).
% 2.23/2.28 tff(8397,plain,(~trans(s59, s14)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.28 tff(8398,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s39) | (~trans(s59, s39)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s39) | (~trans(s59, s39)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8399,plain,
% 2.23/2.28 (((~trans(s59, s39)) | (~always25(s59)) | always25(s39)) <=> ((~always25(s59)) | always25(s39) | (~trans(s59, s39)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8400,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s39)) | (~always25(s59)) | always25(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s39) | (~trans(s59, s39))))),
% 2.23/2.28 inference(monotonicity,[status(thm)],[8399])).
% 2.23/2.28 tff(8401,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s39)) | (~always25(s59)) | always25(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s39) | (~trans(s59, s39)))),
% 2.23/2.28 inference(transitivity,[status(thm)],[8400, 8398])).
% 2.23/2.28 tff(8402,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s39)) | (~always25(s59)) | always25(s39))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8403,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s39) | (~trans(s59, s39))),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8402, 8401])).
% 2.23/2.28 tff(8404,plain,
% 2.23/2.28 ($false),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8403, 7382, 2041, 7739, 5108])).
% 2.23/2.28 tff(8405,plain,(~trans(s59, s39)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.28 tff(8406,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s13, s14)) | (~always25(s13)) | always25(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s13, s14)) | (~always25(s13)) | always25(s14))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8407,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s13, s14)) | (~always25(s13)) | always25(s14))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8408,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s13, s14)) | (~always25(s13)) | always25(s14)),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8407, 8406])).
% 2.23/2.28 tff(8409,plain,
% 2.23/2.28 ((~always25(s13)) | always25(s14)),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8408, 2041, 1536])).
% 2.23/2.28 tff(8410,plain,
% 2.23/2.28 (~always25(s13)),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8409, 5279])).
% 2.23/2.28 tff(8411,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s13) | (~trans(s59, s13)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s13) | (~trans(s59, s13)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8412,plain,
% 2.23/2.28 (((~trans(s59, s13)) | (~always25(s59)) | always25(s13)) <=> ((~always25(s59)) | always25(s13) | (~trans(s59, s13)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8413,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s13)) | (~always25(s59)) | always25(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s13) | (~trans(s59, s13))))),
% 2.23/2.28 inference(monotonicity,[status(thm)],[8412])).
% 2.23/2.28 tff(8414,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s13)) | (~always25(s59)) | always25(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s13) | (~trans(s59, s13)))),
% 2.23/2.28 inference(transitivity,[status(thm)],[8413, 8411])).
% 2.23/2.28 tff(8415,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s13)) | (~always25(s59)) | always25(s13))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8416,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s13) | (~trans(s59, s13))),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8415, 8414])).
% 2.23/2.28 tff(8417,plain,
% 2.23/2.28 ($false),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8416, 7393, 2041, 7739, 8410])).
% 2.23/2.28 tff(8418,plain,(~trans(s59, s13)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.28 tff(8419,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s11) | (~trans(s59, s11)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s11) | (~trans(s59, s11)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8420,plain,
% 2.23/2.28 (((~trans(s59, s11)) | (~always25(s59)) | always25(s11)) <=> ((~always25(s59)) | always25(s11) | (~trans(s59, s11)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8421,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s11)) | (~always25(s59)) | always25(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s11) | (~trans(s59, s11))))),
% 2.23/2.28 inference(monotonicity,[status(thm)],[8420])).
% 2.23/2.28 tff(8422,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s11)) | (~always25(s59)) | always25(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s11) | (~trans(s59, s11)))),
% 2.23/2.28 inference(transitivity,[status(thm)],[8421, 8419])).
% 2.23/2.28 tff(8423,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s11)) | (~always25(s59)) | always25(s11))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8424,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s11) | (~trans(s59, s11))),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8423, 8422])).
% 2.23/2.28 tff(8425,plain,
% 2.23/2.28 ($false),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8424, 7404, 2041, 7739, 5299])).
% 2.23/2.28 tff(8426,plain,(~trans(s59, s11)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.28 tff(8427,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s9, s10)) | (~always25(s9)) | always25(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s9, s10)) | (~always25(s9)) | always25(s10))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8428,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s9, s10)) | (~always25(s9)) | always25(s10))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8429,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s9, s10)) | (~always25(s9)) | always25(s10)),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8428, 8427])).
% 2.23/2.28 tff(8430,plain,
% 2.23/2.28 ((~always25(s9)) | always25(s10)),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8429, 2041, 1203])).
% 2.23/2.28 tff(8431,plain,
% 2.23/2.28 (~always25(s9)),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8430, 5308])).
% 2.23/2.28 tff(8432,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s9) | (~trans(s59, s9)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s9) | (~trans(s59, s9)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8433,plain,
% 2.23/2.28 (((~trans(s59, s9)) | (~always25(s59)) | always25(s9)) <=> ((~always25(s59)) | always25(s9) | (~trans(s59, s9)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8434,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s9)) | (~always25(s59)) | always25(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s9) | (~trans(s59, s9))))),
% 2.23/2.28 inference(monotonicity,[status(thm)],[8433])).
% 2.23/2.28 tff(8435,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s9)) | (~always25(s59)) | always25(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s9) | (~trans(s59, s9)))),
% 2.23/2.28 inference(transitivity,[status(thm)],[8434, 8432])).
% 2.23/2.28 tff(8436,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s9)) | (~always25(s59)) | always25(s9))),
% 2.23/2.28 inference(quant_inst,[status(thm)],[])).
% 2.23/2.28 tff(8437,plain,
% 2.23/2.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s9) | (~trans(s59, s9))),
% 2.23/2.28 inference(modus_ponens,[status(thm)],[8436, 8435])).
% 2.23/2.28 tff(8438,plain,
% 2.23/2.28 ($false),
% 2.23/2.28 inference(unit_resolution,[status(thm)],[8437, 7415, 2041, 7739, 8431])).
% 2.23/2.28 tff(8439,plain,(~trans(s59, s9)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.28 tff(8440,plain,
% 2.23/2.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s15) | (~trans(s59, s15)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s15) | (~trans(s59, s15)))),
% 2.23/2.28 inference(rewrite,[status(thm)],[])).
% 2.23/2.28 tff(8441,plain,
% 2.23/2.28 (((~trans(s59, s15)) | (~always25(s59)) | always25(s15)) <=> ((~always25(s59)) | always25(s15) | (~trans(s59, s15)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8442,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s15)) | (~always25(s59)) | always25(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s15) | (~trans(s59, s15))))),
% 2.23/2.29 inference(monotonicity,[status(thm)],[8441])).
% 2.23/2.29 tff(8443,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s15)) | (~always25(s59)) | always25(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s15) | (~trans(s59, s15)))),
% 2.23/2.29 inference(transitivity,[status(thm)],[8442, 8440])).
% 2.23/2.29 tff(8444,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s15)) | (~always25(s59)) | always25(s15))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8445,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s15) | (~trans(s59, s15))),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8444, 8443])).
% 2.23/2.29 tff(8446,plain,
% 2.23/2.29 ($false),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8445, 7426, 2041, 7739, 5270])).
% 2.23/2.29 tff(8447,plain,(~trans(s59, s15)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.29 tff(8448,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s7) | (~trans(s59, s7)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s7) | (~trans(s59, s7)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8449,plain,
% 2.23/2.29 (((~trans(s59, s7)) | (~always25(s59)) | always25(s7)) <=> ((~always25(s59)) | always25(s7) | (~trans(s59, s7)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8450,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s7)) | (~always25(s59)) | always25(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s7) | (~trans(s59, s7))))),
% 2.23/2.29 inference(monotonicity,[status(thm)],[8449])).
% 2.23/2.29 tff(8451,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s7)) | (~always25(s59)) | always25(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s7) | (~trans(s59, s7)))),
% 2.23/2.29 inference(transitivity,[status(thm)],[8450, 8448])).
% 2.23/2.29 tff(8452,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s7)) | (~always25(s59)) | always25(s7))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8453,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s7) | (~trans(s59, s7))),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8452, 8451])).
% 2.23/2.29 tff(8454,plain,
% 2.23/2.29 ($false),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8453, 7437, 2041, 7739, 5328])).
% 2.23/2.29 tff(8455,plain,(~trans(s59, s7)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.29 tff(8456,assumption,(node18(s59, s58)), introduced(assumption)).
% 2.23/2.29 tff(8457,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s58)) | m_main_v_turn(s58, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s58)) | m_main_v_turn(s58, c_2))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8458,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s58)) | m_main_v_turn(s58, c_2))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8459,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node18(s59, s58)) | m_main_v_turn(s58, c_2)),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8458, 8457])).
% 2.23/2.29 tff(8460,plain,
% 2.23/2.29 ($false),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8459, 760, 8230, 8266, 8210, 8456])).
% 2.23/2.29 tff(8461,plain,(~node18(s59, s58)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.29 tff(8462,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s59, s58)) | node18(s59, s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s59, s58)) | node18(s59, s58))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8463,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s59, s58)) | node18(s59, s58))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8464,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s59, s58)) | node18(s59, s58)),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8463, 8462])).
% 2.23/2.29 tff(8465,plain,
% 2.23/2.29 (~trans(s59, s58)),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8464, 125, 8461])).
% 2.23/2.29 tff(8466,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s53, s54)) | (~always25(s53)) | always25(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s53, s54)) | (~always25(s53)) | always25(s54))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8467,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s53, s54)) | (~always25(s53)) | always25(s54))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8468,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s53, s54)) | (~always25(s53)) | always25(s54)),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8467, 8466])).
% 2.23/2.29 tff(8469,plain,
% 2.23/2.29 ((~always25(s53)) | always25(s54)),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8468, 2041, 4715])).
% 2.23/2.29 tff(8470,plain,
% 2.23/2.29 (~always25(s53)),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8469, 5001])).
% 2.23/2.29 tff(8471,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s53) | (~trans(s59, s53)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s53) | (~trans(s59, s53)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8472,plain,
% 2.23/2.29 (((~trans(s59, s53)) | (~always25(s59)) | always25(s53)) <=> ((~always25(s59)) | always25(s53) | (~trans(s59, s53)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8473,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s53)) | (~always25(s59)) | always25(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s53) | (~trans(s59, s53))))),
% 2.23/2.29 inference(monotonicity,[status(thm)],[8472])).
% 2.23/2.29 tff(8474,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s53)) | (~always25(s59)) | always25(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s53) | (~trans(s59, s53)))),
% 2.23/2.29 inference(transitivity,[status(thm)],[8473, 8471])).
% 2.23/2.29 tff(8475,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s53)) | (~always25(s59)) | always25(s53))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8476,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s53) | (~trans(s59, s53))),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8475, 8474])).
% 2.23/2.29 tff(8477,plain,
% 2.23/2.29 ($false),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8476, 7459, 2041, 7739, 8470])).
% 2.23/2.29 tff(8478,plain,(~trans(s59, s53)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.29 tff(8479,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s56) | (~trans(s59, s56)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s56) | (~trans(s59, s56)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8480,plain,
% 2.23/2.29 (((~trans(s59, s56)) | (~always25(s59)) | always25(s56)) <=> ((~always25(s59)) | always25(s56) | (~trans(s59, s56)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8481,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s56)) | (~always25(s59)) | always25(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s56) | (~trans(s59, s56))))),
% 2.23/2.29 inference(monotonicity,[status(thm)],[8480])).
% 2.23/2.29 tff(8482,plain,
% 2.23/2.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s56)) | (~always25(s59)) | always25(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s56) | (~trans(s59, s56)))),
% 2.23/2.29 inference(transitivity,[status(thm)],[8481, 8479])).
% 2.23/2.29 tff(8483,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s56)) | (~always25(s59)) | always25(s56))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8484,plain,
% 2.23/2.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s56) | (~trans(s59, s56))),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8483, 8482])).
% 2.23/2.29 tff(8485,plain,
% 2.23/2.29 ($false),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8484, 7470, 2041, 7739, 4987])).
% 2.23/2.29 tff(8486,plain,(~trans(s59, s56)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.29 tff(8487,assumption,(node14(s59, s57)), introduced(assumption)).
% 2.23/2.29 tff(8488,plain,
% 2.23/2.29 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s58, c_n2) | (~node13(s58, s59)) | (~m_main_v_state2(s59, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s58, c_n2) | (~node13(s58, s59)) | (~m_main_v_state2(s59, c_n2)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8489,plain,
% 2.23/2.29 (((~node13(s58, s59)) | m_main_v_state2(s58, c_n2) | (~m_main_v_state2(s59, c_n2))) <=> (m_main_v_state2(s58, c_n2) | (~node13(s58, s59)) | (~m_main_v_state2(s59, c_n2)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8490,plain,
% 2.23/2.29 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s58, s59)) | m_main_v_state2(s58, c_n2) | (~m_main_v_state2(s59, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s58, c_n2) | (~node13(s58, s59)) | (~m_main_v_state2(s59, c_n2))))),
% 2.23/2.29 inference(monotonicity,[status(thm)],[8489])).
% 2.23/2.29 tff(8491,plain,
% 2.23/2.29 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s58, s59)) | m_main_v_state2(s58, c_n2) | (~m_main_v_state2(s59, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s58, c_n2) | (~node13(s58, s59)) | (~m_main_v_state2(s59, c_n2)))),
% 2.23/2.29 inference(transitivity,[status(thm)],[8490, 8488])).
% 2.23/2.29 tff(8492,plain,
% 2.23/2.29 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s58, s59)) | m_main_v_state2(s58, c_n2) | (~m_main_v_state2(s59, c_n2)))),
% 2.23/2.29 inference(quant_inst,[status(thm)],[])).
% 2.23/2.29 tff(8493,plain,
% 2.23/2.29 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s58, c_n2) | (~node13(s58, s59)) | (~m_main_v_state2(s59, c_n2))),
% 2.23/2.29 inference(modus_ponens,[status(thm)],[8492, 8491])).
% 2.23/2.29 tff(8494,plain,
% 2.23/2.29 (~m_main_v_state2(s59, c_n2)),
% 2.23/2.29 inference(unit_resolution,[status(thm)],[8493, 311, 8177, 8259])).
% 2.23/2.29 tff(8495,plain,
% 2.23/2.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s59, c_n2) | (~node8(s59)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s59, c_n2) | (~node8(s59)))),
% 2.23/2.29 inference(rewrite,[status(thm)],[])).
% 2.23/2.29 tff(8496,plain,
% 2.23/2.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s59, c_n2) | (~node8(s59)))),
% 2.28/2.29 inference(quant_inst,[status(thm)],[])).
% 2.28/2.29 tff(8497,plain,
% 2.28/2.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s59, c_n2) | (~node8(s59))),
% 2.28/2.29 inference(modus_ponens,[status(thm)],[8496, 8495])).
% 2.28/2.29 tff(8498,plain,
% 2.28/2.29 (~node8(s59)),
% 2.28/2.29 inference(unit_resolution,[status(thm)],[8497, 271, 8494])).
% 2.28/2.29 tff(8499,plain,
% 2.28/2.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s59, c_n2) | (~node9(s59)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s59, c_n2) | (~node9(s59)))),
% 2.28/2.29 inference(rewrite,[status(thm)],[])).
% 2.28/2.29 tff(8500,plain,
% 2.28/2.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s59, c_n2) | (~node9(s59)))),
% 2.28/2.29 inference(quant_inst,[status(thm)],[])).
% 2.28/2.29 tff(8501,plain,
% 2.28/2.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s59, c_n2) | (~node9(s59))),
% 2.28/2.29 inference(modus_ponens,[status(thm)],[8500, 8499])).
% 2.28/2.29 tff(8502,plain,
% 2.28/2.29 (~node9(s59)),
% 2.28/2.29 inference(unit_resolution,[status(thm)],[8501, 88, 8494])).
% 2.28/2.29 tff(8503,plain,
% 2.28/2.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s59, c_n2) | (~node10(s59)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s59, c_n2) | (~node10(s59)))),
% 2.28/2.29 inference(rewrite,[status(thm)],[])).
% 2.28/2.29 tff(8504,plain,
% 2.28/2.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s59, c_n2) | (~node10(s59)))),
% 2.28/2.29 inference(quant_inst,[status(thm)],[])).
% 2.28/2.29 tff(8505,plain,
% 2.28/2.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s59, c_n2) | (~node10(s59))),
% 2.28/2.29 inference(modus_ponens,[status(thm)],[8504, 8503])).
% 2.28/2.29 tff(8506,plain,
% 2.28/2.29 (~node10(s59)),
% 2.28/2.29 inference(unit_resolution,[status(thm)],[8505, 249, 8494])).
% 2.28/2.29 tff(8507,plain,
% 2.28/2.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (m_main_v_state2(s57, c_c2) | (~m_main_v_state1(s59, c_n1)) | node10(s59) | node9(s59) | node8(s59) | (~node14(s59, s57)) | (~m_main_v_state2(s59, c_t2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | m_main_v_state2(s57, c_c2) | (~m_main_v_state1(s59, c_n1)) | node10(s59) | node9(s59) | node8(s59) | (~node14(s59, s57)) | (~m_main_v_state2(s59, c_t2)))),
% 2.28/2.29 inference(rewrite,[status(thm)],[])).
% 2.28/2.29 tff(8508,plain,
% 2.28/2.29 (((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | node9(s59) | node8(s59) | node10(s59) | (~node14(s59, s57)) | m_main_v_state2(s57, c_c2)) <=> (m_main_v_state2(s57, c_c2) | (~m_main_v_state1(s59, c_n1)) | node10(s59) | node9(s59) | node8(s59) | (~node14(s59, s57)) | (~m_main_v_state2(s59, c_t2)))),
% 2.28/2.29 inference(rewrite,[status(thm)],[])).
% 2.28/2.29 tff(8509,plain,
% 2.28/2.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | node9(s59) | node8(s59) | node10(s59) | (~node14(s59, s57)) | m_main_v_state2(s57, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (m_main_v_state2(s57, c_c2) | (~m_main_v_state1(s59, c_n1)) | node10(s59) | node9(s59) | node8(s59) | (~node14(s59, s57)) | (~m_main_v_state2(s59, c_t2))))),
% 2.28/2.29 inference(monotonicity,[status(thm)],[8508])).
% 2.28/2.29 tff(8510,plain,
% 2.28/2.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | node9(s59) | node8(s59) | node10(s59) | (~node14(s59, s57)) | m_main_v_state2(s57, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | m_main_v_state2(s57, c_c2) | (~m_main_v_state1(s59, c_n1)) | node10(s59) | node9(s59) | node8(s59) | (~node14(s59, s57)) | (~m_main_v_state2(s59, c_t2)))),
% 2.28/2.30 inference(transitivity,[status(thm)],[8509, 8507])).
% 2.28/2.30 tff(8511,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | node9(s59) | node8(s59) | node10(s59) | (~node14(s59, s57)) | m_main_v_state2(s57, c_c2))),
% 2.28/2.30 inference(quant_inst,[status(thm)],[])).
% 2.28/2.30 tff(8512,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | m_main_v_state2(s57, c_c2) | (~m_main_v_state1(s59, c_n1)) | node10(s59) | node9(s59) | node8(s59) | (~node14(s59, s57)) | (~m_main_v_state2(s59, c_t2))),
% 2.28/2.30 inference(modus_ponens,[status(thm)],[8511, 8510])).
% 2.28/2.30 tff(8513,plain,
% 2.28/2.30 ($false),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[8512, 617, 8072, 8266, 8210, 8506, 8502, 8498, 8487])).
% 2.28/2.30 tff(8514,plain,(~node14(s59, s57)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.30 tff(8515,plain,
% 2.28/2.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s59, s57)) | node14(s59, s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s59, s57)) | node14(s59, s57))),
% 2.28/2.30 inference(rewrite,[status(thm)],[])).
% 2.28/2.30 tff(8516,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s59, s57)) | node14(s59, s57))),
% 2.28/2.30 inference(quant_inst,[status(thm)],[])).
% 2.28/2.30 tff(8517,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s59, s57)) | node14(s59, s57)),
% 2.28/2.30 inference(modus_ponens,[status(thm)],[8516, 8515])).
% 2.28/2.30 tff(8518,plain,
% 2.28/2.30 (~trans(s59, s57)),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[8517, 46, 8514])).
% 2.28/2.30 tff(8519,plain,
% 2.28/2.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s49, s50)) | (~always25(s49)) | always25(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s49, s50)) | (~always25(s49)) | always25(s50))),
% 2.28/2.30 inference(rewrite,[status(thm)],[])).
% 2.28/2.30 tff(8520,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s49, s50)) | (~always25(s49)) | always25(s50))),
% 2.28/2.30 inference(quant_inst,[status(thm)],[])).
% 2.28/2.30 tff(8521,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s49, s50)) | (~always25(s49)) | always25(s50)),
% 2.28/2.30 inference(modus_ponens,[status(thm)],[8520, 8519])).
% 2.28/2.30 tff(8522,plain,
% 2.28/2.30 ((~always25(s49)) | always25(s50)),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[8521, 2041, 4420])).
% 2.28/2.30 tff(8523,plain,
% 2.28/2.30 (~always25(s49)),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[8522, 5030])).
% 2.28/2.30 tff(8524,assumption,(trans(s59, s49)), introduced(assumption)).
% 2.28/2.30 tff(8525,plain,
% 2.28/2.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s49) | (~trans(s59, s49)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s49) | (~trans(s59, s49)))),
% 2.28/2.30 inference(rewrite,[status(thm)],[])).
% 2.28/2.30 tff(8526,plain,
% 2.28/2.30 (((~trans(s59, s49)) | (~always25(s59)) | always25(s49)) <=> ((~always25(s59)) | always25(s49) | (~trans(s59, s49)))),
% 2.28/2.30 inference(rewrite,[status(thm)],[])).
% 2.28/2.30 tff(8527,plain,
% 2.28/2.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s49)) | (~always25(s59)) | always25(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s49) | (~trans(s59, s49))))),
% 2.28/2.30 inference(monotonicity,[status(thm)],[8526])).
% 2.28/2.30 tff(8528,plain,
% 2.28/2.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s49)) | (~always25(s59)) | always25(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s49) | (~trans(s59, s49)))),
% 2.28/2.30 inference(transitivity,[status(thm)],[8527, 8525])).
% 2.28/2.30 tff(8529,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s49)) | (~always25(s59)) | always25(s49))),
% 2.28/2.30 inference(quant_inst,[status(thm)],[])).
% 2.28/2.30 tff(8530,plain,
% 2.28/2.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s49) | (~trans(s59, s49))),
% 2.28/2.30 inference(modus_ponens,[status(thm)],[8529, 8528])).
% 2.28/2.30 tff(8531,plain,
% 2.28/2.30 ($false),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[8530, 8524, 2041, 7739, 8523])).
% 2.28/2.30 tff(8532,plain,(~trans(s59, s49)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.30 tff(8533,plain,
% 2.28/2.30 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s49) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s53) | trans(s59, s54) | trans(s59, s55) | trans(s59, s56) | trans(s59, s57) | trans(s59, s58) | trans(s59, s59)),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[7727, 7531])).
% 2.28/2.30 tff(8534,plain,
% 2.28/2.30 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s15) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s58) | trans(s59, s59)),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[8533, 8532, 8518, 8486, 8478])).
% 2.28/2.30 tff(8535,plain,
% 2.28/2.30 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s8) | trans(s59, s10) | trans(s59, s11) | trans(s59, s12) | trans(s59, s13) | trans(s59, s14) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s39) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s59)),
% 2.28/2.30 inference(unit_resolution,[status(thm)],[8534, 8465, 8455, 8447, 8439])).
% 2.28/2.30 tff(8536,plain,
% 2.28/2.30 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s28) | trans(s59, s29) | trans(s59, s30) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s37) | trans(s59, s38) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s59)),
% 2.28/2.31 inference(unit_resolution,[status(thm)],[8535, 8426, 8418, 8405, 8397])).
% 2.28/2.31 tff(8537,plain,
% 2.28/2.31 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s24) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s29) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s44) | trans(s59, s45) | trans(s59, s46) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s59)),
% 2.28/2.31 inference(unit_resolution,[status(thm)],[8536, 8389, 8381, 8373, 8360])).
% 2.28/2.31 tff(8538,plain,
% 2.28/2.31 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s23) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s29) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s40) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55) | trans(s59, s59)),
% 2.28/2.31 inference(unit_resolution,[status(thm)],[8537, 8352, 8344, 8336, 8323])).
% 2.28/2.31 tff(8539,plain,
% 2.28/2.31 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s10) | trans(s59, s12) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s29) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s41) | trans(s59, s42) | trans(s59, s43) | trans(s59, s47) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55)),
% 2.28/2.31 inference(unit_resolution,[status(thm)],[8538, 8315, 8307, 8299, 8067])).
% 2.28/2.31 tff(8540,plain,
% 2.28/2.31 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s12) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s20) | trans(s59, s21) | trans(s59, s22) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s42) | trans(s59, s43) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55)),
% 2.28/2.31 inference(unit_resolution,[status(thm)],[8539, 8054, 8046, 8038, 8025])).
% 2.28/2.31 tff(8541,plain,
% 2.28/2.31 (trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s12) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s21) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s31) | trans(s59, s32) | trans(s59, s33) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s43) | trans(s59, s48) | trans(s59, s50) | trans(s59, s51) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8540, 8012, 8004, 7991, 7983])).
% 2.28/2.32 tff(8542,plain,
% 2.28/2.32 (trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s12) | trans(s59, s16) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s21) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s31) | trans(s59, s32) | trans(s59, s34) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s43) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54) | trans(s59, s55)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8541, 7975, 7967, 7954, 7946])).
% 2.28/2.32 tff(8543,plain,
% 2.28/2.32 (trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s21) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s31) | trans(s59, s32) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s43) | trans(s59, s50) | trans(s59, s52) | trans(s59, s54)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8542, 7938, 7930, 7922, 7914])).
% 2.28/2.32 tff(8544,plain,
% 2.28/2.32 (trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s17) | trans(s59, s18) | trans(s59, s19) | trans(s59, s25) | trans(s59, s26) | trans(s59, s27) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s43) | trans(s59, s52) | trans(s59, s54)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8543, 7906, 7898, 7890, 7882])).
% 2.28/2.32 tff(8545,plain,
% 2.28/2.32 (trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s17) | trans(s59, s19) | trans(s59, s25) | trans(s59, s27) | trans(s59, s35) | trans(s59, s36) | trans(s59, s38) | trans(s59, s43) | trans(s59, s54)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8544, 7869, 7861, 7853])).
% 2.28/2.32 tff(8546,plain,
% 2.28/2.32 (trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s8) | trans(s59, s17) | trans(s59, s19) | trans(s59, s27) | trans(s59, s43) | trans(s59, s54)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8545, 7845, 7837, 7829, 7821])).
% 2.28/2.32 tff(8547,plain,
% 2.28/2.32 (trans(s59, s3) | trans(s59, s19) | trans(s59, s27) | trans(s59, s43) | trans(s59, s54)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8546, 7808, 7800, 7792, 7779])).
% 2.28/2.32 tff(8548,plain,
% 2.28/2.32 (trans(s59, s19)),
% 2.28/2.32 inference(unit_resolution,[status(thm)],[8547, 7771, 7763, 7755, 7747])).
% 2.28/2.32 tff(8549,plain,
% 2.28/2.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s19) | (~trans(s59, s19)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s19) | (~trans(s59, s19)))),
% 2.28/2.32 inference(rewrite,[status(thm)],[])).
% 2.28/2.32 tff(8550,plain,
% 2.28/2.32 (((~trans(s59, s19)) | (~always25(s59)) | always25(s19)) <=> ((~always25(s59)) | always25(s19) | (~trans(s59, s19)))),
% 2.28/2.32 inference(rewrite,[status(thm)],[])).
% 2.28/2.32 tff(8551,plain,
% 2.28/2.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s19)) | (~always25(s59)) | always25(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s59)) | always25(s19) | (~trans(s59, s19))))),
% 2.28/2.32 inference(monotonicity,[status(thm)],[8550])).
% 2.28/2.32 tff(8552,plain,
% 2.28/2.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s19)) | (~always25(s59)) | always25(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s19) | (~trans(s59, s19)))),
% 2.28/2.32 inference(transitivity,[status(thm)],[8551, 8549])).
% 2.28/2.32 tff(8553,plain,
% 2.28/2.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s19)) | (~always25(s59)) | always25(s19))),
% 2.28/2.32 inference(quant_inst,[status(thm)],[])).
% 2.28/2.32 tff(8554,plain,
% 2.28/2.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s59)) | always25(s19) | (~trans(s59, s19))),
% 2.28/2.33 inference(modus_ponens,[status(thm)],[8553, 8552])).
% 2.28/2.33 tff(8555,plain,
% 2.28/2.33 ($false),
% 2.28/2.33 inference(unit_resolution,[status(thm)],[8554, 8548, 2041, 7739, 2046])).
% 2.28/2.33 % SZS output end Proof
%------------------------------------------------------------------------------